TSTP Solution File: HWV006-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV006-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 02:10:28 EDT 2022
% Result : Unsatisfiable 1.78s 1.40s
% Output : Proof 1.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : HWV006-1 : TPTP v8.1.0. Released v2.1.0.
% 0.04/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.37 % Computer : n005.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Wed Aug 31 21:58:03 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.23/0.38 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.23/0.38 Usage: tptp [options] [-file:]file
% 0.23/0.38 -h, -? prints this message.
% 0.23/0.38 -smt2 print SMT-LIB2 benchmark.
% 0.23/0.38 -m, -model generate model.
% 0.23/0.38 -p, -proof generate proof.
% 0.23/0.38 -c, -core generate unsat core of named formulas.
% 0.23/0.38 -st, -statistics display statistics.
% 0.23/0.38 -t:timeout set timeout (in second).
% 0.23/0.38 -smt2status display status in smt2 format instead of SZS.
% 0.23/0.38 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.23/0.38 -<param>:<value> configuration parameter and value.
% 0.23/0.38 -o:<output-file> file to place output in.
% 1.78/1.40 % SZS status Unsatisfiable
% 1.78/1.40 % SZS output start Proof
% 1.78/1.40 tff(value_type, type, (
% 1.78/1.40 value: ( $i * $i ) > $o)).
% 1.78/1.40 tff(n1_type, type, (
% 1.78/1.40 n1: $i)).
% 1.78/1.40 tff(in_type, type, (
% 1.78/1.40 in: ( $i * $i ) > $i)).
% 1.78/1.40 tff(and1_type, type, (
% 1.78/1.40 and1: $i > $i)).
% 1.78/1.40 tff(h2_type, type, (
% 1.78/1.40 h2: $i > $i)).
% 1.78/1.40 tff(f_type, type, (
% 1.78/1.40 f: $i)).
% 1.78/1.40 tff(n2_type, type, (
% 1.78/1.40 n2: $i)).
% 1.78/1.40 tff(out_type, type, (
% 1.78/1.40 out: ( $i * $i ) > $i)).
% 1.78/1.40 tff(s_type, type, (
% 1.78/1.40 s: $i)).
% 1.78/1.40 tff(connection_type, type, (
% 1.78/1.40 connection: ( $i * $i ) > $o)).
% 1.78/1.40 tff(type_type, type, (
% 1.78/1.40 type: ( $i * $i ) > $o)).
% 1.78/1.40 tff(fulladder_type, type, (
% 1.78/1.40 fulladder: $i)).
% 1.78/1.40 tff(halfadder_type, type, (
% 1.78/1.40 halfadder: $i)).
% 1.78/1.40 tff(mode_type, type, (
% 1.78/1.40 mode: ( $i * $i ) > $o)).
% 1.78/1.40 tff(ok_type, type, (
% 1.78/1.40 ok: $i)).
% 1.78/1.40 tff(abnormal_type, type, (
% 1.78/1.40 abnormal: $i)).
% 1.78/1.40 tff(or1_type, type, (
% 1.78/1.40 or1: $i > $i)).
% 1.78/1.40 tff(n0_type, type, (
% 1.78/1.40 n0: $i)).
% 1.78/1.40 tff(c_type, type, (
% 1.78/1.40 c: $i)).
% 1.78/1.40 tff(and2_type, type, (
% 1.78/1.40 and2: $i > $i)).
% 1.78/1.40 tff(h1_type, type, (
% 1.78/1.40 h1: $i > $i)).
% 1.78/1.40 tff(or_type, type, (
% 1.78/1.40 or: $i)).
% 1.78/1.40 tff(not1_type, type, (
% 1.78/1.40 not1: $i > $i)).
% 1.78/1.40 tff(and_type, type, (
% 1.78/1.40 and: $i)).
% 1.78/1.40 tff(not_type, type, (
% 1.78/1.40 not: $i)).
% 1.78/1.40 tff(equal_value_type, type, (
% 1.78/1.40 equal_value: ( $i * $i ) > $o)).
% 1.78/1.40 tff(1,plain,
% 1.78/1.40 (type(f, fulladder) <=> type(f, fulladder)),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(2,axiom,(type(f, fulladder)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f_isa_fulladder')).
% 1.78/1.40 tff(3,plain,
% 1.78/1.40 (type(f, fulladder)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[2, 1])).
% 1.78/1.40 tff(4,plain,
% 1.78/1.40 (^[X: $i] : refl(((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X)))) <=> ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X)))))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(5,plain,
% 1.78/1.40 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[4])).
% 1.78/1.40 tff(6,plain,
% 1.78/1.40 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(7,axiom,(![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_connection_outs_outsh2')).
% 1.78/1.40 tff(8,plain,
% 1.78/1.40 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 1.78/1.40 tff(9,plain,(
% 1.78/1.40 ![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))),
% 1.78/1.40 inference(skolemize,[status(sab)],[8])).
% 1.78/1.40 tff(10,plain,
% 1.78/1.40 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 1.78/1.40 tff(11,plain,
% 1.78/1.40 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))) | ((~type(f, fulladder)) | connection(out(s, f), out(s, h2(f))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))) | (~type(f, fulladder)) | connection(out(s, f), out(s, h2(f))))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(12,plain,
% 1.78/1.40 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))) | ((~type(f, fulladder)) | connection(out(s, f), out(s, h2(f))))),
% 1.78/1.40 inference(quant_inst,[status(thm)],[])).
% 1.78/1.40 tff(13,plain,
% 1.78/1.40 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))) | (~type(f, fulladder)) | connection(out(s, f), out(s, h2(f)))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[12, 11])).
% 1.78/1.40 tff(14,plain,
% 1.78/1.40 (connection(out(s, f), out(s, h2(f)))),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[13, 10, 3])).
% 1.78/1.40 tff(15,plain,
% 1.78/1.40 (value(out(s, f), n1) <=> value(out(s, f), n1)),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(16,axiom,(value(out(s, f), n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','outs_1')).
% 1.78/1.40 tff(17,plain,
% 1.78/1.40 (value(out(s, f), n1)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.78/1.40 tff(18,plain,
% 1.78/1.40 (^[V: $i, P2: $i, P1: $i] : refl((value(P2, V) | (~value(P1, V)) | (~connection(P1, P2))) <=> (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2))))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(19,plain,
% 1.78/1.40 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2))) <=> ![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[18])).
% 1.78/1.40 tff(20,plain,
% 1.78/1.40 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2))) <=> ![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(21,plain,
% 1.78/1.40 (^[V: $i, P2: $i, P1: $i] : rewrite((((~connection(P1, P2)) | (~value(P1, V))) | value(P2, V)) <=> (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2))))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(22,plain,
% 1.78/1.40 (![V: $i, P2: $i, P1: $i] : (((~connection(P1, P2)) | (~value(P1, V))) | value(P2, V)) <=> ![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[21])).
% 1.78/1.40 tff(23,axiom,(![V: $i, P2: $i, P1: $i] : (((~connection(P1, P2)) | (~value(P1, V))) | value(P2, V))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','value_propagation1')).
% 1.78/1.40 tff(24,plain,
% 1.78/1.40 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[23, 22])).
% 1.78/1.40 tff(25,plain,
% 1.78/1.40 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[24, 20])).
% 1.78/1.40 tff(26,plain,(
% 1.78/1.40 ![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 1.78/1.40 inference(skolemize,[status(sab)],[25])).
% 1.78/1.40 tff(27,plain,
% 1.78/1.40 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[26, 19])).
% 1.78/1.40 tff(28,plain,
% 1.78/1.40 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))) | value(out(s, h2(f)), n1))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))) | value(out(s, h2(f)), n1))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(29,plain,
% 1.78/1.40 ((value(out(s, h2(f)), n1) | (~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f))))) <=> ((~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))) | value(out(s, h2(f)), n1))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(30,plain,
% 1.78/1.40 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(s, h2(f)), n1) | (~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))) | value(out(s, h2(f)), n1)))),
% 1.78/1.40 inference(monotonicity,[status(thm)],[29])).
% 1.78/1.40 tff(31,plain,
% 1.78/1.40 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(s, h2(f)), n1) | (~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))) | value(out(s, h2(f)), n1))),
% 1.78/1.40 inference(transitivity,[status(thm)],[30, 28])).
% 1.78/1.40 tff(32,plain,
% 1.78/1.40 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(s, h2(f)), n1) | (~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))))),
% 1.78/1.40 inference(quant_inst,[status(thm)],[])).
% 1.78/1.40 tff(33,plain,
% 1.78/1.40 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))) | value(out(s, h2(f)), n1)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.78/1.40 tff(34,plain,
% 1.78/1.40 (value(out(s, h2(f)), n1)),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[33, 27, 17, 14])).
% 1.78/1.40 tff(35,assumption,(~value(out(n1, and1(h2(f))), n1)), introduced(assumption)).
% 1.78/1.40 tff(36,plain,
% 1.78/1.40 (^[X: $i] : refl(((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ((~type(X, fulladder)) | type(h2(X), halfadder)))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(37,plain,
% 1.78/1.40 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[36])).
% 1.78/1.40 tff(38,plain,
% 1.78/1.40 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(39,axiom,(![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_halfadder2')).
% 1.78/1.40 tff(40,plain,
% 1.78/1.40 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 1.78/1.40 tff(41,plain,(
% 1.78/1.40 ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 1.78/1.40 inference(skolemize,[status(sab)],[40])).
% 1.78/1.40 tff(42,plain,
% 1.78/1.40 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[41, 37])).
% 1.78/1.40 tff(43,plain,
% 1.78/1.40 (((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | ((~type(f, fulladder)) | type(h2(f), halfadder))) <=> ((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | (~type(f, fulladder)) | type(h2(f), halfadder))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(44,plain,
% 1.78/1.40 ((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | ((~type(f, fulladder)) | type(h2(f), halfadder))),
% 1.78/1.40 inference(quant_inst,[status(thm)],[])).
% 1.78/1.40 tff(45,plain,
% 1.78/1.40 ((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | (~type(f, fulladder)) | type(h2(f), halfadder)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 1.78/1.40 tff(46,plain,
% 1.78/1.40 (type(h2(f), halfadder)),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[45, 42, 3])).
% 1.78/1.40 tff(47,plain,
% 1.78/1.40 (^[X: $i] : refl(((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X)))) <=> ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X)))))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(48,plain,
% 1.78/1.40 (![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[47])).
% 1.78/1.40 tff(49,plain,
% 1.78/1.40 (![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(50,axiom,(![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_connection_outs_out1and1')).
% 1.78/1.40 tff(51,plain,
% 1.78/1.40 (![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.78/1.40 tff(52,plain,(
% 1.78/1.40 ![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))),
% 1.78/1.40 inference(skolemize,[status(sab)],[51])).
% 1.78/1.40 tff(53,plain,
% 1.78/1.40 (![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[52, 48])).
% 1.78/1.40 tff(54,plain,
% 1.78/1.40 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))) | ((~type(h2(f), halfadder)) | connection(out(s, h2(f)), out(n1, and1(h2(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))) | (~type(h2(f), halfadder)) | connection(out(s, h2(f)), out(n1, and1(h2(f)))))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(55,plain,
% 1.78/1.40 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))) | ((~type(h2(f), halfadder)) | connection(out(s, h2(f)), out(n1, and1(h2(f)))))),
% 1.78/1.40 inference(quant_inst,[status(thm)],[])).
% 1.78/1.40 tff(56,plain,
% 1.78/1.40 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))) | (~type(h2(f), halfadder)) | connection(out(s, h2(f)), out(n1, and1(h2(f))))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.78/1.40 tff(57,plain,
% 1.78/1.40 (connection(out(s, h2(f)), out(n1, and1(h2(f))))),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[56, 53, 46])).
% 1.78/1.40 tff(58,plain,
% 1.78/1.40 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~connection(out(s, h2(f)), out(n1, and1(h2(f))))) | value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~connection(out(s, h2(f)), out(n1, and1(h2(f))))) | value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(59,plain,
% 1.78/1.40 ((value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1)) | (~connection(out(s, h2(f)), out(n1, and1(h2(f)))))) <=> ((~connection(out(s, h2(f)), out(n1, and1(h2(f))))) | value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1)))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(60,plain,
% 1.78/1.40 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1)) | (~connection(out(s, h2(f)), out(n1, and1(h2(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~connection(out(s, h2(f)), out(n1, and1(h2(f))))) | value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1))))),
% 1.78/1.40 inference(monotonicity,[status(thm)],[59])).
% 1.78/1.40 tff(61,plain,
% 1.78/1.40 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1)) | (~connection(out(s, h2(f)), out(n1, and1(h2(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~connection(out(s, h2(f)), out(n1, and1(h2(f))))) | value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1)))),
% 1.78/1.40 inference(transitivity,[status(thm)],[60, 58])).
% 1.78/1.40 tff(62,plain,
% 1.78/1.40 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1)) | (~connection(out(s, h2(f)), out(n1, and1(h2(f))))))),
% 1.78/1.40 inference(quant_inst,[status(thm)],[])).
% 1.78/1.40 tff(63,plain,
% 1.78/1.40 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~connection(out(s, h2(f)), out(n1, and1(h2(f))))) | value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 1.78/1.40 tff(64,plain,
% 1.78/1.40 ($false),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[63, 27, 57, 35, 34])).
% 1.78/1.40 tff(65,plain,(value(out(n1, and1(h2(f))), n1)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.40 tff(66,assumption,(value(out(c, h2(f)), n0)), introduced(assumption)).
% 1.78/1.40 tff(67,assumption,(~value(in(n1, and1(h1(f))), n1)), introduced(assumption)).
% 1.78/1.40 tff(68,plain,
% 1.78/1.40 (^[X: $i] : refl(((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X)))) <=> ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X)))))),
% 1.78/1.40 inference(bind,[status(th)],[])).
% 1.78/1.40 tff(69,plain,
% 1.78/1.40 (![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 1.78/1.40 inference(quant_intro,[status(thm)],[68])).
% 1.78/1.40 tff(70,plain,
% 1.78/1.40 (![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(71,axiom,(![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_connection_inc_in2h1')).
% 1.78/1.40 tff(72,plain,
% 1.78/1.40 (![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.78/1.40 tff(73,plain,(
% 1.78/1.40 ![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 1.78/1.40 inference(skolemize,[status(sab)],[72])).
% 1.78/1.40 tff(74,plain,
% 1.78/1.40 (![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[73, 69])).
% 1.78/1.40 tff(75,plain,
% 1.78/1.40 (((~![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))) | ((~type(f, fulladder)) | connection(in(c, f), in(n2, h1(f))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))) | (~type(f, fulladder)) | connection(in(c, f), in(n2, h1(f))))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(76,plain,
% 1.78/1.40 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))) | ((~type(f, fulladder)) | connection(in(c, f), in(n2, h1(f))))),
% 1.78/1.40 inference(quant_inst,[status(thm)],[])).
% 1.78/1.40 tff(77,plain,
% 1.78/1.40 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))) | (~type(f, fulladder)) | connection(in(c, f), in(n2, h1(f)))),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.78/1.40 tff(78,plain,
% 1.78/1.40 (connection(in(c, f), in(n2, h1(f)))),
% 1.78/1.40 inference(unit_resolution,[status(thm)],[77, 74, 3])).
% 1.78/1.40 tff(79,plain,
% 1.78/1.40 (value(in(c, f), n1) <=> value(in(c, f), n1)),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(80,axiom,(value(in(c, f), n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','inc_1')).
% 1.78/1.40 tff(81,plain,
% 1.78/1.40 (value(in(c, f), n1)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[80, 79])).
% 1.78/1.40 tff(82,plain,
% 1.78/1.40 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(c, f), n1)) | (~connection(in(c, f), in(n2, h1(f)))) | value(in(n2, h1(f)), n1))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(c, f), n1)) | (~connection(in(c, f), in(n2, h1(f)))) | value(in(n2, h1(f)), n1))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(83,plain,
% 1.78/1.40 ((value(in(n2, h1(f)), n1) | (~value(in(c, f), n1)) | (~connection(in(c, f), in(n2, h1(f))))) <=> ((~value(in(c, f), n1)) | (~connection(in(c, f), in(n2, h1(f)))) | value(in(n2, h1(f)), n1))),
% 1.78/1.40 inference(rewrite,[status(thm)],[])).
% 1.78/1.40 tff(84,plain,
% 1.78/1.40 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, h1(f)), n1) | (~value(in(c, f), n1)) | (~connection(in(c, f), in(n2, h1(f)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(c, f), n1)) | (~connection(in(c, f), in(n2, h1(f)))) | value(in(n2, h1(f)), n1)))),
% 1.78/1.40 inference(monotonicity,[status(thm)],[83])).
% 1.78/1.40 tff(85,plain,
% 1.78/1.40 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, h1(f)), n1) | (~value(in(c, f), n1)) | (~connection(in(c, f), in(n2, h1(f)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(c, f), n1)) | (~connection(in(c, f), in(n2, h1(f)))) | value(in(n2, h1(f)), n1))),
% 1.78/1.40 inference(transitivity,[status(thm)],[84, 82])).
