TSTP Solution File: HWV007-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV007-1 : 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 02:10:29 EDT 2022
% Result : Unsatisfiable 2.49s 1.85s
% Output : Proof 2.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : HWV007-1 : TPTP v8.1.0. Released v2.1.0.
% 0.04/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 21:58:18 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 2.49/1.85 % SZS status Unsatisfiable
% 2.49/1.85 % SZS output start Proof
% 2.49/1.85 tff(value_type, type, (
% 2.49/1.85 value: ( $i * $i ) > $o)).
% 2.49/1.85 tff(n1_type, type, (
% 2.49/1.85 n1: $i)).
% 2.49/1.85 tff(out_type, type, (
% 2.49/1.85 out: ( $i * $i ) > $i)).
% 2.49/1.85 tff(h1_type, type, (
% 2.49/1.85 h1: $i > $i)).
% 2.49/1.85 tff(f_type, type, (
% 2.49/1.85 f: $i)).
% 2.49/1.85 tff(s_type, type, (
% 2.49/1.85 s: $i)).
% 2.49/1.85 tff(in_type, type, (
% 2.49/1.85 in: ( $i * $i ) > $i)).
% 2.49/1.85 tff(h2_type, type, (
% 2.49/1.85 h2: $i > $i)).
% 2.49/1.85 tff(n2_type, type, (
% 2.49/1.85 n2: $i)).
% 2.49/1.85 tff(or1_type, type, (
% 2.49/1.85 or1: $i > $i)).
% 2.49/1.85 tff(mode_type, type, (
% 2.49/1.85 mode: ( $i * $i ) > $o)).
% 2.49/1.85 tff(ok_type, type, (
% 2.49/1.85 ok: $i)).
% 2.49/1.85 tff(abnormal_type, type, (
% 2.49/1.85 abnormal: $i)).
% 2.49/1.85 tff(n0_type, type, (
% 2.49/1.85 n0: $i)).
% 2.49/1.85 tff(c_type, type, (
% 2.49/1.85 c: $i)).
% 2.49/1.85 tff(and2_type, type, (
% 2.49/1.85 and2: $i > $i)).
% 2.49/1.85 tff(connection_type, type, (
% 2.49/1.85 connection: ( $i * $i ) > $o)).
% 2.49/1.85 tff(type_type, type, (
% 2.49/1.85 type: ( $i * $i ) > $o)).
% 2.49/1.85 tff(fulladder_type, type, (
% 2.49/1.85 fulladder: $i)).
% 2.49/1.85 tff(equal_value_type, type, (
% 2.49/1.85 equal_value: ( $i * $i ) > $o)).
% 2.49/1.85 tff(halfadder_type, type, (
% 2.49/1.85 halfadder: $i)).
% 2.49/1.85 tff(and_type, type, (
% 2.49/1.85 and: $i)).
% 2.49/1.85 tff(or_type, type, (
% 2.49/1.85 or: $i)).
% 2.49/1.85 tff(and1_type, type, (
% 2.49/1.85 and1: $i > $i)).
% 2.49/1.85 tff(not1_type, type, (
% 2.49/1.85 not1: $i > $i)).
% 2.49/1.85 tff(not_type, type, (
% 2.49/1.85 not: $i)).
% 2.49/1.85 tff(1,assumption,(value(out(c, h1(f)), n0)), introduced(assumption)).
% 2.49/1.85 tff(2,plain,
% 2.49/1.85 (type(f, fulladder) <=> type(f, fulladder)),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(3,axiom,(type(f, fulladder)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f_isa_fulladder')).
% 2.49/1.85 tff(4,plain,
% 2.49/1.85 (type(f, fulladder)),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[3, 2])).
% 2.49/1.85 tff(5,plain,
% 2.49/1.85 (^[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)))))),
% 2.49/1.85 inference(bind,[status(th)],[])).
% 2.49/1.85 tff(6,plain,
% 2.49/1.85 (![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))))),
% 2.49/1.85 inference(quant_intro,[status(thm)],[5])).
% 2.49/1.85 tff(7,plain,
% 2.49/1.85 (![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))))),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(8,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')).
% 2.49/1.85 tff(9,plain,
% 2.49/1.85 (![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[8, 7])).
% 2.49/1.85 tff(10,plain,(
% 2.49/1.85 ![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 2.49/1.85 inference(skolemize,[status(sab)],[9])).