% 1.78/1.40 tff(86,plain,
% 1.78/1.40 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, h1(f)), n1) | (~value(in(c, f), n1)) | (~connection(in(c, f), in(n2, h1(f)))))),
% 1.78/1.40 inference(quant_inst,[status(thm)],[])).
% 1.78/1.40 tff(87,plain,
% 1.78/1.40 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(c, f), n1)) | (~connection(in(c, f), in(n2, h1(f)))) | value(in(n2, h1(f)), n1)),
% 1.78/1.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.78/1.41 tff(88,plain,
% 1.78/1.41 (value(in(n2, h1(f)), n1)),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[87, 27, 81, 78])).
% 1.78/1.41 tff(89,assumption,(~value(in(n2, or1(h1(f))), n1)), introduced(assumption)).
% 1.78/1.41 tff(90,plain,
% 1.78/1.41 (^[X: $i] : refl(((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ((~type(X, fulladder)) | type(h1(X), halfadder)))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(91,plain,
% 1.78/1.41 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[90])).
% 1.78/1.41 tff(92,plain,
% 1.78/1.41 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(93,axiom,(![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_halfadder1')).
% 1.78/1.41 tff(94,plain,
% 1.78/1.41 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.78/1.41 tff(95,plain,(
% 1.78/1.41 ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 1.78/1.41 inference(skolemize,[status(sab)],[94])).
% 1.78/1.41 tff(96,plain,
% 1.78/1.41 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[95, 91])).
% 1.78/1.41 tff(97,plain,
% 1.78/1.41 (((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | ((~type(f, fulladder)) | type(h1(f), halfadder))) <=> ((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | (~type(f, fulladder)) | type(h1(f), halfadder))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(98,plain,
% 1.78/1.41 ((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | ((~type(f, fulladder)) | type(h1(f), halfadder))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(99,plain,
% 1.78/1.41 ((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | (~type(f, fulladder)) | type(h1(f), halfadder)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[98, 97])).
% 1.78/1.41 tff(100,plain,
% 1.78/1.41 (type(h1(f), halfadder)),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[99, 96, 3])).
% 1.78/1.41 tff(101,plain,
% 1.78/1.41 (^[X: $i] : refl(((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X)))) <=> ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X)))))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(102,plain,
% 1.78/1.41 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[101])).
% 1.78/1.41 tff(103,plain,
% 1.78/1.41 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(104,axiom,(![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_connection_in2_in2or1')).
% 1.78/1.41 tff(105,plain,
% 1.78/1.41 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.78/1.41 tff(106,plain,(
% 1.78/1.41 ![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))),
% 1.78/1.41 inference(skolemize,[status(sab)],[105])).
% 1.78/1.41 tff(107,plain,
% 1.78/1.41 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[106, 102])).
% 1.78/1.41 tff(108,plain,
% 1.78/1.41 (((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))) | ((~type(h1(f), halfadder)) | connection(in(n2, h1(f)), in(n2, or1(h1(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))) | (~type(h1(f), halfadder)) | connection(in(n2, h1(f)), in(n2, or1(h1(f)))))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(109,plain,
% 1.78/1.41 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))) | ((~type(h1(f), halfadder)) | connection(in(n2, h1(f)), in(n2, or1(h1(f)))))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(110,plain,
% 1.78/1.41 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))) | (~type(h1(f), halfadder)) | connection(in(n2, h1(f)), in(n2, or1(h1(f))))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[109, 108])).
% 1.78/1.41 tff(111,plain,
% 1.78/1.41 (connection(in(n2, h1(f)), in(n2, or1(h1(f))))),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[110, 107, 100])).
% 1.78/1.41 tff(112,plain,
% 1.78/1.41 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, or1(h1(f))), n1) | (~value(in(n2, h1(f)), n1)) | (~connection(in(n2, h1(f)), in(n2, or1(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(in(n2, or1(h1(f))), n1) | (~value(in(n2, h1(f)), n1)) | (~connection(in(n2, h1(f)), in(n2, or1(h1(f))))))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(113,plain,
% 1.78/1.41 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, or1(h1(f))), n1) | (~value(in(n2, h1(f)), n1)) | (~connection(in(n2, h1(f)), in(n2, or1(h1(f))))))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(114,plain,
% 1.78/1.41 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(in(n2, or1(h1(f))), n1) | (~value(in(n2, h1(f)), n1)) | (~connection(in(n2, h1(f)), in(n2, or1(h1(f)))))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[113, 112])).
% 1.78/1.41 tff(115,plain,
% 1.78/1.41 ($false),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[114, 27, 111, 89, 88])).
% 1.78/1.41 tff(116,plain,(value(in(n2, or1(h1(f))), n1)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.41 tff(117,plain,
% 1.78/1.41 (^[X: $i] : refl(((~type(X, halfadder)) | type(or1(X), or)) <=> ((~type(X, halfadder)) | type(or1(X), or)))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(118,plain,
% 1.78/1.41 (![X: $i] : ((~type(X, halfadder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[117])).
% 1.78/1.41 tff(119,plain,
% 1.78/1.41 (![X: $i] : ((~type(X, halfadder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(120,axiom,(![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_or1')).
% 1.78/1.41 tff(121,plain,
% 1.78/1.41 (![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.78/1.41 tff(122,plain,(
% 1.78/1.41 ![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))),
% 1.78/1.41 inference(skolemize,[status(sab)],[121])).
% 1.78/1.41 tff(123,plain,
% 1.78/1.41 (![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[122, 118])).
% 1.78/1.41 tff(124,plain,
% 1.78/1.41 (((~![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))) | ((~type(h1(f), halfadder)) | type(or1(h1(f)), or))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))) | (~type(h1(f), halfadder)) | type(or1(h1(f)), or))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(125,plain,
% 1.78/1.41 ((~![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))) | ((~type(h1(f), halfadder)) | type(or1(h1(f)), or))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(126,plain,
% 1.78/1.41 ((~![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))) | (~type(h1(f), halfadder)) | type(or1(h1(f)), or)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[125, 124])).
% 1.78/1.41 tff(127,plain,
% 1.78/1.41 (type(or1(h1(f)), or)),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[126, 123, 100])).
% 1.78/1.41 tff(128,plain,
% 1.78/1.41 ((~mode(or1(h1(f)), abnormal)) <=> (~mode(or1(h1(f)), abnormal))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(129,axiom,(~mode(or1(h1(f)), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_or1h1')).
% 1.78/1.41 tff(130,plain,
% 1.78/1.41 (~mode(or1(h1(f)), abnormal)),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[129, 128])).
% 1.78/1.41 tff(131,plain,
% 1.78/1.41 (^[Any: $i, K: $i] : refl((mode(K, abnormal) | mode(K, ok) | (~type(K, Any))) <=> (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(132,plain,
% 1.78/1.41 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))) <=> ![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[131])).
% 1.78/1.41 tff(133,plain,
% 1.78/1.41 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))) <=> ![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(134,plain,
% 1.78/1.41 (^[Any: $i, K: $i] : rewrite((((~type(K, Any)) | mode(K, ok)) | mode(K, abnormal)) <=> (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(135,plain,
% 1.78/1.41 (![Any: $i, K: $i] : (((~type(K, Any)) | mode(K, ok)) | mode(K, abnormal)) <=> ![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[134])).
% 1.78/1.41 tff(136,axiom,(![Any: $i, K: $i] : (((~type(K, Any)) | mode(K, ok)) | mode(K, abnormal))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','ok_or_abnormal')).
% 1.78/1.41 tff(137,plain,
% 1.78/1.41 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[136, 135])).
% 1.78/1.41 tff(138,plain,
% 1.78/1.41 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[137, 133])).
% 1.78/1.41 tff(139,plain,(
% 1.78/1.41 ![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 1.78/1.41 inference(skolemize,[status(sab)],[138])).
% 1.78/1.41 tff(140,plain,
% 1.78/1.41 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[139, 132])).
% 1.78/1.41 tff(141,plain,
% 1.78/1.41 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(or1(h1(f)), abnormal) | mode(or1(h1(f)), ok) | (~type(or1(h1(f)), or)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(or1(h1(f)), abnormal) | mode(or1(h1(f)), ok) | (~type(or1(h1(f)), or)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(142,plain,
% 1.78/1.41 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(or1(h1(f)), abnormal) | mode(or1(h1(f)), ok) | (~type(or1(h1(f)), or)))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(143,plain,
% 1.78/1.41 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(or1(h1(f)), abnormal) | mode(or1(h1(f)), ok) | (~type(or1(h1(f)), or))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[142, 141])).
% 1.78/1.41 tff(144,plain,
% 1.78/1.41 (mode(or1(h1(f)), ok)),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[143, 140, 130, 127])).
% 1.78/1.41 tff(145,plain,
% 1.78/1.41 (^[Any: $i, K: $i] : refl(((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or))) <=> ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or))))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(146,plain,
% 1.78/1.41 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or))) <=> ![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or)))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[145])).
% 1.78/1.41 tff(147,plain,
% 1.78/1.41 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or))) <=> ![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(148,plain,
% 1.78/1.41 (^[Any: $i, K: $i] : trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, or))) | (~value(in(Any, K), n1))) <=> ((~mode(K, ok)) | (~value(in(Any, K), n1)) | (~type(K, or)))), (((((~mode(K, ok)) | (~type(K, or))) | (~value(in(Any, K), n1))) | value(out(n1, K), n1)) <=> (((~mode(K, ok)) | (~value(in(Any, K), n1)) | (~type(K, or))) | value(out(n1, K), n1)))), rewrite((((~mode(K, ok)) | (~value(in(Any, K), n1)) | (~type(K, or))) | value(out(n1, K), n1)) <=> ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or)))), (((((~mode(K, ok)) | (~type(K, or))) | (~value(in(Any, K), n1))) | value(out(n1, K), n1)) <=> ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or)))))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(149,plain,
% 1.78/1.41 (![Any: $i, K: $i] : ((((~mode(K, ok)) | (~type(K, or))) | (~value(in(Any, K), n1))) | value(out(n1, K), n1)) <=> ![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or)))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[148])).
% 1.78/1.41 tff(150,axiom,(![Any: $i, K: $i] : ((((~mode(K, ok)) | (~type(K, or))) | (~value(in(Any, K), n1))) | value(out(n1, K), n1))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','or_1x_1')).
% 1.78/1.41 tff(151,plain,
% 1.78/1.41 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or)))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[150, 149])).
% 1.78/1.41 tff(152,plain,
% 1.78/1.41 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or)))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[151, 147])).
% 1.78/1.41 tff(153,plain,(
% 1.78/1.41 ![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or)))),
% 1.78/1.41 inference(skolemize,[status(sab)],[152])).
% 1.78/1.41 tff(154,plain,
% 1.78/1.41 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or)))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[153, 146])).
% 1.78/1.41 tff(155,plain,
% 1.78/1.41 (((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or)))) | ((~mode(or1(h1(f)), ok)) | value(out(n1, or1(h1(f))), n1) | (~type(or1(h1(f)), or)) | (~value(in(n2, or1(h1(f))), n1)))) <=> ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or)))) | (~mode(or1(h1(f)), ok)) | value(out(n1, or1(h1(f))), n1) | (~type(or1(h1(f)), or)) | (~value(in(n2, or1(h1(f))), n1)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(156,plain,
% 1.78/1.41 (((~mode(or1(h1(f)), ok)) | value(out(n1, or1(h1(f))), n1) | (~value(in(n2, or1(h1(f))), n1)) | (~type(or1(h1(f)), or))) <=> ((~mode(or1(h1(f)), ok)) | value(out(n1, or1(h1(f))), n1) | (~type(or1(h1(f)), or)) | (~value(in(n2, or1(h1(f))), n1)))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(157,plain,
% 1.78/1.41 (((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or)))) | ((~mode(or1(h1(f)), ok)) | value(out(n1, or1(h1(f))), n1) | (~value(in(n2, or1(h1(f))), n1)) | (~type(or1(h1(f)), or)))) <=> ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or)))) | ((~mode(or1(h1(f)), ok)) | value(out(n1, or1(h1(f))), n1) | (~type(or1(h1(f)), or)) | (~value(in(n2, or1(h1(f))), n1))))),
% 1.78/1.41 inference(monotonicity,[status(thm)],[156])).
% 1.78/1.41 tff(158,plain,
% 1.78/1.41 (((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or)))) | ((~mode(or1(h1(f)), ok)) | value(out(n1, or1(h1(f))), n1) | (~value(in(n2, or1(h1(f))), n1)) | (~type(or1(h1(f)), or)))) <=> ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or)))) | (~mode(or1(h1(f)), ok)) | value(out(n1, or1(h1(f))), n1) | (~type(or1(h1(f)), or)) | (~value(in(n2, or1(h1(f))), n1)))),
% 1.78/1.41 inference(transitivity,[status(thm)],[157, 155])).
% 1.78/1.41 tff(159,plain,
% 1.78/1.41 ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or)))) | ((~mode(or1(h1(f)), ok)) | value(out(n1, or1(h1(f))), n1) | (~value(in(n2, or1(h1(f))), n1)) | (~type(or1(h1(f)), or)))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(160,plain,
% 1.78/1.41 ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(Any, K), n1)) | (~type(K, or)))) | (~mode(or1(h1(f)), ok)) | value(out(n1, or1(h1(f))), n1) | (~type(or1(h1(f)), or)) | (~value(in(n2, or1(h1(f))), n1))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[159, 158])).
% 1.78/1.41 tff(161,plain,
% 1.78/1.41 ((~mode(or1(h1(f)), ok)) | value(out(n1, or1(h1(f))), n1) | (~value(in(n2, or1(h1(f))), n1))),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[160, 154, 127])).
% 1.78/1.41 tff(162,plain,
% 1.78/1.41 (value(out(n1, or1(h1(f))), n1) | (~value(in(n2, or1(h1(f))), n1))),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[161, 144])).
% 1.78/1.41 tff(163,plain,
% 1.78/1.41 (value(out(n1, or1(h1(f))), n1)),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[162, 116])).
% 1.78/1.41 tff(164,plain,
% 1.78/1.41 (^[X: $i] : refl(((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X)))) <=> ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X)))))),
% 1.78/1.41 inference(bind,[status(th)],[])).
% 1.78/1.41 tff(165,plain,
% 1.78/1.41 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))),
% 1.78/1.41 inference(quant_intro,[status(thm)],[164])).
% 1.78/1.41 tff(166,plain,
% 1.78/1.41 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(167,axiom,(![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_connection_out1or1_in1_and1')).
% 1.78/1.41 tff(168,plain,
% 1.78/1.41 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.78/1.41 tff(169,plain,(
% 1.78/1.41 ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))),
% 1.78/1.41 inference(skolemize,[status(sab)],[168])).
% 1.78/1.41 tff(170,plain,
% 1.78/1.41 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[169, 165])).
% 1.78/1.41 tff(171,plain,
% 1.78/1.41 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))) | ((~type(h1(f), halfadder)) | connection(out(n1, or1(h1(f))), in(n1, and1(h1(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))) | (~type(h1(f), halfadder)) | connection(out(n1, or1(h1(f))), in(n1, and1(h1(f)))))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(172,plain,
% 1.78/1.41 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))) | ((~type(h1(f), halfadder)) | connection(out(n1, or1(h1(f))), in(n1, and1(h1(f)))))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(173,plain,
% 1.78/1.41 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))) | (~type(h1(f), halfadder)) | connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[172, 171])).
% 1.78/1.41 tff(174,plain,
% 1.78/1.41 (connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[173, 170, 100])).
% 1.78/1.41 tff(175,plain,
% 1.78/1.41 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(out(n1, or1(h1(f))), n1)) | value(in(n1, and1(h1(f))), n1) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(n1, or1(h1(f))), n1)) | value(in(n1, and1(h1(f))), n1) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(176,plain,
% 1.78/1.41 ((value(in(n1, and1(h1(f))), n1) | (~value(out(n1, or1(h1(f))), n1)) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f)))))) <=> ((~value(out(n1, or1(h1(f))), n1)) | value(in(n1, and1(h1(f))), n1) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))))),
% 1.78/1.41 inference(rewrite,[status(thm)],[])).
% 1.78/1.41 tff(177,plain,
% 1.78/1.41 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, and1(h1(f))), n1) | (~value(out(n1, or1(h1(f))), n1)) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(out(n1, or1(h1(f))), n1)) | value(in(n1, and1(h1(f))), n1) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f)))))))),
% 1.78/1.41 inference(monotonicity,[status(thm)],[176])).
% 1.78/1.41 tff(178,plain,
% 1.78/1.41 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, and1(h1(f))), n1) | (~value(out(n1, or1(h1(f))), n1)) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(n1, or1(h1(f))), n1)) | value(in(n1, and1(h1(f))), n1) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))))),
% 1.78/1.41 inference(transitivity,[status(thm)],[177, 175])).
% 1.78/1.41 tff(179,plain,
% 1.78/1.41 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, and1(h1(f))), n1) | (~value(out(n1, or1(h1(f))), n1)) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))))),
% 1.78/1.41 inference(quant_inst,[status(thm)],[])).
% 1.78/1.41 tff(180,plain,
% 1.78/1.41 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(n1, or1(h1(f))), n1)) | value(in(n1, and1(h1(f))), n1) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f)))))),
% 1.78/1.41 inference(modus_ponens,[status(thm)],[179, 178])).
% 1.78/1.41 tff(181,plain,
% 1.78/1.41 ($false),
% 1.78/1.41 inference(unit_resolution,[status(thm)],[180, 27, 174, 163, 67])).
% 1.78/1.41 tff(182,plain,(value(in(n1, and1(h1(f))), n1)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.41 tff(183,assumption,(~value(in(n2, and1(h1(f))), n1)), introduced(assumption)).
% 1.78/1.41 tff(184,assumption,(~value(in(n1, h1(f)), n0)), introduced(assumption)).
% 1.78/1.41 tff(185,plain,
% 1.78/1.41 (^[X: $i] : refl(((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X)))) <=> ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X)))))),
% 1.78/1.42 inference(bind,[status(th)],[])).
% 1.78/1.42 tff(186,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 1.78/1.42 inference(quant_intro,[status(thm)],[185])).
% 1.78/1.42 tff(187,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(188,axiom,(![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_connection_in2_in1h1')).
% 1.78/1.42 tff(189,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.78/1.42 tff(190,plain,(
% 1.78/1.42 ![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 1.78/1.42 inference(skolemize,[status(sab)],[189])).
% 1.78/1.42 tff(191,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[190, 186])).
% 1.78/1.42 tff(192,plain,
% 1.78/1.42 (((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | ((~type(f, fulladder)) | connection(in(n2, f), in(n1, h1(f))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | (~type(f, fulladder)) | connection(in(n2, f), in(n1, h1(f))))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(193,plain,
% 1.78/1.42 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | ((~type(f, fulladder)) | connection(in(n2, f), in(n1, h1(f))))),
% 1.78/1.42 inference(quant_inst,[status(thm)],[])).
% 1.78/1.42 tff(194,plain,
% 1.78/1.42 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | (~type(f, fulladder)) | connection(in(n2, f), in(n1, h1(f)))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.78/1.42 tff(195,plain,
% 1.78/1.42 (connection(in(n2, f), in(n1, h1(f)))),
% 1.78/1.42 inference(unit_resolution,[status(thm)],[194, 191, 3])).
% 1.78/1.42 tff(196,plain,
% 1.78/1.42 (value(in(n2, f), n0) <=> value(in(n2, f), n0)),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(197,axiom,(value(in(n2, f), n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','in2_0')).
% 1.78/1.42 tff(198,plain,
% 1.78/1.42 (value(in(n2, f), n0)),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[197, 196])).
% 1.78/1.42 tff(199,plain,
% 1.78/1.42 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(n2, f), n0)) | (~connection(in(n2, f), in(n1, h1(f)))) | value(in(n1, h1(f)), n0))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n2, f), n0)) | (~connection(in(n2, f), in(n1, h1(f)))) | value(in(n1, h1(f)), n0))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(200,plain,
% 1.78/1.42 ((value(in(n1, h1(f)), n0) | (~value(in(n2, f), n0)) | (~connection(in(n2, f), in(n1, h1(f))))) <=> ((~value(in(n2, f), n0)) | (~connection(in(n2, f), in(n1, h1(f)))) | value(in(n1, h1(f)), n0))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(201,plain,
% 1.78/1.42 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, h1(f)), n0) | (~value(in(n2, f), n0)) | (~connection(in(n2, f), in(n1, h1(f)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(n2, f), n0)) | (~connection(in(n2, f), in(n1, h1(f)))) | value(in(n1, h1(f)), n0)))),
% 1.78/1.42 inference(monotonicity,[status(thm)],[200])).
% 1.78/1.42 tff(202,plain,
% 1.78/1.42 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, h1(f)), n0) | (~value(in(n2, f), n0)) | (~connection(in(n2, f), in(n1, h1(f)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n2, f), n0)) | (~connection(in(n2, f), in(n1, h1(f)))) | value(in(n1, h1(f)), n0))),
% 1.78/1.42 inference(transitivity,[status(thm)],[201, 199])).
% 1.78/1.42 tff(203,plain,
% 1.78/1.42 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, h1(f)), n0) | (~value(in(n2, f), n0)) | (~connection(in(n2, f), in(n1, h1(f)))))),
% 1.78/1.42 inference(quant_inst,[status(thm)],[])).
% 1.78/1.42 tff(204,plain,
% 1.78/1.42 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n2, f), n0)) | (~connection(in(n2, f), in(n1, h1(f)))) | value(in(n1, h1(f)), n0)),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[203, 202])).
% 1.78/1.42 tff(205,plain,
% 1.78/1.42 ($false),
% 1.78/1.42 inference(unit_resolution,[status(thm)],[204, 27, 198, 195, 184])).
% 1.78/1.42 tff(206,plain,(value(in(n1, h1(f)), n0)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.42 tff(207,assumption,(~value(in(n1, and2(h1(f))), n0)), introduced(assumption)).
% 1.78/1.42 tff(208,plain,
% 1.78/1.42 (^[X: $i] : refl(((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X)))) <=> ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X)))))),
% 1.78/1.42 inference(bind,[status(th)],[])).
% 1.78/1.42 tff(209,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 1.78/1.42 inference(quant_intro,[status(thm)],[208])).
% 1.78/1.42 tff(210,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(211,axiom,(![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_connection_in1_in1and2')).
% 1.78/1.42 tff(212,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[211, 210])).
% 1.78/1.42 tff(213,plain,(
% 1.78/1.42 ![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 1.78/1.42 inference(skolemize,[status(sab)],[212])).
% 1.78/1.42 tff(214,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[213, 209])).
% 1.78/1.42 tff(215,plain,
% 1.78/1.42 (((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h1(f), halfadder)) | connection(in(n1, h1(f)), in(n1, and2(h1(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h1(f), halfadder)) | connection(in(n1, h1(f)), in(n1, and2(h1(f)))))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(216,plain,
% 1.78/1.42 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h1(f), halfadder)) | connection(in(n1, h1(f)), in(n1, and2(h1(f)))))),
% 1.78/1.42 inference(quant_inst,[status(thm)],[])).
% 1.78/1.42 tff(217,plain,
% 1.78/1.42 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h1(f), halfadder)) | connection(in(n1, h1(f)), in(n1, and2(h1(f))))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[216, 215])).
% 1.78/1.42 tff(218,plain,
% 1.78/1.42 (connection(in(n1, h1(f)), in(n1, and2(h1(f))))),
% 1.78/1.42 inference(unit_resolution,[status(thm)],[217, 214, 100])).
% 1.78/1.42 tff(219,plain,
% 1.78/1.42 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, and2(h1(f))), n0) | (~value(in(n1, h1(f)), n0)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(in(n1, and2(h1(f))), n0) | (~value(in(n1, h1(f)), n0)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(220,plain,
% 1.78/1.42 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, and2(h1(f))), n0) | (~value(in(n1, h1(f)), n0)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))))),
% 1.78/1.42 inference(quant_inst,[status(thm)],[])).
% 1.78/1.42 tff(221,plain,
% 1.78/1.42 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(in(n1, and2(h1(f))), n0) | (~value(in(n1, h1(f)), n0)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f)))))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[220, 219])).
% 1.78/1.42 tff(222,plain,
% 1.78/1.42 ($false),
% 1.78/1.42 inference(unit_resolution,[status(thm)],[221, 27, 218, 207, 206])).
% 1.78/1.42 tff(223,plain,(value(in(n1, and2(h1(f))), n0)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.42 tff(224,plain,
% 1.78/1.42 (^[X: $i] : refl(((~type(X, halfadder)) | type(and2(X), and)) <=> ((~type(X, halfadder)) | type(and2(X), and)))),
% 1.78/1.42 inference(bind,[status(th)],[])).
% 1.78/1.42 tff(225,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 1.78/1.42 inference(quant_intro,[status(thm)],[224])).
% 1.78/1.42 tff(226,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(227,axiom,(![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_and2')).
% 1.78/1.42 tff(228,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[227, 226])).
% 1.78/1.42 tff(229,plain,(
% 1.78/1.42 ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 1.78/1.42 inference(skolemize,[status(sab)],[228])).
% 1.78/1.42 tff(230,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[229, 225])).
% 1.78/1.42 tff(231,plain,
% 1.78/1.42 (((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h1(f), halfadder)) | type(and2(h1(f)), and))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h1(f), halfadder)) | type(and2(h1(f)), and))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(232,plain,
% 1.78/1.42 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h1(f), halfadder)) | type(and2(h1(f)), and))),
% 1.78/1.42 inference(quant_inst,[status(thm)],[])).
% 1.78/1.42 tff(233,plain,
% 1.78/1.42 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h1(f), halfadder)) | type(and2(h1(f)), and)),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[232, 231])).
% 1.78/1.42 tff(234,plain,
% 1.78/1.42 (type(and2(h1(f)), and)),
% 1.78/1.42 inference(unit_resolution,[status(thm)],[233, 230, 100])).
% 1.78/1.42 tff(235,plain,
% 1.78/1.42 ((~mode(and2(h1(f)), abnormal)) <=> (~mode(and2(h1(f)), abnormal))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(236,axiom,(~mode(and2(h1(f)), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_and2h1')).
% 1.78/1.42 tff(237,plain,
% 1.78/1.42 (~mode(and2(h1(f)), abnormal)),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[236, 235])).
% 1.78/1.42 tff(238,plain,
% 1.78/1.42 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h1(f)), abnormal) | mode(and2(h1(f)), ok) | (~type(and2(h1(f)), and)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h1(f)), abnormal) | mode(and2(h1(f)), ok) | (~type(and2(h1(f)), and)))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(239,plain,
% 1.78/1.42 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h1(f)), abnormal) | mode(and2(h1(f)), ok) | (~type(and2(h1(f)), and)))),
% 1.78/1.42 inference(quant_inst,[status(thm)],[])).
% 1.78/1.42 tff(240,plain,
% 1.78/1.42 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h1(f)), abnormal) | mode(and2(h1(f)), ok) | (~type(and2(h1(f)), and))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[239, 238])).
% 1.78/1.42 tff(241,plain,
% 1.78/1.42 (mode(and2(h1(f)), ok)),
% 1.78/1.42 inference(unit_resolution,[status(thm)],[240, 140, 237, 234])).
% 1.78/1.42 tff(242,plain,
% 1.78/1.42 (^[Any: $i, K: $i] : refl(((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and))) <=> ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and))))),
% 1.78/1.42 inference(bind,[status(th)],[])).
% 1.78/1.42 tff(243,plain,
% 1.78/1.42 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and))) <=> ![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 1.78/1.42 inference(quant_intro,[status(thm)],[242])).
% 1.78/1.42 tff(244,plain,
% 1.78/1.42 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and))) <=> ![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(245,plain,
% 1.78/1.42 (^[Any: $i, K: $i] : trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, and))) | (~value(in(Any, K), n0))) <=> ((~mode(K, ok)) | (~value(in(Any, K), n0)) | (~type(K, and)))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(in(Any, K), n0))) | value(out(n1, K), n0)) <=> (((~mode(K, ok)) | (~value(in(Any, K), n0)) | (~type(K, and))) | value(out(n1, K), n0)))), rewrite((((~mode(K, ok)) | (~value(in(Any, K), n0)) | (~type(K, and))) | value(out(n1, K), n0)) <=> ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(in(Any, K), n0))) | value(out(n1, K), n0)) <=> ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))))),
% 1.78/1.42 inference(bind,[status(th)],[])).
% 1.78/1.42 tff(246,plain,
% 1.78/1.42 (![Any: $i, K: $i] : ((((~mode(K, ok)) | (~type(K, and))) | (~value(in(Any, K), n0))) | value(out(n1, K), n0)) <=> ![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 1.78/1.42 inference(quant_intro,[status(thm)],[245])).
% 1.78/1.42 tff(247,axiom,(![Any: $i, K: $i] : ((((~mode(K, ok)) | (~type(K, and))) | (~value(in(Any, K), n0))) | value(out(n1, K), n0))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','and_0x_0')).
% 1.78/1.42 tff(248,plain,
% 1.78/1.42 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[247, 246])).
% 1.78/1.42 tff(249,plain,
% 1.78/1.42 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[248, 244])).
% 1.78/1.42 tff(250,plain,(
% 1.78/1.42 ![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 1.78/1.42 inference(skolemize,[status(sab)],[249])).
% 1.78/1.42 tff(251,plain,
% 1.78/1.42 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[250, 243])).
% 1.78/1.42 tff(252,plain,
% 1.78/1.42 (((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h1(f)), ok)) | value(out(n1, and2(h1(f))), n0) | (~value(in(n1, and2(h1(f))), n0)) | (~type(and2(h1(f)), and)))) <=> ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | (~mode(and2(h1(f)), ok)) | value(out(n1, and2(h1(f))), n0) | (~value(in(n1, and2(h1(f))), n0)) | (~type(and2(h1(f)), and)))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(253,plain,
% 1.78/1.42 ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h1(f)), ok)) | value(out(n1, and2(h1(f))), n0) | (~value(in(n1, and2(h1(f))), n0)) | (~type(and2(h1(f)), and)))),
% 1.78/1.42 inference(quant_inst,[status(thm)],[])).
% 1.78/1.42 tff(254,plain,
% 1.78/1.42 ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | (~mode(and2(h1(f)), ok)) | value(out(n1, and2(h1(f))), n0) | (~value(in(n1, and2(h1(f))), n0)) | (~type(and2(h1(f)), and))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[253, 252])).
% 1.78/1.42 tff(255,plain,
% 1.78/1.42 ((~mode(and2(h1(f)), ok)) | value(out(n1, and2(h1(f))), n0) | (~value(in(n1, and2(h1(f))), n0))),
% 1.78/1.42 inference(unit_resolution,[status(thm)],[254, 251, 234])).
% 1.78/1.42 tff(256,plain,
% 1.78/1.42 (value(out(n1, and2(h1(f))), n0) | (~value(in(n1, and2(h1(f))), n0))),
% 1.78/1.42 inference(unit_resolution,[status(thm)],[255, 241])).
% 1.78/1.42 tff(257,plain,
% 1.78/1.42 (value(out(n1, and2(h1(f))), n0)),
% 1.78/1.42 inference(unit_resolution,[status(thm)],[256, 223])).
% 1.78/1.42 tff(258,assumption,(~value(in(n1, not1(h1(f))), n0)), introduced(assumption)).
% 1.78/1.42 tff(259,plain,
% 1.78/1.42 (^[X: $i] : refl(((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X)))) <=> ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X)))))),
% 1.78/1.42 inference(bind,[status(th)],[])).
% 1.78/1.42 tff(260,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))),
% 1.78/1.42 inference(quant_intro,[status(thm)],[259])).
% 1.78/1.42 tff(261,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(262,axiom,(![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_connection_out1and2_in1not1')).
% 1.78/1.42 tff(263,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[262, 261])).
% 1.78/1.42 tff(264,plain,(
% 1.78/1.42 ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))),
% 1.78/1.42 inference(skolemize,[status(sab)],[263])).
% 1.78/1.42 tff(265,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[264, 260])).
% 1.78/1.42 tff(266,plain,
% 1.78/1.42 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))) | ((~type(h1(f), halfadder)) | connection(out(n1, and2(h1(f))), in(n1, not1(h1(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))) | (~type(h1(f), halfadder)) | connection(out(n1, and2(h1(f))), in(n1, not1(h1(f)))))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(267,plain,
% 1.78/1.42 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))) | ((~type(h1(f), halfadder)) | connection(out(n1, and2(h1(f))), in(n1, not1(h1(f)))))),
% 1.78/1.42 inference(quant_inst,[status(thm)],[])).
% 1.78/1.42 tff(268,plain,
% 1.78/1.42 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))) | (~type(h1(f), halfadder)) | connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[267, 266])).
% 1.78/1.42 tff(269,plain,
% 1.78/1.42 (connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))),
% 1.78/1.42 inference(unit_resolution,[status(thm)],[268, 265, 100])).
% 1.78/1.42 tff(270,plain,
% 1.78/1.42 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, not1(h1(f))), n0) | (~value(out(n1, and2(h1(f))), n0)) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(in(n1, not1(h1(f))), n0) | (~value(out(n1, and2(h1(f))), n0)) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(271,plain,
% 1.78/1.42 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, not1(h1(f))), n0) | (~value(out(n1, and2(h1(f))), n0)) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))))),
% 1.78/1.42 inference(quant_inst,[status(thm)],[])).
% 1.78/1.42 tff(272,plain,
% 1.78/1.42 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(in(n1, not1(h1(f))), n0) | (~value(out(n1, and2(h1(f))), n0)) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f)))))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[271, 270])).
% 1.78/1.42 tff(273,plain,
% 1.78/1.42 ($false),
% 1.78/1.42 inference(unit_resolution,[status(thm)],[272, 27, 269, 258, 257])).