% 2.49/1.85 tff(11,plain,
% 2.49/1.85 (![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[10, 6])).
% 2.49/1.85 tff(12,plain,
% 2.49/1.85 (((~![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))))),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(13,plain,
% 2.49/1.85 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))) | ((~type(f, fulladder)) | connection(in(c, f), in(n2, h1(f))))),
% 2.49/1.85 inference(quant_inst,[status(thm)],[])).
% 2.49/1.85 tff(14,plain,
% 2.49/1.85 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))) | (~type(f, fulladder)) | connection(in(c, f), in(n2, h1(f)))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[13, 12])).
% 2.49/1.85 tff(15,plain,
% 2.49/1.85 (connection(in(c, f), in(n2, h1(f)))),
% 2.49/1.85 inference(unit_resolution,[status(thm)],[14, 11, 4])).
% 2.49/1.85 tff(16,plain,
% 2.49/1.85 (value(in(c, f), n1) <=> value(in(c, f), n1)),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(17,axiom,(value(in(c, f), n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','inc_1')).
% 2.49/1.85 tff(18,plain,
% 2.49/1.85 (value(in(c, f), n1)),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[17, 16])).
% 2.49/1.85 tff(19,plain,
% 2.49/1.85 ((~equal_value(n0, n1)) <=> (~equal_value(n0, n1))),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(20,axiom,(~equal_value(n0, n1)), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','equal_value1')).
% 2.49/1.85 tff(21,plain,
% 2.49/1.85 (~equal_value(n0, n1)),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[20, 19])).
% 2.49/1.85 tff(22,plain,
% 2.49/1.85 (^[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))))),
% 2.49/1.85 inference(bind,[status(th)],[])).
% 2.49/1.85 tff(23,plain,
% 2.49/1.85 (![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)))),
% 2.49/1.85 inference(quant_intro,[status(thm)],[22])).
% 2.49/1.85 tff(24,plain,
% 2.49/1.85 (![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)))),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(25,plain,
% 2.49/1.85 (^[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)))))),
% 2.49/1.85 inference(bind,[status(th)],[])).
% 2.49/1.85 tff(26,plain,
% 2.49/1.85 (![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)))),
% 2.49/1.85 inference(quant_intro,[status(thm)],[25])).
% 2.49/1.85 tff(27,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')).
% 2.49/1.85 tff(28,plain,
% 2.49/1.85 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[27, 26])).
% 2.49/1.85 tff(29,plain,
% 2.49/1.85 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[28, 24])).
% 2.49/1.85 tff(30,plain,(
% 2.49/1.85 ![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 2.49/1.85 inference(skolemize,[status(sab)],[29])).
% 2.49/1.85 tff(31,plain,
% 2.49/1.85 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[30, 23])).
% 2.49/1.85 tff(32,plain,
% 2.49/1.85 (((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(in(c, f), n1)) | (~value(in(c, f), n0)))) <=> ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n0, n1) | (~value(in(c, f), n1)) | (~value(in(c, f), n0)))),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(33,plain,
% 2.49/1.85 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(in(c, f), n1)) | (~value(in(c, f), n0)))),
% 2.49/1.85 inference(quant_inst,[status(thm)],[])).
% 2.49/1.85 tff(34,plain,
% 2.49/1.85 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n0, n1) | (~value(in(c, f), n1)) | (~value(in(c, f), n0))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[33, 32])).
% 2.49/1.85 tff(35,plain,
% 2.49/1.85 (~value(in(c, f), n0)),
% 2.49/1.85 inference(unit_resolution,[status(thm)],[34, 31, 21, 18])).
% 2.49/1.85 tff(36,plain,
% 2.49/1.85 (^[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))))),
% 2.49/1.85 inference(bind,[status(th)],[])).
% 2.49/1.85 tff(37,plain,
% 2.49/1.85 (![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)))),
% 2.49/1.85 inference(quant_intro,[status(thm)],[36])).
% 2.49/1.85 tff(38,plain,
% 2.49/1.85 (![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)))),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(39,plain,
% 2.49/1.85 (^[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))))),
% 2.49/1.85 inference(bind,[status(th)],[])).
% 2.49/1.85 tff(40,plain,
% 2.49/1.85 (![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)))),
% 2.49/1.85 inference(quant_intro,[status(thm)],[39])).
% 2.49/1.85 tff(41,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')).
% 2.49/1.85 tff(42,plain,
% 2.49/1.85 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[41, 40])).