% 1.78/1.42 tff(274,plain,(value(in(n1, not1(h1(f))), n0)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.42 tff(275,plain,
% 1.78/1.42 (^[X: $i] : refl(((~type(X, halfadder)) | type(not1(X), not)) <=> ((~type(X, halfadder)) | type(not1(X), not)))),
% 1.78/1.42 inference(bind,[status(th)],[])).
% 1.78/1.42 tff(276,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, halfadder)) | type(not1(X), not)) <=> ![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))),
% 1.78/1.42 inference(quant_intro,[status(thm)],[275])).
% 1.78/1.42 tff(277,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, halfadder)) | type(not1(X), not)) <=> ![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(278,axiom,(![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_not1')).
% 1.78/1.42 tff(279,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[278, 277])).
% 1.78/1.42 tff(280,plain,(
% 1.78/1.42 ![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))),
% 1.78/1.42 inference(skolemize,[status(sab)],[279])).
% 1.78/1.42 tff(281,plain,
% 1.78/1.42 (![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[280, 276])).
% 1.78/1.42 tff(282,plain,
% 1.78/1.42 (((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | ((~type(h1(f), halfadder)) | type(not1(h1(f)), not))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | (~type(h1(f), halfadder)) | type(not1(h1(f)), not))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(283,plain,
% 1.78/1.42 ((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | ((~type(h1(f), halfadder)) | type(not1(h1(f)), not))),
% 1.78/1.42 inference(quant_inst,[status(thm)],[])).
% 1.78/1.42 tff(284,plain,
% 1.78/1.42 ((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | (~type(h1(f), halfadder)) | type(not1(h1(f)), not)),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[283, 282])).
% 1.78/1.42 tff(285,plain,
% 1.78/1.42 (type(not1(h1(f)), not)),
% 1.78/1.42 inference(unit_resolution,[status(thm)],[284, 281, 100])).
% 1.78/1.42 tff(286,plain,
% 1.78/1.42 ((~mode(not1(h1(f)), abnormal)) <=> (~mode(not1(h1(f)), abnormal))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(287,axiom,(~mode(not1(h1(f)), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_not1h1')).
% 1.78/1.42 tff(288,plain,
% 1.78/1.42 (~mode(not1(h1(f)), abnormal)),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[287, 286])).
% 1.78/1.42 tff(289,plain,
% 1.78/1.42 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(not1(h1(f)), abnormal) | mode(not1(h1(f)), ok) | (~type(not1(h1(f)), not)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(not1(h1(f)), abnormal) | mode(not1(h1(f)), ok) | (~type(not1(h1(f)), not)))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(290,plain,
% 1.78/1.42 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(not1(h1(f)), abnormal) | mode(not1(h1(f)), ok) | (~type(not1(h1(f)), not)))),
% 1.78/1.42 inference(quant_inst,[status(thm)],[])).
% 1.78/1.42 tff(291,plain,
% 1.78/1.42 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(not1(h1(f)), abnormal) | mode(not1(h1(f)), ok) | (~type(not1(h1(f)), not))),
% 1.78/1.42 inference(modus_ponens,[status(thm)],[290, 289])).
% 1.78/1.42 tff(292,plain,
% 1.78/1.42 (mode(not1(h1(f)), ok)),
% 1.78/1.42 inference(unit_resolution,[status(thm)],[291, 140, 288, 285])).
% 1.78/1.42 tff(293,plain,
% 1.78/1.42 (^[K: $i] : refl(((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not))) <=> ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not))))),
% 1.78/1.42 inference(bind,[status(th)],[])).
% 1.78/1.42 tff(294,plain,
% 1.78/1.42 (![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not))) <=> ![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not)))),
% 1.78/1.42 inference(quant_intro,[status(thm)],[293])).
% 1.78/1.42 tff(295,plain,
% 1.78/1.42 (![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not))) <=> ![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not)))),
% 1.78/1.42 inference(rewrite,[status(thm)],[])).
% 1.78/1.42 tff(296,plain,
% 1.78/1.42 (^[K: $i] : trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, not))) | (~value(in(n1, K), n0))) <=> ((~mode(K, ok)) | (~value(in(n1, K), n0)) | (~type(K, not)))), (((((~mode(K, ok)) | (~type(K, not))) | (~value(in(n1, K), n0))) | value(out(n1, K), n1)) <=> (((~mode(K, ok)) | (~value(in(n1, K), n0)) | (~type(K, not))) | value(out(n1, K), n1)))), rewrite((((~mode(K, ok)) | (~value(in(n1, K), n0)) | (~type(K, not))) | value(out(n1, K), n1)) <=> ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not)))), (((((~mode(K, ok)) | (~type(K, not))) | (~value(in(n1, K), n0))) | value(out(n1, K), n1)) <=> ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not)))))),
% 1.78/1.42 inference(bind,[status(th)],[])).
% 1.78/1.42 tff(297,plain,
% 1.78/1.42 (![K: $i] : ((((~mode(K, ok)) | (~type(K, not))) | (~value(in(n1, K), n0))) | value(out(n1, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not)))),
% 1.78/1.43 inference(quant_intro,[status(thm)],[296])).
% 1.78/1.43 tff(298,axiom,(![K: $i] : ((((~mode(K, ok)) | (~type(K, not))) | (~value(in(n1, K), n0))) | value(out(n1, K), n1))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','not_0_1_fw')).
% 1.78/1.43 tff(299,plain,
% 1.78/1.43 (![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not)))),
% 1.78/1.43 inference(modus_ponens,[status(thm)],[298, 297])).
% 1.78/1.43 tff(300,plain,
% 1.78/1.43 (![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not)))),
% 1.78/1.43 inference(modus_ponens,[status(thm)],[299, 295])).
% 1.78/1.43 tff(301,plain,(
% 1.78/1.43 ![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not)))),
% 1.78/1.43 inference(skolemize,[status(sab)],[300])).
% 1.78/1.43 tff(302,plain,
% 1.78/1.43 (![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not)))),
% 1.78/1.43 inference(modus_ponens,[status(thm)],[301, 294])).
% 1.78/1.43 tff(303,plain,
% 1.78/1.43 (((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not)))) | ((~mode(not1(h1(f)), ok)) | value(out(n1, not1(h1(f))), n1) | (~type(not1(h1(f)), not)) | (~value(in(n1, not1(h1(f))), n0)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not)))) | (~mode(not1(h1(f)), ok)) | value(out(n1, not1(h1(f))), n1) | (~type(not1(h1(f)), not)) | (~value(in(n1, not1(h1(f))), n0)))),
% 1.78/1.43 inference(rewrite,[status(thm)],[])).
% 1.78/1.43 tff(304,plain,
% 1.78/1.43 (((~mode(not1(h1(f)), ok)) | value(out(n1, not1(h1(f))), n1) | (~value(in(n1, not1(h1(f))), n0)) | (~type(not1(h1(f)), not))) <=> ((~mode(not1(h1(f)), ok)) | value(out(n1, not1(h1(f))), n1) | (~type(not1(h1(f)), not)) | (~value(in(n1, not1(h1(f))), n0)))),
% 1.78/1.43 inference(rewrite,[status(thm)],[])).
% 1.78/1.43 tff(305,plain,
% 1.78/1.43 (((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not)))) | ((~mode(not1(h1(f)), ok)) | value(out(n1, not1(h1(f))), n1) | (~value(in(n1, not1(h1(f))), n0)) | (~type(not1(h1(f)), not)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not)))) | ((~mode(not1(h1(f)), ok)) | value(out(n1, not1(h1(f))), n1) | (~type(not1(h1(f)), not)) | (~value(in(n1, not1(h1(f))), n0))))),
% 1.78/1.43 inference(monotonicity,[status(thm)],[304])).
% 1.78/1.43 tff(306,plain,
% 1.78/1.43 (((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not)))) | ((~mode(not1(h1(f)), ok)) | value(out(n1, not1(h1(f))), n1) | (~value(in(n1, not1(h1(f))), n0)) | (~type(not1(h1(f)), not)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not)))) | (~mode(not1(h1(f)), ok)) | value(out(n1, not1(h1(f))), n1) | (~type(not1(h1(f)), not)) | (~value(in(n1, not1(h1(f))), n0)))),
% 1.78/1.43 inference(transitivity,[status(thm)],[305, 303])).
% 1.78/1.43 tff(307,plain,
% 1.78/1.43 ((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not)))) | ((~mode(not1(h1(f)), ok)) | value(out(n1, not1(h1(f))), n1) | (~value(in(n1, not1(h1(f))), n0)) | (~type(not1(h1(f)), not)))),
% 1.78/1.43 inference(quant_inst,[status(thm)],[])).
% 1.78/1.43 tff(308,plain,
% 1.78/1.43 ((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n1) | (~value(in(n1, K), n0)) | (~type(K, not)))) | (~mode(not1(h1(f)), ok)) | value(out(n1, not1(h1(f))), n1) | (~type(not1(h1(f)), not)) | (~value(in(n1, not1(h1(f))), n0))),
% 1.78/1.43 inference(modus_ponens,[status(thm)],[307, 306])).
% 1.78/1.43 tff(309,plain,
% 1.78/1.43 ((~mode(not1(h1(f)), ok)) | value(out(n1, not1(h1(f))), n1) | (~value(in(n1, not1(h1(f))), n0))),
% 1.78/1.43 inference(unit_resolution,[status(thm)],[308, 302, 285])).
% 1.78/1.43 tff(310,plain,
% 1.78/1.43 (value(out(n1, not1(h1(f))), n1) | (~value(in(n1, not1(h1(f))), n0))),
% 1.78/1.43 inference(unit_resolution,[status(thm)],[309, 292])).
% 1.78/1.43 tff(311,plain,
% 1.78/1.43 (value(out(n1, not1(h1(f))), n1)),
% 1.78/1.43 inference(unit_resolution,[status(thm)],[310, 274])).
% 1.78/1.43 tff(312,plain,
% 1.78/1.43 (^[X: $i] : refl(((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X)))) <=> ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X)))))),
% 1.78/1.43 inference(bind,[status(th)],[])).
% 1.78/1.43 tff(313,plain,
% 1.78/1.43 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))),
% 1.78/1.43 inference(quant_intro,[status(thm)],[312])).
% 1.78/1.43 tff(314,plain,
% 1.78/1.43 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))),
% 1.78/1.43 inference(rewrite,[status(thm)],[])).
% 1.78/1.43 tff(315,axiom,(![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_connection_out1not1_in2and1')).
% 1.78/1.43 tff(316,plain,
% 1.78/1.43 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))),
% 1.78/1.43 inference(modus_ponens,[status(thm)],[315, 314])).
% 1.78/1.43 tff(317,plain,(
% 1.78/1.43 ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))),
% 1.78/1.43 inference(skolemize,[status(sab)],[316])).
% 1.78/1.43 tff(318,plain,
% 1.78/1.43 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))),
% 1.78/1.43 inference(modus_ponens,[status(thm)],[317, 313])).
% 1.78/1.43 tff(319,plain,
% 1.78/1.43 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))) | ((~type(h1(f), halfadder)) | connection(out(n1, not1(h1(f))), in(n2, and1(h1(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))) | (~type(h1(f), halfadder)) | connection(out(n1, not1(h1(f))), in(n2, and1(h1(f)))))),
% 1.78/1.43 inference(rewrite,[status(thm)],[])).
% 1.78/1.43 tff(320,plain,
% 1.78/1.43 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))) | ((~type(h1(f), halfadder)) | connection(out(n1, not1(h1(f))), in(n2, and1(h1(f)))))),
% 1.78/1.43 inference(quant_inst,[status(thm)],[])).
% 1.78/1.43 tff(321,plain,
% 1.78/1.43 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))) | (~type(h1(f), halfadder)) | connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))),
% 1.78/1.43 inference(modus_ponens,[status(thm)],[320, 319])).
% 1.78/1.43 tff(322,plain,
% 1.78/1.43 (connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))),
% 1.78/1.43 inference(unit_resolution,[status(thm)],[321, 318, 100])).
% 1.78/1.43 tff(323,plain,
% 1.78/1.43 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(out(n1, not1(h1(f))), n1)) | value(in(n2, and1(h1(f))), n1) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(n1, not1(h1(f))), n1)) | value(in(n2, and1(h1(f))), n1) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))))),
% 1.78/1.43 inference(rewrite,[status(thm)],[])).
% 1.78/1.43 tff(324,plain,
% 1.78/1.43 ((value(in(n2, and1(h1(f))), n1) | (~value(out(n1, not1(h1(f))), n1)) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f)))))) <=> ((~value(out(n1, not1(h1(f))), n1)) | value(in(n2, and1(h1(f))), n1) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))))),
% 1.78/1.43 inference(rewrite,[status(thm)],[])).
% 1.78/1.43 tff(325,plain,
% 1.78/1.43 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, and1(h1(f))), n1) | (~value(out(n1, not1(h1(f))), n1)) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(out(n1, not1(h1(f))), n1)) | value(in(n2, and1(h1(f))), n1) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f)))))))),
% 1.78/1.43 inference(monotonicity,[status(thm)],[324])).
% 1.78/1.43 tff(326,plain,
% 1.78/1.43 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, and1(h1(f))), n1) | (~value(out(n1, not1(h1(f))), n1)) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(n1, not1(h1(f))), n1)) | value(in(n2, and1(h1(f))), n1) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))))),
% 1.78/1.43 inference(transitivity,[status(thm)],[325, 323])).
% 1.78/1.43 tff(327,plain,
% 1.78/1.43 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, and1(h1(f))), n1) | (~value(out(n1, not1(h1(f))), n1)) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))))),
% 1.78/1.43 inference(quant_inst,[status(thm)],[])).
% 1.78/1.43 tff(328,plain,
% 1.78/1.43 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(n1, not1(h1(f))), n1)) | value(in(n2, and1(h1(f))), n1) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f)))))),
% 1.78/1.43 inference(modus_ponens,[status(thm)],[327, 326])).
% 1.78/1.43 tff(329,plain,
% 1.78/1.43 ($false),
% 1.78/1.43 inference(unit_resolution,[status(thm)],[328, 27, 322, 311, 183])).
% 1.78/1.43 tff(330,plain,(value(in(n2, and1(h1(f))), n1)), inference(lemma,lemma(discharge,[]))).
% 1.78/1.43 tff(331,plain,
% 1.78/1.43 (^[X: $i] : refl(((~type(X, halfadder)) | type(and1(X), and)) <=> ((~type(X, halfadder)) | type(and1(X), and)))),
% 1.78/1.43 inference(bind,[status(th)],[])).
% 1.78/1.43 tff(332,plain,
% 1.78/1.43 (![X: $i] : ((~type(X, halfadder)) | type(and1(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))),
% 1.78/1.43 inference(quant_intro,[status(thm)],[331])).
% 1.78/1.43 tff(333,plain,
% 1.78/1.43 (![X: $i] : ((~type(X, halfadder)) | type(and1(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))),
% 1.78/1.43 inference(rewrite,[status(thm)],[])).
% 1.78/1.43 tff(334,axiom,(![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_and1')).
% 1.78/1.43 tff(335,plain,
% 1.78/1.43 (![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))),
% 1.78/1.43 inference(modus_ponens,[status(thm)],[334, 333])).
% 1.78/1.43 tff(336,plain,(
% 1.78/1.43 ![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))),
% 1.78/1.43 inference(skolemize,[status(sab)],[335])).
% 1.78/1.43 tff(337,plain,
% 1.78/1.43 (![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))),
% 1.78/1.43 inference(modus_ponens,[status(thm)],[336, 332])).
% 1.78/1.43 tff(338,plain,
% 1.78/1.43 (((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | ((~type(h1(f), halfadder)) | type(and1(h1(f)), and))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | (~type(h1(f), halfadder)) | type(and1(h1(f)), and))),
% 1.78/1.43 inference(rewrite,[status(thm)],[])).
% 1.78/1.43 tff(339,plain,
% 1.78/1.43 ((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | ((~type(h1(f), halfadder)) | type(and1(h1(f)), and))),
% 1.78/1.43 inference(quant_inst,[status(thm)],[])).
% 1.78/1.43 tff(340,plain,
% 1.78/1.43 ((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | (~type(h1(f), halfadder)) | type(and1(h1(f)), and)),
% 1.78/1.43 inference(modus_ponens,[status(thm)],[339, 338])).
% 1.78/1.43 tff(341,plain,
% 1.78/1.43 (type(and1(h1(f)), and)),
% 1.78/1.43 inference(unit_resolution,[status(thm)],[340, 337, 100])).
% 1.78/1.43 tff(342,plain,
% 1.78/1.43 ((~mode(and1(h1(f)), abnormal)) <=> (~mode(and1(h1(f)), abnormal))),
% 1.78/1.43 inference(rewrite,[status(thm)],[])).
% 1.78/1.43 tff(343,axiom,(~mode(and1(h1(f)), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_and1h1')).
% 1.78/1.43 tff(344,plain,
% 1.78/1.43 (~mode(and1(h1(f)), abnormal)),
% 1.78/1.43 inference(modus_ponens,[status(thm)],[343, 342])).
% 1.78/1.43 tff(345,plain,
% 1.78/1.43 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and1(h1(f)), abnormal) | mode(and1(h1(f)), ok) | (~type(and1(h1(f)), and)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and1(h1(f)), abnormal) | mode(and1(h1(f)), ok) | (~type(and1(h1(f)), and)))),
% 1.78/1.43 inference(rewrite,[status(thm)],[])).
% 1.78/1.43 tff(346,plain,
% 1.78/1.43 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and1(h1(f)), abnormal) | mode(and1(h1(f)), ok) | (~type(and1(h1(f)), and)))),
% 1.78/1.43 inference(quant_inst,[status(thm)],[])).
% 1.78/1.43 tff(347,plain,
% 1.78/1.43 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and1(h1(f)), abnormal) | mode(and1(h1(f)), ok) | (~type(and1(h1(f)), and))),
% 1.78/1.43 inference(modus_ponens,[status(thm)],[346, 345])).
% 1.78/1.43 tff(348,plain,
% 1.78/1.43 (mode(and1(h1(f)), ok)),
% 1.78/1.43 inference(unit_resolution,[status(thm)],[347, 140, 344, 341])).
% 1.78/1.43 tff(349,plain,
% 1.78/1.43 (^[K: $i] : refl(((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1))) <=> ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1))))),
% 1.78/1.43 inference(bind,[status(th)],[])).
% 1.78/1.43 tff(350,plain,
% 1.78/1.43 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1))) <=> ![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))),
% 1.78/1.43 inference(quant_intro,[status(thm)],[349])).
% 1.78/1.43 tff(351,plain,
% 1.78/1.43 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1))) <=> ![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))),
% 1.78/1.43 inference(rewrite,[status(thm)],[])).
% 1.78/1.43 tff(352,plain,
% 1.78/1.43 (^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, and))) | (~value(in(n1, K), n1))) <=> ((~mode(K, ok)) | (~type(K, and)) | (~value(in(n1, K), n1)))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(in(n1, K), n1))) | (~value(in(n2, K), n1))) <=> (((~mode(K, ok)) | (~type(K, and)) | (~value(in(n1, K), n1))) | (~value(in(n2, K), n1))))), rewrite((((~mode(K, ok)) | (~type(K, and)) | (~value(in(n1, K), n1))) | (~value(in(n2, K), n1))) <=> ((~mode(K, ok)) | (~type(K, and)) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(in(n1, K), n1))) | (~value(in(n2, K), n1))) <=> ((~mode(K, ok)) | (~type(K, and)) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1))))), ((((((~mode(K, ok)) | (~type(K, and))) | (~value(in(n1, K), n1))) | (~value(in(n2, K), n1))) | value(out(n1, K), n1)) <=> (((~mode(K, ok)) | (~type(K, and)) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1))) | value(out(n1, K), n1)))), rewrite((((~mode(K, ok)) | (~type(K, and)) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1))) | value(out(n1, K), n1)) <=> ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))), ((((((~mode(K, ok)) | (~type(K, and))) | (~value(in(n1, K), n1))) | (~value(in(n2, K), n1))) | value(out(n1, K), n1)) <=> ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))))),
% 1.78/1.43 inference(bind,[status(th)],[])).
% 1.78/1.43 tff(353,plain,
% 1.78/1.43 (![K: $i] : (((((~mode(K, ok)) | (~type(K, and))) | (~value(in(n1, K), n1))) | (~value(in(n2, K), n1))) | value(out(n1, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))),
% 1.78/1.43 inference(quant_intro,[status(thm)],[352])).
% 1.78/1.43 tff(354,axiom,(![K: $i] : (((((~mode(K, ok)) | (~type(K, and))) | (~value(in(n1, K), n1))) | (~value(in(n2, K), n1))) | value(out(n1, K), n1))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','and_11_1')).
% 1.78/1.43 tff(355,plain,
% 1.78/1.43 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))),
% 1.78/1.43 inference(modus_ponens,[status(thm)],[354, 353])).
% 1.78/1.43 tff(356,plain,
% 1.78/1.43 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))),
% 1.78/1.43 inference(modus_ponens,[status(thm)],[355, 351])).
% 1.78/1.43 tff(357,plain,(
% 1.78/1.43 ![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))),
% 1.78/1.43 inference(skolemize,[status(sab)],[356])).
% 1.78/1.43 tff(358,plain,
% 1.78/1.43 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))),
% 1.78/1.43 inference(modus_ponens,[status(thm)],[357, 350])).
% 1.78/1.43 tff(359,plain,
% 1.78/1.43 (((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))) | ((~mode(and1(h1(f)), ok)) | value(out(n1, and1(h1(f))), n1) | (~value(in(n1, and1(h1(f))), n1)) | (~type(and1(h1(f)), and)) | (~value(in(n2, and1(h1(f))), n1)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))) | (~mode(and1(h1(f)), ok)) | value(out(n1, and1(h1(f))), n1) | (~value(in(n1, and1(h1(f))), n1)) | (~type(and1(h1(f)), and)) | (~value(in(n2, and1(h1(f))), n1)))),
% 1.78/1.44 inference(rewrite,[status(thm)],[])).
% 1.78/1.44 tff(360,plain,
% 1.78/1.44 (((~mode(and1(h1(f)), ok)) | (~type(and1(h1(f)), and)) | value(out(n1, and1(h1(f))), n1) | (~value(in(n2, and1(h1(f))), n1)) | (~value(in(n1, and1(h1(f))), n1))) <=> ((~mode(and1(h1(f)), ok)) | value(out(n1, and1(h1(f))), n1) | (~value(in(n1, and1(h1(f))), n1)) | (~type(and1(h1(f)), and)) | (~value(in(n2, and1(h1(f))), n1)))),
% 1.78/1.44 inference(rewrite,[status(thm)],[])).
% 1.78/1.44 tff(361,plain,
% 1.78/1.44 (((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))) | ((~mode(and1(h1(f)), ok)) | (~type(and1(h1(f)), and)) | value(out(n1, and1(h1(f))), n1) | (~value(in(n2, and1(h1(f))), n1)) | (~value(in(n1, and1(h1(f))), n1)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))) | ((~mode(and1(h1(f)), ok)) | value(out(n1, and1(h1(f))), n1) | (~value(in(n1, and1(h1(f))), n1)) | (~type(and1(h1(f)), and)) | (~value(in(n2, and1(h1(f))), n1))))),
% 1.78/1.44 inference(monotonicity,[status(thm)],[360])).
% 1.78/1.44 tff(362,plain,
% 1.78/1.44 (((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))) | ((~mode(and1(h1(f)), ok)) | (~type(and1(h1(f)), and)) | value(out(n1, and1(h1(f))), n1) | (~value(in(n2, and1(h1(f))), n1)) | (~value(in(n1, and1(h1(f))), n1)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))) | (~mode(and1(h1(f)), ok)) | value(out(n1, and1(h1(f))), n1) | (~value(in(n1, and1(h1(f))), n1)) | (~type(and1(h1(f)), and)) | (~value(in(n2, and1(h1(f))), n1)))),
% 1.78/1.44 inference(transitivity,[status(thm)],[361, 359])).
% 1.78/1.44 tff(363,plain,
% 1.78/1.44 ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))) | ((~mode(and1(h1(f)), ok)) | (~type(and1(h1(f)), and)) | value(out(n1, and1(h1(f))), n1) | (~value(in(n2, and1(h1(f))), n1)) | (~value(in(n1, and1(h1(f))), n1)))),
% 1.78/1.44 inference(quant_inst,[status(thm)],[])).
% 1.78/1.44 tff(364,plain,
% 1.78/1.44 ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))) | (~mode(and1(h1(f)), ok)) | value(out(n1, and1(h1(f))), n1) | (~value(in(n1, and1(h1(f))), n1)) | (~type(and1(h1(f)), and)) | (~value(in(n2, and1(h1(f))), n1))),
% 1.78/1.44 inference(modus_ponens,[status(thm)],[363, 362])).
% 1.78/1.44 tff(365,plain,
% 1.78/1.44 ((~mode(and1(h1(f)), ok)) | value(out(n1, and1(h1(f))), n1) | (~value(in(n1, and1(h1(f))), n1)) | (~value(in(n2, and1(h1(f))), n1))),
% 1.78/1.44 inference(unit_resolution,[status(thm)],[364, 358, 341])).
% 1.78/1.44 tff(366,plain,
% 1.78/1.44 (value(out(n1, and1(h1(f))), n1) | (~value(in(n1, and1(h1(f))), n1)) | (~value(in(n2, and1(h1(f))), n1))),
% 1.78/1.44 inference(unit_resolution,[status(thm)],[365, 348])).
% 1.78/1.44 tff(367,plain,
% 1.78/1.44 (value(out(n1, and1(h1(f))), n1) | (~value(in(n1, and1(h1(f))), n1))),
% 1.78/1.44 inference(unit_resolution,[status(thm)],[366, 330])).
% 1.78/1.44 tff(368,plain,
% 1.78/1.44 (value(out(n1, and1(h1(f))), n1)),
% 1.78/1.44 inference(unit_resolution,[status(thm)],[367, 182])).
% 1.78/1.44 tff(369,plain,
% 1.78/1.44 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))) | ((~type(h1(f), halfadder)) | connection(out(s, h1(f)), out(n1, and1(h1(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))) | (~type(h1(f), halfadder)) | connection(out(s, h1(f)), out(n1, and1(h1(f)))))),
% 1.78/1.44 inference(rewrite,[status(thm)],[])).
% 1.78/1.44 tff(370,plain,
% 1.78/1.44 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))) | ((~type(h1(f), halfadder)) | connection(out(s, h1(f)), out(n1, and1(h1(f)))))),
% 1.78/1.44 inference(quant_inst,[status(thm)],[])).
% 1.78/1.44 tff(371,plain,
% 1.78/1.44 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))) | (~type(h1(f), halfadder)) | connection(out(s, h1(f)), out(n1, and1(h1(f))))),
% 1.78/1.44 inference(modus_ponens,[status(thm)],[370, 369])).
% 1.78/1.44 tff(372,plain,
% 1.78/1.44 (connection(out(s, h1(f)), out(n1, and1(h1(f))))),
% 1.78/1.44 inference(unit_resolution,[status(thm)],[371, 53, 100])).
% 1.78/1.44 tff(373,plain,
% 1.78/1.44 (^[V: $i, P2: $i, P1: $i] : refl((value(P1, V) | (~connection(P1, P2)) | (~value(P2, V))) <=> (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V))))),
% 1.78/1.44 inference(bind,[status(th)],[])).
% 1.78/1.44 tff(374,plain,
% 1.78/1.44 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V))) <=> ![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 1.78/1.44 inference(quant_intro,[status(thm)],[373])).
% 1.78/1.44 tff(375,plain,
% 1.78/1.44 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V))) <=> ![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 1.78/1.44 inference(rewrite,[status(thm)],[])).
% 1.78/1.44 tff(376,plain,
% 1.78/1.44 (^[V: $i, P2: $i, P1: $i] : rewrite((((~connection(P1, P2)) | (~value(P2, V))) | value(P1, V)) <=> (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V))))),
% 1.78/1.44 inference(bind,[status(th)],[])).
% 1.78/1.44 tff(377,plain,
% 1.78/1.44 (![V: $i, P2: $i, P1: $i] : (((~connection(P1, P2)) | (~value(P2, V))) | value(P1, V)) <=> ![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 1.78/1.44 inference(quant_intro,[status(thm)],[376])).
% 1.78/1.44 tff(378,axiom,(![V: $i, P2: $i, P1: $i] : (((~connection(P1, P2)) | (~value(P2, V))) | value(P1, V))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','value_propagation2')).
% 1.78/1.44 tff(379,plain,
% 1.78/1.44 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 1.78/1.44 inference(modus_ponens,[status(thm)],[378, 377])).
% 1.78/1.44 tff(380,plain,
% 1.78/1.44 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 1.78/1.44 inference(modus_ponens,[status(thm)],[379, 375])).
% 1.78/1.44 tff(381,plain,(
% 1.78/1.44 ![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 1.78/1.44 inference(skolemize,[status(sab)],[380])).
% 1.78/1.44 tff(382,plain,
% 1.78/1.44 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 1.78/1.44 inference(modus_ponens,[status(thm)],[381, 374])).
% 1.78/1.44 tff(383,plain,
% 1.78/1.44 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(out(n1, and1(h1(f))), n1)) | value(out(s, h1(f)), n1) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and1(h1(f))), n1)) | value(out(s, h1(f)), n1) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))))),
% 1.78/1.44 inference(rewrite,[status(thm)],[])).
% 1.78/1.44 tff(384,plain,
% 1.78/1.44 ((value(out(s, h1(f)), n1) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))) | (~value(out(n1, and1(h1(f))), n1))) <=> ((~value(out(n1, and1(h1(f))), n1)) | value(out(s, h1(f)), n1) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))))),
% 1.78/1.44 inference(rewrite,[status(thm)],[])).
% 1.78/1.44 tff(385,plain,
% 1.78/1.44 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(s, h1(f)), n1) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))) | (~value(out(n1, and1(h1(f))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(out(n1, and1(h1(f))), n1)) | value(out(s, h1(f)), n1) | (~connection(out(s, h1(f)), out(n1, and1(h1(f)))))))),
% 1.78/1.44 inference(monotonicity,[status(thm)],[384])).
% 1.78/1.44 tff(386,plain,
% 1.78/1.44 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(s, h1(f)), n1) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))) | (~value(out(n1, and1(h1(f))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and1(h1(f))), n1)) | value(out(s, h1(f)), n1) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))))),
% 1.78/1.44 inference(transitivity,[status(thm)],[385, 383])).
% 1.78/1.44 tff(387,plain,
% 1.78/1.44 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(s, h1(f)), n1) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))) | (~value(out(n1, and1(h1(f))), n1)))),
% 1.88/1.44 inference(quant_inst,[status(thm)],[])).
% 1.88/1.44 tff(388,plain,
% 1.88/1.44 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and1(h1(f))), n1)) | value(out(s, h1(f)), n1) | (~connection(out(s, h1(f)), out(n1, and1(h1(f)))))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[387, 386])).
% 1.88/1.44 tff(389,plain,
% 1.88/1.44 (value(out(s, h1(f)), n1)),
% 1.88/1.44 inference(unit_resolution,[status(thm)],[388, 382, 372, 368])).
% 1.88/1.44 tff(390,plain,
% 1.88/1.44 ((~equal_value(n0, n1)) <=> (~equal_value(n0, n1))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(391,axiom,(~equal_value(n0, n1)), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','equal_value1')).
% 1.88/1.44 tff(392,plain,
% 1.88/1.44 (~equal_value(n0, n1)),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[391, 390])).
% 1.88/1.44 tff(393,plain,
% 1.88/1.44 (^[P: $i, V1: $i, V2: $i] : refl((equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1))) <=> (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1))))),
% 1.88/1.44 inference(bind,[status(th)],[])).
% 1.88/1.44 tff(394,plain,
% 1.88/1.44 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1))) <=> ![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 1.88/1.44 inference(quant_intro,[status(thm)],[393])).
% 1.88/1.44 tff(395,plain,
% 1.88/1.44 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1))) <=> ![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(396,plain,
% 1.88/1.44 (^[P: $i, V1: $i, V2: $i] : trans(monotonicity(rewrite(((~value(P, V1)) | (~value(P, V2))) <=> ((~value(P, V2)) | (~value(P, V1)))), ((((~value(P, V1)) | (~value(P, V2))) | equal_value(V1, V2)) <=> (((~value(P, V2)) | (~value(P, V1))) | equal_value(V1, V2)))), rewrite((((~value(P, V2)) | (~value(P, V1))) | equal_value(V1, V2)) <=> (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))), ((((~value(P, V1)) | (~value(P, V2))) | equal_value(V1, V2)) <=> (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))))),
% 1.88/1.44 inference(bind,[status(th)],[])).
% 1.88/1.44 tff(397,plain,
% 1.88/1.44 (![P: $i, V1: $i, V2: $i] : (((~value(P, V1)) | (~value(P, V2))) | equal_value(V1, V2)) <=> ![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 1.88/1.44 inference(quant_intro,[status(thm)],[396])).
% 1.88/1.44 tff(398,axiom,(![P: $i, V1: $i, V2: $i] : (((~value(P, V1)) | (~value(P, V2))) | equal_value(V1, V2))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','unique_value')).
% 1.88/1.44 tff(399,plain,
% 1.88/1.44 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[398, 397])).
% 1.88/1.44 tff(400,plain,
% 1.88/1.44 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[399, 395])).
% 1.88/1.44 tff(401,plain,(
% 1.88/1.44 ![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 1.88/1.44 inference(skolemize,[status(sab)],[400])).
% 1.88/1.44 tff(402,plain,
% 1.88/1.44 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[401, 394])).
% 1.88/1.44 tff(403,plain,
% 1.88/1.44 (((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(out(s, h1(f)), n1)) | (~value(out(s, h1(f)), n0)))) <=> ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n0, n1) | (~value(out(s, h1(f)), n1)) | (~value(out(s, h1(f)), n0)))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(404,plain,
% 1.88/1.44 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(out(s, h1(f)), n1)) | (~value(out(s, h1(f)), n0)))),
% 1.88/1.44 inference(quant_inst,[status(thm)],[])).