% 2.49/1.85 tff(43,plain,
% 2.49/1.85 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[42, 38])).
% 2.49/1.85 tff(44,plain,(
% 2.49/1.85 ![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 2.49/1.85 inference(skolemize,[status(sab)],[43])).
% 2.49/1.85 tff(45,plain,
% 2.49/1.85 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[44, 37])).
% 2.49/1.85 tff(46,plain,
% 2.49/1.85 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(c, f), n0) | (~connection(in(c, f), in(n2, h1(f)))) | (~value(in(n2, h1(f)), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(c, f), n0) | (~connection(in(c, f), in(n2, h1(f)))) | (~value(in(n2, h1(f)), n0)))),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(47,plain,
% 2.49/1.85 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(c, f), n0) | (~connection(in(c, f), in(n2, h1(f)))) | (~value(in(n2, h1(f)), n0)))),
% 2.49/1.85 inference(quant_inst,[status(thm)],[])).
% 2.49/1.85 tff(48,plain,
% 2.49/1.85 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(c, f), n0) | (~connection(in(c, f), in(n2, h1(f)))) | (~value(in(n2, h1(f)), n0))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[47, 46])).
% 2.49/1.85 tff(49,plain,
% 2.49/1.85 (~value(in(n2, h1(f)), n0)),
% 2.49/1.85 inference(unit_resolution,[status(thm)],[48, 45, 35, 15])).
% 2.49/1.85 tff(50,plain,
% 2.49/1.85 (^[X: $i] : refl(((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ((~type(X, fulladder)) | type(h1(X), halfadder)))),
% 2.49/1.85 inference(bind,[status(th)],[])).
% 2.49/1.85 tff(51,plain,
% 2.49/1.85 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 2.49/1.85 inference(quant_intro,[status(thm)],[50])).
% 2.49/1.85 tff(52,plain,
% 2.49/1.85 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(53,axiom,(![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_halfadder1')).
% 2.49/1.85 tff(54,plain,
% 2.49/1.85 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[53, 52])).
% 2.49/1.85 tff(55,plain,(
% 2.49/1.85 ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 2.49/1.85 inference(skolemize,[status(sab)],[54])).
% 2.49/1.85 tff(56,plain,
% 2.49/1.85 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[55, 51])).
% 2.49/1.85 tff(57,plain,
% 2.49/1.85 (((~![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))),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(58,plain,
% 2.49/1.85 ((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | ((~type(f, fulladder)) | type(h1(f), halfadder))),
% 2.49/1.85 inference(quant_inst,[status(thm)],[])).
% 2.49/1.85 tff(59,plain,
% 2.49/1.85 ((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | (~type(f, fulladder)) | type(h1(f), halfadder)),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[58, 57])).
% 2.49/1.85 tff(60,plain,
% 2.49/1.85 (type(h1(f), halfadder)),
% 2.49/1.85 inference(unit_resolution,[status(thm)],[59, 56, 4])).
% 2.49/1.85 tff(61,plain,
% 2.49/1.85 (^[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)))))),
% 2.49/1.85 inference(bind,[status(th)],[])).
% 2.49/1.85 tff(62,plain,
% 2.49/1.85 (![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))))),
% 2.49/1.85 inference(quant_intro,[status(thm)],[61])).
% 2.49/1.85 tff(63,plain,
% 2.49/1.85 (![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))))),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(64,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')).
% 2.49/1.85 tff(65,plain,
% 2.49/1.85 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[64, 63])).
% 2.49/1.85 tff(66,plain,(
% 2.49/1.85 ![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 2.49/1.85 inference(skolemize,[status(sab)],[65])).
% 2.49/1.85 tff(67,plain,
% 2.49/1.85 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[66, 62])).
% 2.49/1.85 tff(68,plain,
% 2.49/1.85 (((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))) | ((~type(h1(f), halfadder)) | connection(in(n2, h1(f)), in(n2, and2(h1(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))) | (~type(h1(f), halfadder)) | connection(in(n2, h1(f)), in(n2, and2(h1(f)))))),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(69,plain,
% 2.49/1.85 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))) | ((~type(h1(f), halfadder)) | connection(in(n2, h1(f)), in(n2, and2(h1(f)))))),
% 2.49/1.85 inference(quant_inst,[status(thm)],[])).
% 2.49/1.85 tff(70,plain,
% 2.49/1.85 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))) | (~type(h1(f), halfadder)) | connection(in(n2, h1(f)), in(n2, and2(h1(f))))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[69, 68])).