% 1.88/1.44 tff(405,plain,
% 1.88/1.44 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n0, n1) | (~value(out(s, h1(f)), n1)) | (~value(out(s, h1(f)), n0))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[404, 403])).
% 1.88/1.44 tff(406,plain,
% 1.88/1.44 (~value(out(s, h1(f)), n0)),
% 1.88/1.44 inference(unit_resolution,[status(thm)],[405, 402, 392, 389])).
% 1.88/1.44 tff(407,plain,
% 1.88/1.44 (^[X: $i] : refl(((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X)))) <=> ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X)))))),
% 1.88/1.44 inference(bind,[status(th)],[])).
% 1.88/1.44 tff(408,plain,
% 1.88/1.44 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))),
% 1.88/1.44 inference(quant_intro,[status(thm)],[407])).
% 1.88/1.44 tff(409,plain,
% 1.88/1.44 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(410,axiom,(![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_connection_outsh1_in2h2')).
% 1.88/1.44 tff(411,plain,
% 1.88/1.44 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[410, 409])).
% 1.88/1.44 tff(412,plain,(
% 1.88/1.44 ![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))),
% 1.88/1.44 inference(skolemize,[status(sab)],[411])).
% 1.88/1.44 tff(413,plain,
% 1.88/1.44 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[412, 408])).
% 1.88/1.44 tff(414,plain,
% 1.88/1.44 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))) | ((~type(f, fulladder)) | connection(out(s, h1(f)), in(n2, h2(f))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))) | (~type(f, fulladder)) | connection(out(s, h1(f)), in(n2, h2(f))))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(415,plain,
% 1.88/1.44 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))) | ((~type(f, fulladder)) | connection(out(s, h1(f)), in(n2, h2(f))))),
% 1.88/1.44 inference(quant_inst,[status(thm)],[])).
% 1.88/1.44 tff(416,plain,
% 1.88/1.44 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))) | (~type(f, fulladder)) | connection(out(s, h1(f)), in(n2, h2(f)))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[415, 414])).
% 1.88/1.44 tff(417,plain,
% 1.88/1.44 (connection(out(s, h1(f)), in(n2, h2(f)))),
% 1.88/1.44 inference(unit_resolution,[status(thm)],[416, 413, 3])).
% 1.88/1.44 tff(418,plain,
% 1.88/1.44 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n2, h2(f)), n0)) | value(out(s, h1(f)), n0) | (~connection(out(s, h1(f)), in(n2, h2(f)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, h2(f)), n0)) | value(out(s, h1(f)), n0) | (~connection(out(s, h1(f)), in(n2, h2(f)))))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(419,plain,
% 1.88/1.44 ((value(out(s, h1(f)), n0) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | (~value(in(n2, h2(f)), n0))) <=> ((~value(in(n2, h2(f)), n0)) | value(out(s, h1(f)), n0) | (~connection(out(s, h1(f)), in(n2, h2(f)))))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(420,plain,
% 1.88/1.44 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(s, h1(f)), n0) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | (~value(in(n2, h2(f)), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n2, h2(f)), n0)) | value(out(s, h1(f)), n0) | (~connection(out(s, h1(f)), in(n2, h2(f))))))),
% 1.88/1.44 inference(monotonicity,[status(thm)],[419])).
% 1.88/1.44 tff(421,plain,
% 1.88/1.44 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(s, h1(f)), n0) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | (~value(in(n2, h2(f)), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, h2(f)), n0)) | value(out(s, h1(f)), n0) | (~connection(out(s, h1(f)), in(n2, h2(f)))))),
% 1.88/1.44 inference(transitivity,[status(thm)],[420, 418])).
% 1.88/1.44 tff(422,plain,
% 1.88/1.44 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(s, h1(f)), n0) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | (~value(in(n2, h2(f)), n0)))),
% 1.88/1.44 inference(quant_inst,[status(thm)],[])).
% 1.88/1.44 tff(423,plain,
% 1.88/1.44 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, h2(f)), n0)) | value(out(s, h1(f)), n0) | (~connection(out(s, h1(f)), in(n2, h2(f))))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[422, 421])).
% 1.88/1.44 tff(424,plain,
% 1.88/1.44 (~value(in(n2, h2(f)), n0)),
% 1.88/1.44 inference(unit_resolution,[status(thm)],[423, 382, 417, 406])).
% 1.88/1.44 tff(425,plain,
% 1.88/1.44 (^[X: $i] : refl(((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X)))) <=> ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X)))))),
% 1.88/1.44 inference(bind,[status(th)],[])).
% 1.88/1.44 tff(426,plain,
% 1.88/1.44 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 1.88/1.44 inference(quant_intro,[status(thm)],[425])).
% 1.88/1.44 tff(427,plain,
% 1.88/1.44 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(428,axiom,(![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_connection_in2_in2and2')).
% 1.88/1.44 tff(429,plain,
% 1.88/1.44 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[428, 427])).
% 1.88/1.44 tff(430,plain,(
% 1.88/1.44 ![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 1.88/1.44 inference(skolemize,[status(sab)],[429])).
% 1.88/1.44 tff(431,plain,
% 1.88/1.44 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[430, 426])).
% 1.88/1.44 tff(432,plain,
% 1.88/1.44 (((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))) | ((~type(h2(f), halfadder)) | connection(in(n2, h2(f)), in(n2, and2(h2(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))) | (~type(h2(f), halfadder)) | connection(in(n2, h2(f)), in(n2, and2(h2(f)))))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(433,plain,
% 1.88/1.44 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))) | ((~type(h2(f), halfadder)) | connection(in(n2, h2(f)), in(n2, and2(h2(f)))))),
% 1.88/1.44 inference(quant_inst,[status(thm)],[])).
% 1.88/1.44 tff(434,plain,
% 1.88/1.44 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))) | (~type(h2(f), halfadder)) | connection(in(n2, h2(f)), in(n2, and2(h2(f))))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[433, 432])).
% 1.88/1.44 tff(435,plain,
% 1.88/1.44 (connection(in(n2, h2(f)), in(n2, and2(h2(f))))),
% 1.88/1.44 inference(unit_resolution,[status(thm)],[434, 431, 46])).
% 1.88/1.44 tff(436,plain,
% 1.88/1.44 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n2, and2(h2(f))), n0)) | value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, and2(h2(f))), n0)) | value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f))))))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(437,plain,
% 1.88/1.44 ((value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f))))) | (~value(in(n2, and2(h2(f))), n0))) <=> ((~value(in(n2, and2(h2(f))), n0)) | value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f))))))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(438,plain,
% 1.88/1.44 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f))))) | (~value(in(n2, and2(h2(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n2, and2(h2(f))), n0)) | value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f)))))))),
% 1.88/1.44 inference(monotonicity,[status(thm)],[437])).
% 1.88/1.44 tff(439,plain,
% 1.88/1.44 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f))))) | (~value(in(n2, and2(h2(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, and2(h2(f))), n0)) | value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f))))))),
% 1.88/1.44 inference(transitivity,[status(thm)],[438, 436])).
% 1.88/1.44 tff(440,plain,
% 1.88/1.44 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f))))) | (~value(in(n2, and2(h2(f))), n0)))),
% 1.88/1.44 inference(quant_inst,[status(thm)],[])).
% 1.88/1.44 tff(441,plain,
% 1.88/1.44 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, and2(h2(f))), n0)) | value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f)))))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[440, 439])).
% 1.88/1.44 tff(442,plain,
% 1.88/1.44 (~value(in(n2, and2(h2(f))), n0)),
% 1.88/1.44 inference(unit_resolution,[status(thm)],[441, 382, 435, 424])).
% 1.88/1.44 tff(443,plain,
% 1.88/1.44 (^[X: $i] : refl(((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X)))) <=> ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X)))))),
% 1.88/1.44 inference(bind,[status(th)],[])).
% 1.88/1.44 tff(444,plain,
% 1.88/1.44 (![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 1.88/1.44 inference(quant_intro,[status(thm)],[443])).
% 1.88/1.44 tff(445,plain,
% 1.88/1.44 (![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(446,axiom,(![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_connection_in1_in1h2')).
% 1.88/1.44 tff(447,plain,
% 1.88/1.44 (![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[446, 445])).
% 1.88/1.44 tff(448,plain,(
% 1.88/1.44 ![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 1.88/1.44 inference(skolemize,[status(sab)],[447])).
% 1.88/1.44 tff(449,plain,
% 1.88/1.44 (![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[448, 444])).
% 1.88/1.44 tff(450,plain,
% 1.88/1.44 (((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | ((~type(f, fulladder)) | connection(in(n1, f), in(n1, h2(f))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | (~type(f, fulladder)) | connection(in(n1, f), in(n1, h2(f))))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(451,plain,
% 1.88/1.44 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | ((~type(f, fulladder)) | connection(in(n1, f), in(n1, h2(f))))),
% 1.88/1.44 inference(quant_inst,[status(thm)],[])).
% 1.88/1.44 tff(452,plain,
% 1.88/1.44 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | (~type(f, fulladder)) | connection(in(n1, f), in(n1, h2(f)))),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[451, 450])).
% 1.88/1.44 tff(453,plain,
% 1.88/1.44 (connection(in(n1, f), in(n1, h2(f)))),
% 1.88/1.44 inference(unit_resolution,[status(thm)],[452, 449, 3])).
% 1.88/1.44 tff(454,plain,
% 1.88/1.44 (value(in(n1, f), n1) <=> value(in(n1, f), n1)),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(455,axiom,(value(in(n1, f), n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','in1_1')).
% 1.88/1.44 tff(456,plain,
% 1.88/1.44 (value(in(n1, f), n1)),
% 1.88/1.44 inference(modus_ponens,[status(thm)],[455, 454])).
% 1.88/1.44 tff(457,plain,
% 1.88/1.44 (((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(in(n1, f), n1)) | (~value(in(n1, f), n0)))) <=> ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n0, n1) | (~value(in(n1, f), n1)) | (~value(in(n1, f), n0)))),
% 1.88/1.44 inference(rewrite,[status(thm)],[])).
% 1.88/1.44 tff(458,plain,
% 1.88/1.44 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(in(n1, f), n1)) | (~value(in(n1, f), n0)))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(459,plain,
% 1.88/1.45 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n0, n1) | (~value(in(n1, f), n1)) | (~value(in(n1, f), n0))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[458, 457])).
% 1.88/1.45 tff(460,plain,
% 1.88/1.45 (~value(in(n1, f), n0)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[459, 402, 392, 456])).
% 1.88/1.45 tff(461,plain,
% 1.88/1.45 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, f), n0) | (~connection(in(n1, f), in(n1, h2(f)))) | (~value(in(n1, h2(f)), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, f), n0) | (~connection(in(n1, f), in(n1, h2(f)))) | (~value(in(n1, h2(f)), n0)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(462,plain,
% 1.88/1.45 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, f), n0) | (~connection(in(n1, f), in(n1, h2(f)))) | (~value(in(n1, h2(f)), n0)))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(463,plain,
% 1.88/1.45 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, f), n0) | (~connection(in(n1, f), in(n1, h2(f)))) | (~value(in(n1, h2(f)), n0))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[462, 461])).
% 1.88/1.45 tff(464,plain,
% 1.88/1.45 (~value(in(n1, h2(f)), n0)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[463, 382, 460, 453])).
% 1.88/1.45 tff(465,plain,
% 1.88/1.45 (((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h2(f), halfadder)) | connection(in(n1, h2(f)), in(n1, and2(h2(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h2(f), halfadder)) | connection(in(n1, h2(f)), in(n1, and2(h2(f)))))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(466,plain,
% 1.88/1.45 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h2(f), halfadder)) | connection(in(n1, h2(f)), in(n1, and2(h2(f)))))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(467,plain,
% 1.88/1.45 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h2(f), halfadder)) | connection(in(n1, h2(f)), in(n1, and2(h2(f))))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[466, 465])).
% 1.88/1.45 tff(468,plain,
% 1.88/1.45 (connection(in(n1, h2(f)), in(n1, and2(h2(f))))),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[467, 214, 46])).
% 1.88/1.45 tff(469,plain,
% 1.88/1.45 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h2(f)), n0) | (~value(in(n1, and2(h2(f))), n0)) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h2(f)), n0) | (~value(in(n1, and2(h2(f))), n0)) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f))))))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(470,plain,
% 1.88/1.45 ((value(in(n1, h2(f)), n0) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f))))) | (~value(in(n1, and2(h2(f))), n0))) <=> (value(in(n1, h2(f)), n0) | (~value(in(n1, and2(h2(f))), n0)) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f))))))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(471,plain,
% 1.88/1.45 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h2(f)), n0) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f))))) | (~value(in(n1, and2(h2(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h2(f)), n0) | (~value(in(n1, and2(h2(f))), n0)) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f)))))))),
% 1.88/1.45 inference(monotonicity,[status(thm)],[470])).
% 1.88/1.45 tff(472,plain,
% 1.88/1.45 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h2(f)), n0) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f))))) | (~value(in(n1, and2(h2(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h2(f)), n0) | (~value(in(n1, and2(h2(f))), n0)) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f))))))),
% 1.88/1.45 inference(transitivity,[status(thm)],[471, 469])).
% 1.88/1.45 tff(473,plain,
% 1.88/1.45 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h2(f)), n0) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f))))) | (~value(in(n1, and2(h2(f))), n0)))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(474,plain,
% 1.88/1.45 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h2(f)), n0) | (~value(in(n1, and2(h2(f))), n0)) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f)))))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[473, 472])).
% 1.88/1.45 tff(475,plain,
% 1.88/1.45 (~value(in(n1, and2(h2(f))), n0)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[474, 382, 468, 464])).
% 1.88/1.45 tff(476,plain,
% 1.88/1.45 (((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h2(f), halfadder)) | type(and2(h2(f)), and))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h2(f), halfadder)) | type(and2(h2(f)), and))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(477,plain,
% 1.88/1.45 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h2(f), halfadder)) | type(and2(h2(f)), and))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(478,plain,
% 1.88/1.45 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h2(f), halfadder)) | type(and2(h2(f)), and)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[477, 476])).
% 1.88/1.45 tff(479,plain,
% 1.88/1.45 (type(and2(h2(f)), and)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[478, 230, 46])).
% 1.88/1.45 tff(480,plain,
% 1.88/1.45 ((~mode(and2(h2(f)), abnormal)) <=> (~mode(and2(h2(f)), abnormal))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(481,axiom,(~mode(and2(h2(f)), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_and2')).
% 1.88/1.45 tff(482,plain,
% 1.88/1.45 (~mode(and2(h2(f)), abnormal)),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[481, 480])).
% 1.88/1.45 tff(483,plain,
% 1.88/1.45 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h2(f)), abnormal) | mode(and2(h2(f)), ok) | (~type(and2(h2(f)), and)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h2(f)), abnormal) | mode(and2(h2(f)), ok) | (~type(and2(h2(f)), and)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(484,plain,
% 1.88/1.45 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h2(f)), abnormal) | mode(and2(h2(f)), ok) | (~type(and2(h2(f)), and)))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(485,plain,
% 1.88/1.45 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h2(f)), abnormal) | mode(and2(h2(f)), ok) | (~type(and2(h2(f)), and))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[484, 483])).
% 1.88/1.45 tff(486,plain,
% 1.88/1.45 (mode(and2(h2(f)), ok)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[485, 140, 482, 479])).
% 1.88/1.45 tff(487,plain,
% 1.88/1.45 (^[K: $i] : refl(((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0))) <=> ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(488,plain,
% 1.88/1.45 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0))) <=> ![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[487])).
% 1.88/1.45 tff(489,plain,
% 1.88/1.45 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0))) <=> ![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(490,plain,
% 1.88/1.45 (^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n0))) <=> ((~mode(K, ok)) | (~type(K, and)) | (~value(out(n1, K), n0)))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) <=> (((~mode(K, ok)) | (~type(K, and)) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)))), rewrite((((~mode(K, ok)) | (~type(K, and)) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) <=> ((~mode(K, ok)) | (~type(K, and)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) <=> ((~mode(K, ok)) | (~type(K, and)) | value(in(n1, K), n0) | (~value(out(n1, K), n0))))), ((((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) | value(in(n2, K), n0)) <=> (((~mode(K, ok)) | (~type(K, and)) | value(in(n1, K), n0) | (~value(out(n1, K), n0))) | value(in(n2, K), n0)))), rewrite((((~mode(K, ok)) | (~type(K, and)) | value(in(n1, K), n0) | (~value(out(n1, K), n0))) | value(in(n2, K), n0)) <=> ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))), ((((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) | value(in(n2, K), n0)) <=> ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(491,plain,
% 1.88/1.45 (![K: $i] : (((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) | value(in(n2, K), n0)) <=> ![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[490])).
% 1.88/1.45 tff(492,axiom,(![K: $i] : (((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) | value(in(n2, K), n0))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','and_0_00')).
% 1.88/1.45 tff(493,plain,
% 1.88/1.45 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[492, 491])).
% 1.88/1.45 tff(494,plain,
% 1.88/1.45 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[493, 489])).
% 1.88/1.45 tff(495,plain,(
% 1.88/1.45 ![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 1.88/1.45 inference(skolemize,[status(sab)],[494])).
% 1.88/1.45 tff(496,plain,
% 1.88/1.45 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[495, 488])).
% 1.88/1.45 tff(497,plain,
% 1.88/1.45 (((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | ((~mode(and2(h2(f)), ok)) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)) | value(in(n2, and2(h2(f))), n0) | (~type(and2(h2(f)), and)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | (~mode(and2(h2(f)), ok)) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)) | value(in(n2, and2(h2(f))), n0) | (~type(and2(h2(f)), and)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(498,plain,
% 1.88/1.45 (((~mode(and2(h2(f)), ok)) | (~type(and2(h2(f)), and)) | value(in(n2, and2(h2(f))), n0) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0))) <=> ((~mode(and2(h2(f)), ok)) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)) | value(in(n2, and2(h2(f))), n0) | (~type(and2(h2(f)), and)))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(499,plain,
% 1.88/1.45 (((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | ((~mode(and2(h2(f)), ok)) | (~type(and2(h2(f)), and)) | value(in(n2, and2(h2(f))), n0) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | ((~mode(and2(h2(f)), ok)) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)) | value(in(n2, and2(h2(f))), n0) | (~type(and2(h2(f)), and))))),
% 1.88/1.45 inference(monotonicity,[status(thm)],[498])).
% 1.88/1.45 tff(500,plain,
% 1.88/1.45 (((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | ((~mode(and2(h2(f)), ok)) | (~type(and2(h2(f)), and)) | value(in(n2, and2(h2(f))), n0) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | (~mode(and2(h2(f)), ok)) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)) | value(in(n2, and2(h2(f))), n0) | (~type(and2(h2(f)), and)))),
% 1.88/1.45 inference(transitivity,[status(thm)],[499, 497])).
% 1.88/1.45 tff(501,plain,
% 1.88/1.45 ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | ((~mode(and2(h2(f)), ok)) | (~type(and2(h2(f)), and)) | value(in(n2, and2(h2(f))), n0) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(502,plain,
% 1.88/1.45 ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | (~mode(and2(h2(f)), ok)) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)) | value(in(n2, and2(h2(f))), n0) | (~type(and2(h2(f)), and))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[501, 500])).
% 1.88/1.45 tff(503,plain,
% 1.88/1.45 ((~mode(and2(h2(f)), ok)) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)) | value(in(n2, and2(h2(f))), n0)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[502, 496, 479])).
% 1.88/1.45 tff(504,plain,
% 1.88/1.45 ((~value(out(n1, and2(h2(f))), n0)) | value(in(n2, and2(h2(f))), n0)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[503, 486, 475])).
% 1.88/1.45 tff(505,plain,
% 1.88/1.45 (~value(out(n1, and2(h2(f))), n0)),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[504, 442])).
% 1.88/1.45 tff(506,plain,
% 1.88/1.45 (^[X: $i] : refl(((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X)))) <=> ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X)))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(507,plain,
% 1.88/1.45 (![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[506])).
% 1.88/1.45 tff(508,plain,
% 1.88/1.45 (![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(509,axiom,(![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_connection_outc_out1and2')).
% 1.88/1.45 tff(510,plain,
% 1.88/1.45 (![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[509, 508])).
% 1.88/1.45 tff(511,plain,(
% 1.88/1.45 ![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 1.88/1.45 inference(skolemize,[status(sab)],[510])).
% 1.88/1.45 tff(512,plain,
% 1.88/1.45 (![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[511, 507])).
% 1.88/1.45 tff(513,plain,
% 1.88/1.45 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h2(f), halfadder)) | connection(out(c, h2(f)), out(n1, and2(h2(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h2(f), halfadder)) | connection(out(c, h2(f)), out(n1, and2(h2(f)))))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(514,plain,
% 1.88/1.45 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h2(f), halfadder)) | connection(out(c, h2(f)), out(n1, and2(h2(f)))))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(515,plain,
% 1.88/1.45 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h2(f), halfadder)) | connection(out(c, h2(f)), out(n1, and2(h2(f))))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[514, 513])).
% 1.88/1.45 tff(516,plain,
% 1.88/1.45 (connection(out(c, h2(f)), out(n1, and2(h2(f))))),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[515, 512, 46])).
% 1.88/1.45 tff(517,plain,
% 1.88/1.45 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and2(h2(f))), n0) | (~value(out(c, h2(f)), n0)) | (~connection(out(c, h2(f)), out(n1, and2(h2(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, and2(h2(f))), n0) | (~value(out(c, h2(f)), n0)) | (~connection(out(c, h2(f)), out(n1, and2(h2(f))))))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(518,plain,
% 1.88/1.45 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and2(h2(f))), n0) | (~value(out(c, h2(f)), n0)) | (~connection(out(c, h2(f)), out(n1, and2(h2(f))))))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(519,plain,
% 1.88/1.45 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, and2(h2(f))), n0) | (~value(out(c, h2(f)), n0)) | (~connection(out(c, h2(f)), out(n1, and2(h2(f)))))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[518, 517])).
% 1.88/1.45 tff(520,plain,
% 1.88/1.45 ($false),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[519, 27, 516, 505, 66])).
% 1.88/1.45 tff(521,plain,(~value(out(c, h2(f)), n0)), inference(lemma,lemma(discharge,[]))).
% 1.88/1.45 tff(522,plain,
% 1.88/1.45 (^[X: $i] : refl(((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X)))) <=> ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X)))))),
% 1.88/1.45 inference(bind,[status(th)],[])).
% 1.88/1.45 tff(523,plain,
% 1.88/1.45 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 1.88/1.45 inference(quant_intro,[status(thm)],[522])).
% 1.88/1.45 tff(524,plain,
% 1.88/1.45 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(525,axiom,(![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_connection_outch2_in1or1')).
% 1.88/1.45 tff(526,plain,
% 1.88/1.45 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[525, 524])).
% 1.88/1.45 tff(527,plain,(
% 1.88/1.45 ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 1.88/1.45 inference(skolemize,[status(sab)],[526])).
% 1.88/1.45 tff(528,plain,
% 1.88/1.45 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[527, 523])).
% 1.88/1.45 tff(529,plain,
% 1.88/1.45 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | ((~type(f, fulladder)) | connection(out(c, h2(f)), in(n1, or1(f))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | (~type(f, fulladder)) | connection(out(c, h2(f)), in(n1, or1(f))))),
% 1.88/1.45 inference(rewrite,[status(thm)],[])).
% 1.88/1.45 tff(530,plain,
% 1.88/1.45 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | ((~type(f, fulladder)) | connection(out(c, h2(f)), in(n1, or1(f))))),
% 1.88/1.45 inference(quant_inst,[status(thm)],[])).
% 1.88/1.45 tff(531,plain,
% 1.88/1.45 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | (~type(f, fulladder)) | connection(out(c, h2(f)), in(n1, or1(f)))),
% 1.88/1.45 inference(modus_ponens,[status(thm)],[530, 529])).
% 1.88/1.45 tff(532,plain,
% 1.88/1.45 (connection(out(c, h2(f)), in(n1, or1(f)))),
% 1.88/1.45 inference(unit_resolution,[status(thm)],[531, 528, 3])).
% 1.88/1.45 tff(533,plain,
% 1.88/1.45 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n1, or1(f)), n0)) | value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, or1(f)), n0)) | value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f)))))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(534,plain,
% 1.88/1.46 ((value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f)))) | (~value(in(n1, or1(f)), n0))) <=> ((~value(in(n1, or1(f)), n0)) | value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f)))))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(535,plain,
% 1.88/1.46 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f)))) | (~value(in(n1, or1(f)), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n1, or1(f)), n0)) | value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f))))))),
% 1.88/1.46 inference(monotonicity,[status(thm)],[534])).
% 1.88/1.46 tff(536,plain,
% 1.88/1.46 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f)))) | (~value(in(n1, or1(f)), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, or1(f)), n0)) | value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f)))))),
% 1.88/1.46 inference(transitivity,[status(thm)],[535, 533])).
% 1.88/1.46 tff(537,plain,
% 1.88/1.46 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f)))) | (~value(in(n1, or1(f)), n0)))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(538,plain,
% 1.88/1.46 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, or1(f)), n0)) | value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f))))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[537, 536])).
% 1.88/1.46 tff(539,plain,
% 1.88/1.46 ((~value(in(n1, or1(f)), n0)) | value(out(c, h2(f)), n0)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[538, 382, 532])).
% 1.88/1.46 tff(540,plain,
% 1.88/1.46 (~value(in(n1, or1(f)), n0)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[539, 521])).
% 1.88/1.46 tff(541,assumption,(~value(out(n1, or1(f)), n0)), introduced(assumption)).
% 1.88/1.46 tff(542,plain,
% 1.88/1.46 (^[X: $i] : refl(((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X)))) <=> ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X)))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(543,plain,
% 1.88/1.46 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[542])).
% 1.88/1.46 tff(544,plain,
% 1.88/1.46 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(545,axiom,(![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_connection_outc_out1or1')).
% 1.88/1.46 tff(546,plain,
% 1.88/1.46 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[545, 544])).
% 1.88/1.46 tff(547,plain,(
% 1.88/1.46 ![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 1.88/1.46 inference(skolemize,[status(sab)],[546])).
% 1.88/1.46 tff(548,plain,
% 1.88/1.46 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[547, 543])).
% 1.88/1.46 tff(549,plain,
% 1.88/1.46 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | ((~type(f, fulladder)) | connection(out(c, f), out(n1, or1(f))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | (~type(f, fulladder)) | connection(out(c, f), out(n1, or1(f))))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(550,plain,
% 1.88/1.46 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | ((~type(f, fulladder)) | connection(out(c, f), out(n1, or1(f))))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(551,plain,
% 1.88/1.46 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | (~type(f, fulladder)) | connection(out(c, f), out(n1, or1(f)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[550, 549])).
% 1.88/1.46 tff(552,plain,
% 1.88/1.46 (connection(out(c, f), out(n1, or1(f)))),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[551, 548, 3])).
% 1.88/1.46 tff(553,plain,
% 1.88/1.46 (value(out(c, f), n0) <=> value(out(c, f), n0)),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(554,axiom,(value(out(c, f), n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','outc_0')).
% 1.88/1.46 tff(555,plain,
% 1.88/1.46 (value(out(c, f), n0)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[554, 553])).
% 1.88/1.46 tff(556,plain,
% 1.88/1.46 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))) | value(out(n1, or1(f)), n0))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))) | value(out(n1, or1(f)), n0))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(557,plain,
% 1.88/1.46 ((value(out(n1, or1(f)), n0) | (~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f))))) <=> ((~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))) | value(out(n1, or1(f)), n0))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(558,plain,
% 1.88/1.46 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, or1(f)), n0) | (~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))) | value(out(n1, or1(f)), n0)))),
% 1.88/1.46 inference(monotonicity,[status(thm)],[557])).
% 1.88/1.46 tff(559,plain,
% 1.88/1.46 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, or1(f)), n0) | (~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))) | value(out(n1, or1(f)), n0))),
% 1.88/1.46 inference(transitivity,[status(thm)],[558, 556])).
% 1.88/1.46 tff(560,plain,
% 1.88/1.46 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, or1(f)), n0) | (~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(561,plain,
% 1.88/1.46 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))) | value(out(n1, or1(f)), n0)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[560, 559])).
% 1.88/1.46 tff(562,plain,
% 1.88/1.46 ($false),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[561, 27, 555, 552, 541])).
% 1.88/1.46 tff(563,plain,(value(out(n1, or1(f)), n0)), inference(lemma,lemma(discharge,[]))).
% 1.88/1.46 tff(564,plain,
% 1.88/1.46 (^[X: $i] : refl(((~type(X, fulladder)) | type(or1(X), or)) <=> ((~type(X, fulladder)) | type(or1(X), or)))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(565,plain,
% 1.88/1.46 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[564])).
% 1.88/1.46 tff(566,plain,
% 1.88/1.46 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(567,axiom,(![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_or1')).
% 1.88/1.46 tff(568,plain,
% 1.88/1.46 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[567, 566])).
% 1.88/1.46 tff(569,plain,(
% 1.88/1.46 ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 1.88/1.46 inference(skolemize,[status(sab)],[568])).
% 1.88/1.46 tff(570,plain,
% 1.88/1.46 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[569, 565])).
% 1.88/1.46 tff(571,plain,
% 1.88/1.46 (((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | ((~type(f, fulladder)) | type(or1(f), or))) <=> ((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | (~type(f, fulladder)) | type(or1(f), or))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(572,plain,
% 1.88/1.46 ((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | ((~type(f, fulladder)) | type(or1(f), or))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(573,plain,
% 1.88/1.46 ((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | (~type(f, fulladder)) | type(or1(f), or)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[572, 571])).
% 1.88/1.46 tff(574,plain,
% 1.88/1.46 (type(or1(f), or)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[573, 570, 3])).
% 1.88/1.46 tff(575,plain,
% 1.88/1.46 (^[K: $i] : refl(((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or))) <=> ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(576,plain,
% 1.88/1.46 (![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or))) <=> ![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[575])).
% 1.88/1.46 tff(577,plain,
% 1.88/1.46 (![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or))) <=> ![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(578,plain,
% 1.88/1.46 (^[K: $i] : trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n0)) | (~type(K, or)))), (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n0)) | (~type(K, or))) | value(in(n1, K), n0)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n0)) | (~type(K, or))) | value(in(n1, K), n0)) <=> ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))), (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) <=> ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(579,plain,
% 1.88/1.46 (![K: $i] : ((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) <=> ![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[578])).
% 1.88/1.46 tff(580,axiom,(![K: $i] : ((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','or_0_0x')).
% 1.88/1.46 tff(581,plain,
% 1.88/1.46 (![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[580, 579])).
% 1.88/1.46 tff(582,plain,
% 1.88/1.46 (![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[581, 577])).
% 1.88/1.46 tff(583,plain,(
% 1.88/1.46 ![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 1.88/1.46 inference(skolemize,[status(sab)],[582])).
% 1.88/1.46 tff(584,plain,
% 1.88/1.46 (![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[583, 576])).
% 1.88/1.46 tff(585,plain,
% 1.88/1.46 (((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n1, or1(f)), n0) | (~type(or1(f), or)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | (~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n1, or1(f)), n0) | (~type(or1(f), or)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(586,plain,
% 1.88/1.46 (((~mode(or1(f), ok)) | value(in(n1, or1(f)), n0) | (~value(out(n1, or1(f)), n0)) | (~type(or1(f), or))) <=> ((~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n1, or1(f)), n0) | (~type(or1(f), or)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(587,plain,
% 1.88/1.46 (((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(f), ok)) | value(in(n1, or1(f)), n0) | (~value(out(n1, or1(f)), n0)) | (~type(or1(f), or)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n1, or1(f)), n0) | (~type(or1(f), or))))),
% 1.88/1.46 inference(monotonicity,[status(thm)],[586])).
% 1.88/1.46 tff(588,plain,
% 1.88/1.46 (((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(f), ok)) | value(in(n1, or1(f)), n0) | (~value(out(n1, or1(f)), n0)) | (~type(or1(f), or)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | (~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n1, or1(f)), n0) | (~type(or1(f), or)))),
% 1.88/1.46 inference(transitivity,[status(thm)],[587, 585])).
% 1.88/1.46 tff(589,plain,
% 1.88/1.46 ((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(f), ok)) | value(in(n1, or1(f)), n0) | (~value(out(n1, or1(f)), n0)) | (~type(or1(f), or)))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(590,plain,
% 1.88/1.46 ((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | (~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n1, or1(f)), n0) | (~type(or1(f), or))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[589, 588])).
% 1.88/1.46 tff(591,plain,
% 1.88/1.46 ((~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n1, or1(f)), n0)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[590, 584, 574])).
% 1.88/1.46 tff(592,plain,
% 1.88/1.46 ((~mode(or1(f), ok)) | value(in(n1, or1(f)), n0)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[591, 563])).
% 1.88/1.46 tff(593,plain,
% 1.88/1.46 (~mode(or1(f), ok)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[592, 540])).
% 1.88/1.46 tff(594,plain,
% 1.88/1.46 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(or1(f), abnormal) | mode(or1(f), ok) | (~type(or1(f), or)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(or1(f), abnormal) | mode(or1(f), ok) | (~type(or1(f), or)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(595,plain,
% 1.88/1.46 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(or1(f), abnormal) | mode(or1(f), ok) | (~type(or1(f), or)))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(596,plain,
% 1.88/1.46 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(or1(f), abnormal) | mode(or1(f), ok) | (~type(or1(f), or))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[595, 594])).
% 1.88/1.46 tff(597,plain,
% 1.88/1.46 (mode(or1(f), abnormal) | mode(or1(f), ok)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[596, 140, 574])).
% 1.88/1.46 tff(598,plain,
% 1.88/1.46 (mode(or1(f), abnormal)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[597, 593])).