% 2.49/1.85 tff(71,plain,
% 2.49/1.85 (connection(in(n2, h1(f)), in(n2, and2(h1(f))))),
% 2.49/1.85 inference(unit_resolution,[status(thm)],[70, 67, 60])).
% 2.49/1.85 tff(72,plain,
% 2.49/1.85 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h1(f)), n0) | (~value(in(n2, and2(h1(f))), n0)) | (~connection(in(n2, h1(f)), in(n2, and2(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n2, h1(f)), n0) | (~value(in(n2, and2(h1(f))), n0)) | (~connection(in(n2, h1(f)), in(n2, and2(h1(f))))))),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(73,plain,
% 2.49/1.85 ((value(in(n2, h1(f)), n0) | (~connection(in(n2, h1(f)), in(n2, and2(h1(f))))) | (~value(in(n2, and2(h1(f))), n0))) <=> (value(in(n2, h1(f)), n0) | (~value(in(n2, and2(h1(f))), n0)) | (~connection(in(n2, h1(f)), in(n2, and2(h1(f))))))),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(74,plain,
% 2.49/1.85 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h1(f)), n0) | (~connection(in(n2, h1(f)), in(n2, and2(h1(f))))) | (~value(in(n2, and2(h1(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h1(f)), n0) | (~value(in(n2, and2(h1(f))), n0)) | (~connection(in(n2, h1(f)), in(n2, and2(h1(f)))))))),
% 2.49/1.85 inference(monotonicity,[status(thm)],[73])).
% 2.49/1.85 tff(75,plain,
% 2.49/1.85 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h1(f)), n0) | (~connection(in(n2, h1(f)), in(n2, and2(h1(f))))) | (~value(in(n2, and2(h1(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n2, h1(f)), n0) | (~value(in(n2, and2(h1(f))), n0)) | (~connection(in(n2, h1(f)), in(n2, and2(h1(f))))))),
% 2.49/1.85 inference(transitivity,[status(thm)],[74, 72])).
% 2.49/1.85 tff(76,plain,
% 2.49/1.85 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h1(f)), n0) | (~connection(in(n2, h1(f)), in(n2, and2(h1(f))))) | (~value(in(n2, and2(h1(f))), n0)))),
% 2.49/1.85 inference(quant_inst,[status(thm)],[])).
% 2.49/1.85 tff(77,plain,
% 2.49/1.85 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n2, h1(f)), n0) | (~value(in(n2, and2(h1(f))), n0)) | (~connection(in(n2, h1(f)), in(n2, and2(h1(f)))))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[76, 75])).
% 2.49/1.85 tff(78,plain,
% 2.49/1.85 (~value(in(n2, and2(h1(f))), n0)),
% 2.49/1.85 inference(unit_resolution,[status(thm)],[77, 45, 71, 49])).
% 2.49/1.85 tff(79,plain,
% 2.49/1.85 (^[X: $i] : refl(((~type(X, halfadder)) | type(and2(X), and)) <=> ((~type(X, halfadder)) | type(and2(X), and)))),
% 2.49/1.85 inference(bind,[status(th)],[])).
% 2.49/1.85 tff(80,plain,
% 2.49/1.85 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 2.49/1.85 inference(quant_intro,[status(thm)],[79])).
% 2.49/1.85 tff(81,plain,
% 2.49/1.85 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(82,axiom,(![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_and2')).
% 2.49/1.85 tff(83,plain,
% 2.49/1.85 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[82, 81])).
% 2.49/1.85 tff(84,plain,(
% 2.49/1.85 ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 2.49/1.85 inference(skolemize,[status(sab)],[83])).
% 2.49/1.85 tff(85,plain,
% 2.49/1.85 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[84, 80])).
% 2.49/1.85 tff(86,plain,
% 2.49/1.85 (((~![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))),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(87,plain,
% 2.49/1.85 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h1(f), halfadder)) | type(and2(h1(f)), and))),
% 2.49/1.85 inference(quant_inst,[status(thm)],[])).
% 2.49/1.85 tff(88,plain,
% 2.49/1.85 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h1(f), halfadder)) | type(and2(h1(f)), and)),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[87, 86])).
% 2.49/1.85 tff(89,plain,
% 2.49/1.85 (type(and2(h1(f)), and)),
% 2.49/1.85 inference(unit_resolution,[status(thm)],[88, 85, 60])).
% 2.49/1.85 tff(90,plain,
% 2.49/1.85 ((~mode(and2(h1(f)), abnormal)) <=> (~mode(and2(h1(f)), abnormal))),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(91,axiom,(~mode(and2(h1(f)), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_and2h1')).
% 2.49/1.85 tff(92,plain,
% 2.49/1.85 (~mode(and2(h1(f)), abnormal)),
% 2.49/1.85 inference(modus_ponens,[status(thm)],[91, 90])).
% 2.49/1.85 tff(93,plain,
% 2.49/1.85 (^[Any: $i, K: $i] : refl((mode(K, abnormal) | mode(K, ok) | (~type(K, Any))) <=> (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))))),
% 2.49/1.85 inference(bind,[status(th)],[])).
% 2.49/1.85 tff(94,plain,
% 2.49/1.85 (![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)))),
% 2.49/1.85 inference(quant_intro,[status(thm)],[93])).
% 2.49/1.85 tff(95,plain,
% 2.49/1.85 (![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)))),
% 2.49/1.85 inference(rewrite,[status(thm)],[])).
% 2.49/1.85 tff(96,plain,
% 2.49/1.85 (^[Any: $i, K: $i] : rewrite((((~type(K, Any)) | mode(K, ok)) | mode(K, abnormal)) <=> (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))))),
% 2.49/1.85 inference(bind,[status(th)],[])).
% 2.49/1.85 tff(97,plain,
% 2.49/1.85 (![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)))),
% 2.49/1.85 inference(quant_intro,[status(thm)],[96])).
% 2.49/1.85 tff(98,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')).
% 2.49/1.86 tff(99,plain,
% 2.49/1.86 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[98, 97])).
% 2.49/1.86 tff(100,plain,
% 2.49/1.86 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[99, 95])).
% 2.49/1.86 tff(101,plain,(
% 2.49/1.86 ![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 2.49/1.86 inference(skolemize,[status(sab)],[100])).
% 2.49/1.86 tff(102,plain,
% 2.49/1.86 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[101, 94])).
% 2.49/1.86 tff(103,plain,
% 2.49/1.86 (((~![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)))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(104,plain,
% 2.49/1.86 ((~![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)))),
% 2.49/1.86 inference(quant_inst,[status(thm)],[])).
% 2.49/1.86 tff(105,plain,
% 2.49/1.86 ((~![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))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[104, 103])).
% 2.49/1.86 tff(106,plain,
% 2.49/1.86 (mode(and2(h1(f)), ok)),
% 2.49/1.86 inference(unit_resolution,[status(thm)],[105, 102, 92, 89])).
% 2.49/1.86 tff(107,plain,
% 2.49/1.86 (^[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)))))),
% 2.49/1.86 inference(bind,[status(th)],[])).
% 2.49/1.86 tff(108,plain,
% 2.49/1.86 (![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))))),
% 2.49/1.86 inference(quant_intro,[status(thm)],[107])).
% 2.49/1.86 tff(109,plain,
% 2.49/1.86 (![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))))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(110,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')).
% 2.49/1.86 tff(111,plain,
% 2.49/1.86 (![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[110, 109])).
% 2.49/1.86 tff(112,plain,(
% 2.49/1.86 ![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 2.49/1.86 inference(skolemize,[status(sab)],[111])).
% 2.49/1.86 tff(113,plain,
% 2.49/1.86 (![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[112, 108])).
% 2.49/1.86 tff(114,plain,
% 2.49/1.86 (((~![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))))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(115,plain,
% 2.49/1.86 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | ((~type(f, fulladder)) | connection(in(n2, f), in(n1, h1(f))))),
% 2.49/1.86 inference(quant_inst,[status(thm)],[])).
% 2.49/1.86 tff(116,plain,
% 2.49/1.86 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | (~type(f, fulladder)) | connection(in(n2, f), in(n1, h1(f)))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[115, 114])).
% 2.49/1.86 tff(117,plain,
% 2.49/1.86 (connection(in(n2, f), in(n1, h1(f)))),
% 2.49/1.86 inference(unit_resolution,[status(thm)],[116, 113, 4])).
% 2.49/1.86 tff(118,plain,
% 2.49/1.86 (value(in(n2, f), n1) <=> value(in(n2, f), n1)),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(119,axiom,(value(in(n2, f), n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','in2_0')).
% 2.49/1.86 tff(120,plain,
% 2.49/1.86 (value(in(n2, f), n1)),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[119, 118])).