% 1.88/1.46 tff(599,plain,
% 1.88/1.46 (((~mode(or1(f), abnormal)) | (~mode(and1(h2(f)), abnormal))) <=> ((~mode(or1(f), abnormal)) | (~mode(and1(h2(f)), abnormal)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(600,axiom,((~mode(or1(f), abnormal)) | (~mode(and1(h2(f)), abnormal))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_or1_and1h2')).
% 1.88/1.46 tff(601,plain,
% 1.88/1.46 ((~mode(or1(f), abnormal)) | (~mode(and1(h2(f)), abnormal))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[600, 599])).
% 1.88/1.46 tff(602,plain,
% 1.88/1.46 (~mode(and1(h2(f)), abnormal)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[601, 598])).
% 1.88/1.46 tff(603,plain,
% 1.88/1.46 (((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | ((~type(h2(f), halfadder)) | type(and1(h2(f)), and))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | (~type(h2(f), halfadder)) | type(and1(h2(f)), and))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(604,plain,
% 1.88/1.46 ((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | ((~type(h2(f), halfadder)) | type(and1(h2(f)), and))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(605,plain,
% 1.88/1.46 ((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | (~type(h2(f), halfadder)) | type(and1(h2(f)), and)),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[604, 603])).
% 1.88/1.46 tff(606,plain,
% 1.88/1.46 (type(and1(h2(f)), and)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[605, 337, 46])).
% 1.88/1.46 tff(607,plain,
% 1.88/1.46 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and1(h2(f)), abnormal) | mode(and1(h2(f)), ok) | (~type(and1(h2(f)), and)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and1(h2(f)), abnormal) | mode(and1(h2(f)), ok) | (~type(and1(h2(f)), and)))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(608,plain,
% 1.88/1.46 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and1(h2(f)), abnormal) | mode(and1(h2(f)), ok) | (~type(and1(h2(f)), and)))),
% 1.88/1.46 inference(quant_inst,[status(thm)],[])).
% 1.88/1.46 tff(609,plain,
% 1.88/1.46 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and1(h2(f)), abnormal) | mode(and1(h2(f)), ok) | (~type(and1(h2(f)), and))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[608, 607])).
% 1.88/1.46 tff(610,plain,
% 1.88/1.46 (mode(and1(h2(f)), abnormal) | mode(and1(h2(f)), ok)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[609, 140, 606])).
% 1.88/1.46 tff(611,plain,
% 1.88/1.46 (mode(and1(h2(f)), ok)),
% 1.88/1.46 inference(unit_resolution,[status(thm)],[610, 602])).
% 1.88/1.46 tff(612,plain,
% 1.88/1.46 (^[K: $i] : refl(((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1)))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(613,plain,
% 1.88/1.46 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[612])).
% 1.88/1.46 tff(614,plain,
% 1.88/1.46 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))),
% 1.88/1.46 inference(rewrite,[status(thm)],[])).
% 1.88/1.46 tff(615,plain,
% 1.88/1.46 (^[K: $i] : trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n2, K), n1)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and))) | value(in(n2, K), n1)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and))) | value(in(n2, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n2, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))))),
% 1.88/1.46 inference(bind,[status(th)],[])).
% 1.88/1.46 tff(616,plain,
% 1.88/1.46 (![K: $i] : ((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n2, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))),
% 1.88/1.46 inference(quant_intro,[status(thm)],[615])).
% 1.88/1.46 tff(617,axiom,(![K: $i] : ((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n2, K), n1))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','and_1_x1')).
% 1.88/1.46 tff(618,plain,
% 1.88/1.46 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[617, 616])).
% 1.88/1.46 tff(619,plain,
% 1.88/1.46 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[618, 614])).
% 1.88/1.46 tff(620,plain,(
% 1.88/1.46 ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))),
% 1.88/1.46 inference(skolemize,[status(sab)],[619])).
% 1.88/1.46 tff(621,plain,
% 1.88/1.46 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))),
% 1.88/1.46 inference(modus_ponens,[status(thm)],[620, 613])).
% 1.88/1.46 tff(622,plain,
% 1.88/1.46 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))) | ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n2, and1(h2(f))), n1) | (~type(and1(h2(f)), and)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))) | (~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n2, and1(h2(f))), n1) | (~type(and1(h2(f)), and)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(623,plain,
% 1.88/1.47 (((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | (~type(and1(h2(f)), and)) | value(in(n2, and1(h2(f))), n1)) <=> ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n2, and1(h2(f))), n1) | (~type(and1(h2(f)), and)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(624,plain,
% 1.88/1.47 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))) | ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | (~type(and1(h2(f)), and)) | value(in(n2, and1(h2(f))), n1))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))) | ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n2, and1(h2(f))), n1) | (~type(and1(h2(f)), and))))),
% 1.88/1.47 inference(monotonicity,[status(thm)],[623])).
% 1.88/1.47 tff(625,plain,
% 1.88/1.47 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))) | ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | (~type(and1(h2(f)), and)) | value(in(n2, and1(h2(f))), n1))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))) | (~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n2, and1(h2(f))), n1) | (~type(and1(h2(f)), and)))),
% 1.88/1.47 inference(transitivity,[status(thm)],[624, 622])).
% 1.88/1.47 tff(626,plain,
% 1.88/1.47 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))) | ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | (~type(and1(h2(f)), and)) | value(in(n2, and1(h2(f))), n1))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.88/1.47 tff(627,plain,
% 1.88/1.47 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))) | (~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n2, and1(h2(f))), n1) | (~type(and1(h2(f)), and))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[626, 625])).
% 1.88/1.47 tff(628,plain,
% 1.88/1.47 ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n2, and1(h2(f))), n1)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[627, 621, 606])).
% 1.88/1.47 tff(629,plain,
% 1.88/1.47 (value(in(n2, and1(h2(f))), n1)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[628, 611, 65])).
% 1.88/1.47 tff(630,plain,
% 1.88/1.47 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))) | ((~type(h2(f), halfadder)) | connection(out(n1, not1(h2(f))), in(n2, and1(h2(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))) | (~type(h2(f), halfadder)) | connection(out(n1, not1(h2(f))), in(n2, and1(h2(f)))))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(631,plain,
% 1.88/1.47 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))) | ((~type(h2(f), halfadder)) | connection(out(n1, not1(h2(f))), in(n2, and1(h2(f)))))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.88/1.47 tff(632,plain,
% 1.88/1.47 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))) | (~type(h2(f), halfadder)) | connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[631, 630])).
% 1.88/1.47 tff(633,plain,
% 1.88/1.47 (connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[632, 318, 46])).
% 1.88/1.47 tff(634,plain,
% 1.88/1.47 (((~mode(or1(f), abnormal)) | (~mode(not1(h2(f)), abnormal))) <=> ((~mode(or1(f), abnormal)) | (~mode(not1(h2(f)), abnormal)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(635,axiom,((~mode(or1(f), abnormal)) | (~mode(not1(h2(f)), abnormal))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_or1_not1h2')).
% 1.88/1.47 tff(636,plain,
% 1.88/1.47 ((~mode(or1(f), abnormal)) | (~mode(not1(h2(f)), abnormal))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[635, 634])).
% 1.88/1.47 tff(637,plain,
% 1.88/1.47 (~mode(not1(h2(f)), abnormal)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[636, 598])).
% 1.88/1.47 tff(638,plain,
% 1.88/1.47 (((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | ((~type(h2(f), halfadder)) | type(not1(h2(f)), not))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | (~type(h2(f), halfadder)) | type(not1(h2(f)), not))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(639,plain,
% 1.88/1.47 ((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | ((~type(h2(f), halfadder)) | type(not1(h2(f)), not))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.88/1.47 tff(640,plain,
% 1.88/1.47 ((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | (~type(h2(f), halfadder)) | type(not1(h2(f)), not)),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[639, 638])).
% 1.88/1.47 tff(641,plain,
% 1.88/1.47 (type(not1(h2(f)), not)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[640, 281, 46])).
% 1.88/1.47 tff(642,plain,
% 1.88/1.47 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(not1(h2(f)), abnormal) | mode(not1(h2(f)), ok) | (~type(not1(h2(f)), not)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(not1(h2(f)), abnormal) | mode(not1(h2(f)), ok) | (~type(not1(h2(f)), not)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(643,plain,
% 1.88/1.47 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(not1(h2(f)), abnormal) | mode(not1(h2(f)), ok) | (~type(not1(h2(f)), not)))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.88/1.47 tff(644,plain,
% 1.88/1.47 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(not1(h2(f)), abnormal) | mode(not1(h2(f)), ok) | (~type(not1(h2(f)), not))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[643, 642])).
% 1.88/1.47 tff(645,plain,
% 1.88/1.47 (mode(not1(h2(f)), abnormal) | mode(not1(h2(f)), ok)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[644, 140, 641])).
% 1.88/1.47 tff(646,plain,
% 1.88/1.47 (mode(not1(h2(f)), ok)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[645, 637])).
% 1.88/1.47 tff(647,plain,
% 1.88/1.47 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))) | ((~type(h2(f), halfadder)) | connection(out(n1, and2(h2(f))), in(n1, not1(h2(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))) | (~type(h2(f), halfadder)) | connection(out(n1, and2(h2(f))), in(n1, not1(h2(f)))))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(648,plain,
% 1.88/1.47 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))) | ((~type(h2(f), halfadder)) | connection(out(n1, and2(h2(f))), in(n1, not1(h2(f)))))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.88/1.47 tff(649,plain,
% 1.88/1.47 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))) | (~type(h2(f), halfadder)) | connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[648, 647])).
% 1.88/1.47 tff(650,plain,
% 1.88/1.47 (connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[649, 265, 46])).
% 1.88/1.47 tff(651,plain,
% 1.88/1.47 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, and2(h2(f))), n0) | (~value(in(n1, not1(h2(f))), n0)) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, and2(h2(f))), n0) | (~value(in(n1, not1(h2(f))), n0)) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(652,plain,
% 1.88/1.47 ((value(out(n1, and2(h2(f))), n0) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))) | (~value(in(n1, not1(h2(f))), n0))) <=> (value(out(n1, and2(h2(f))), n0) | (~value(in(n1, not1(h2(f))), n0)) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(653,plain,
% 1.88/1.47 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, and2(h2(f))), n0) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))) | (~value(in(n1, not1(h2(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, and2(h2(f))), n0) | (~value(in(n1, not1(h2(f))), n0)) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f)))))))),
% 1.88/1.47 inference(monotonicity,[status(thm)],[652])).
% 1.88/1.47 tff(654,plain,
% 1.88/1.47 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, and2(h2(f))), n0) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))) | (~value(in(n1, not1(h2(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, and2(h2(f))), n0) | (~value(in(n1, not1(h2(f))), n0)) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))))),
% 1.88/1.47 inference(transitivity,[status(thm)],[653, 651])).
% 1.88/1.47 tff(655,plain,
% 1.88/1.47 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, and2(h2(f))), n0) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))) | (~value(in(n1, not1(h2(f))), n0)))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.88/1.47 tff(656,plain,
% 1.88/1.47 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, and2(h2(f))), n0) | (~value(in(n1, not1(h2(f))), n0)) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f)))))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[655, 654])).
% 1.88/1.47 tff(657,plain,
% 1.88/1.47 (~value(in(n1, not1(h2(f))), n0)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[656, 382, 650, 505])).
% 1.88/1.47 tff(658,plain,
% 1.88/1.47 (^[K: $i] : refl(((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not))))),
% 1.88/1.47 inference(bind,[status(th)],[])).
% 1.88/1.47 tff(659,plain,
% 1.88/1.47 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not))) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))),
% 1.88/1.47 inference(quant_intro,[status(thm)],[658])).
% 1.88/1.47 tff(660,plain,
% 1.88/1.47 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not))) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(661,plain,
% 1.88/1.47 (^[K: $i] : trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, not))) | (~value(out(n1, K), n1))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, not)))), (((((~mode(K, ok)) | (~type(K, not))) | (~value(out(n1, K), n1))) | value(in(n1, K), n0)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, not))) | value(in(n1, K), n0)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, not))) | value(in(n1, K), n0)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))), (((((~mode(K, ok)) | (~type(K, not))) | (~value(out(n1, K), n1))) | value(in(n1, K), n0)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))))),
% 1.88/1.47 inference(bind,[status(th)],[])).
% 1.88/1.47 tff(662,plain,
% 1.88/1.47 (![K: $i] : ((((~mode(K, ok)) | (~type(K, not))) | (~value(out(n1, K), n1))) | value(in(n1, K), n0)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))),
% 1.88/1.47 inference(quant_intro,[status(thm)],[661])).
% 1.88/1.47 tff(663,axiom,(![K: $i] : ((((~mode(K, ok)) | (~type(K, not))) | (~value(out(n1, K), n1))) | value(in(n1, K), n0))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','not_1_0_bw')).
% 1.88/1.47 tff(664,plain,
% 1.88/1.47 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[663, 662])).
% 1.88/1.47 tff(665,plain,
% 1.88/1.47 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[664, 660])).
% 1.88/1.47 tff(666,plain,(
% 1.88/1.47 ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))),
% 1.88/1.47 inference(skolemize,[status(sab)],[665])).
% 1.88/1.47 tff(667,plain,
% 1.88/1.47 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[666, 659])).
% 1.88/1.47 tff(668,plain,
% 1.88/1.47 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))) | ((~mode(not1(h2(f)), ok)) | (~value(out(n1, not1(h2(f))), n1)) | value(in(n1, not1(h2(f))), n0) | (~type(not1(h2(f)), not)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))) | (~mode(not1(h2(f)), ok)) | (~value(out(n1, not1(h2(f))), n1)) | value(in(n1, not1(h2(f))), n0) | (~type(not1(h2(f)), not)))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(669,plain,
% 1.88/1.47 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))) | ((~mode(not1(h2(f)), ok)) | (~value(out(n1, not1(h2(f))), n1)) | value(in(n1, not1(h2(f))), n0) | (~type(not1(h2(f)), not)))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.88/1.47 tff(670,plain,
% 1.88/1.47 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))) | (~mode(not1(h2(f)), ok)) | (~value(out(n1, not1(h2(f))), n1)) | value(in(n1, not1(h2(f))), n0) | (~type(not1(h2(f)), not))),
% 1.88/1.47 inference(modus_ponens,[status(thm)],[669, 668])).
% 1.88/1.47 tff(671,plain,
% 1.88/1.47 ((~mode(not1(h2(f)), ok)) | (~value(out(n1, not1(h2(f))), n1)) | value(in(n1, not1(h2(f))), n0) | (~type(not1(h2(f)), not))),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[670, 667])).
% 1.88/1.47 tff(672,plain,
% 1.88/1.47 ((~mode(not1(h2(f)), ok)) | (~value(out(n1, not1(h2(f))), n1)) | value(in(n1, not1(h2(f))), n0)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[671, 641])).
% 1.88/1.47 tff(673,plain,
% 1.88/1.47 ((~mode(not1(h2(f)), ok)) | (~value(out(n1, not1(h2(f))), n1))),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[672, 657])).
% 1.88/1.47 tff(674,plain,
% 1.88/1.47 (~value(out(n1, not1(h2(f))), n1)),
% 1.88/1.47 inference(unit_resolution,[status(thm)],[673, 646])).
% 1.88/1.47 tff(675,plain,
% 1.88/1.47 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, not1(h2(f))), n1) | (~value(in(n2, and1(h2(f))), n1)) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, not1(h2(f))), n1) | (~value(in(n2, and1(h2(f))), n1)) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(676,plain,
% 1.88/1.47 ((value(out(n1, not1(h2(f))), n1) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))) | (~value(in(n2, and1(h2(f))), n1))) <=> (value(out(n1, not1(h2(f))), n1) | (~value(in(n2, and1(h2(f))), n1)) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))))),
% 1.88/1.47 inference(rewrite,[status(thm)],[])).
% 1.88/1.47 tff(677,plain,
% 1.88/1.47 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, not1(h2(f))), n1) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))) | (~value(in(n2, and1(h2(f))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, not1(h2(f))), n1) | (~value(in(n2, and1(h2(f))), n1)) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f)))))))),
% 1.88/1.47 inference(monotonicity,[status(thm)],[676])).
% 1.88/1.47 tff(678,plain,
% 1.88/1.47 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, not1(h2(f))), n1) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))) | (~value(in(n2, and1(h2(f))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, not1(h2(f))), n1) | (~value(in(n2, and1(h2(f))), n1)) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))))),
% 1.88/1.47 inference(transitivity,[status(thm)],[677, 675])).
% 1.88/1.47 tff(679,plain,
% 1.88/1.47 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, not1(h2(f))), n1) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))) | (~value(in(n2, and1(h2(f))), n1)))),
% 1.88/1.47 inference(quant_inst,[status(thm)],[])).
% 1.92/1.48 tff(680,plain,
% 1.92/1.48 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, not1(h2(f))), n1) | (~value(in(n2, and1(h2(f))), n1)) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f)))))),
% 1.92/1.48 inference(modus_ponens,[status(thm)],[679, 678])).
% 1.92/1.48 tff(681,plain,
% 1.92/1.48 ($false),
% 1.92/1.48 inference(unit_resolution,[status(thm)],[680, 382, 674, 633, 629])).
% 1.92/1.48 % SZS output end Proof
%------------------------------------------------------------------------------