% 2.49/1.86 tff(121,plain,
% 2.49/1.86 (((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(in(n2, f), n1)) | (~value(in(n2, f), n0)))) <=> ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n0, n1) | (~value(in(n2, f), n1)) | (~value(in(n2, f), n0)))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(122,plain,
% 2.49/1.86 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(in(n2, f), n1)) | (~value(in(n2, f), n0)))),
% 2.49/1.86 inference(quant_inst,[status(thm)],[])).
% 2.49/1.86 tff(123,plain,
% 2.49/1.86 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n0, n1) | (~value(in(n2, f), n1)) | (~value(in(n2, f), n0))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[122, 121])).
% 2.49/1.86 tff(124,plain,
% 2.49/1.86 (~value(in(n2, f), n0)),
% 2.49/1.86 inference(unit_resolution,[status(thm)],[123, 31, 21, 120])).
% 2.49/1.86 tff(125,plain,
% 2.49/1.86 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (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(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n2, f), n0) | (~connection(in(n2, f), in(n1, h1(f)))) | (~value(in(n1, h1(f)), n0)))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(126,plain,
% 2.49/1.86 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, f), n0) | (~connection(in(n2, f), in(n1, h1(f)))) | (~value(in(n1, h1(f)), n0)))),
% 2.49/1.86 inference(quant_inst,[status(thm)],[])).
% 2.49/1.86 tff(127,plain,
% 2.49/1.86 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n2, f), n0) | (~connection(in(n2, f), in(n1, h1(f)))) | (~value(in(n1, h1(f)), n0))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[126, 125])).
% 2.49/1.86 tff(128,plain,
% 2.49/1.86 (~value(in(n1, h1(f)), n0)),
% 2.49/1.86 inference(unit_resolution,[status(thm)],[127, 45, 124, 117])).
% 2.49/1.86 tff(129,plain,
% 2.49/1.86 (^[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)))))),
% 2.49/1.86 inference(bind,[status(th)],[])).
% 2.49/1.86 tff(130,plain,
% 2.49/1.86 (![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))))),
% 2.49/1.86 inference(quant_intro,[status(thm)],[129])).
% 2.49/1.86 tff(131,plain,
% 2.49/1.86 (![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))))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(132,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')).
% 2.49/1.86 tff(133,plain,
% 2.49/1.86 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[132, 131])).
% 2.49/1.86 tff(134,plain,(
% 2.49/1.86 ![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 2.49/1.86 inference(skolemize,[status(sab)],[133])).
% 2.49/1.86 tff(135,plain,
% 2.49/1.86 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[134, 130])).
% 2.49/1.86 tff(136,plain,
% 2.49/1.86 (((~![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)))))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(137,plain,
% 2.49/1.86 ((~![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)))))),
% 2.49/1.86 inference(quant_inst,[status(thm)],[])).
% 2.49/1.86 tff(138,plain,
% 2.49/1.86 ((~![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))))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[137, 136])).
% 2.49/1.86 tff(139,plain,
% 2.49/1.86 (connection(in(n1, h1(f)), in(n1, and2(h1(f))))),
% 2.49/1.86 inference(unit_resolution,[status(thm)],[138, 135, 60])).
% 2.49/1.86 tff(140,plain,
% 2.49/1.86 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h1(f)), n0) | (~value(in(n1, and2(h1(f))), n0)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h1(f)), n0) | (~value(in(n1, and2(h1(f))), n0)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(141,plain,
% 2.49/1.86 ((value(in(n1, h1(f)), n0) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))) | (~value(in(n1, and2(h1(f))), n0))) <=> (value(in(n1, h1(f)), n0) | (~value(in(n1, and2(h1(f))), n0)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(142,plain,
% 2.49/1.86 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h1(f)), n0) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))) | (~value(in(n1, and2(h1(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h1(f)), n0) | (~value(in(n1, and2(h1(f))), n0)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f)))))))),
% 2.49/1.86 inference(monotonicity,[status(thm)],[141])).
% 2.49/1.86 tff(143,plain,
% 2.49/1.86 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h1(f)), n0) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))) | (~value(in(n1, and2(h1(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h1(f)), n0) | (~value(in(n1, and2(h1(f))), n0)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))))),
% 2.49/1.86 inference(transitivity,[status(thm)],[142, 140])).
% 2.49/1.86 tff(144,plain,
% 2.49/1.86 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h1(f)), n0) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))) | (~value(in(n1, and2(h1(f))), n0)))),
% 2.49/1.86 inference(quant_inst,[status(thm)],[])).
% 2.49/1.86 tff(145,plain,
% 2.49/1.86 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h1(f)), n0) | (~value(in(n1, and2(h1(f))), n0)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f)))))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[144, 143])).
% 2.49/1.86 tff(146,plain,
% 2.49/1.86 (~value(in(n1, and2(h1(f))), n0)),
% 2.49/1.86 inference(unit_resolution,[status(thm)],[145, 45, 139, 128])).
% 2.49/1.86 tff(147,plain,
% 2.49/1.86 (^[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))))),
% 2.49/1.86 inference(bind,[status(th)],[])).
% 2.49/1.86 tff(148,plain,
% 2.49/1.86 (![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)))),
% 2.49/1.86 inference(quant_intro,[status(thm)],[147])).
% 2.49/1.86 tff(149,plain,
% 2.49/1.86 (![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)))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(150,plain,
% 2.49/1.86 (^[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)))))),
% 2.49/1.86 inference(bind,[status(th)],[])).
% 2.49/1.86 tff(151,plain,
% 2.49/1.86 (![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)))),
% 2.49/1.86 inference(quant_intro,[status(thm)],[150])).
% 2.49/1.86 tff(152,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')).
% 2.49/1.86 tff(153,plain,
% 2.49/1.86 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[152, 151])).
% 2.49/1.86 tff(154,plain,
% 2.49/1.86 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[153, 149])).
% 2.49/1.86 tff(155,plain,(
% 2.49/1.86 ![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 2.49/1.86 inference(skolemize,[status(sab)],[154])).
% 2.49/1.86 tff(156,plain,
% 2.49/1.86 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[155, 148])).
% 2.49/1.86 tff(157,plain,
% 2.49/1.86 (((~![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(h1(f)), ok)) | value(in(n1, and2(h1(f))), n0) | (~value(out(n1, and2(h1(f))), n0)) | value(in(n2, and2(h1(f))), n0) | (~type(and2(h1(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(h1(f)), ok)) | value(in(n1, and2(h1(f))), n0) | (~value(out(n1, and2(h1(f))), n0)) | value(in(n2, and2(h1(f))), n0) | (~type(and2(h1(f)), and)))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(158,plain,
% 2.49/1.86 (((~mode(and2(h1(f)), ok)) | (~type(and2(h1(f)), and)) | value(in(n2, and2(h1(f))), n0) | value(in(n1, and2(h1(f))), n0) | (~value(out(n1, and2(h1(f))), n0))) <=> ((~mode(and2(h1(f)), ok)) | value(in(n1, and2(h1(f))), n0) | (~value(out(n1, and2(h1(f))), n0)) | value(in(n2, and2(h1(f))), n0) | (~type(and2(h1(f)), and)))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(159,plain,
% 2.49/1.86 (((~![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(h1(f)), ok)) | (~type(and2(h1(f)), and)) | value(in(n2, and2(h1(f))), n0) | value(in(n1, and2(h1(f))), n0) | (~value(out(n1, and2(h1(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(h1(f)), ok)) | value(in(n1, and2(h1(f))), n0) | (~value(out(n1, and2(h1(f))), n0)) | value(in(n2, and2(h1(f))), n0) | (~type(and2(h1(f)), and))))),
% 2.49/1.86 inference(monotonicity,[status(thm)],[158])).
% 2.49/1.86 tff(160,plain,
% 2.49/1.86 (((~![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(h1(f)), ok)) | (~type(and2(h1(f)), and)) | value(in(n2, and2(h1(f))), n0) | value(in(n1, and2(h1(f))), n0) | (~value(out(n1, and2(h1(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(h1(f)), ok)) | value(in(n1, and2(h1(f))), n0) | (~value(out(n1, and2(h1(f))), n0)) | value(in(n2, and2(h1(f))), n0) | (~type(and2(h1(f)), and)))),
% 2.49/1.86 inference(transitivity,[status(thm)],[159, 157])).
% 2.49/1.86 tff(161,plain,
% 2.49/1.86 ((~![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(h1(f)), ok)) | (~type(and2(h1(f)), and)) | value(in(n2, and2(h1(f))), n0) | value(in(n1, and2(h1(f))), n0) | (~value(out(n1, and2(h1(f))), n0)))),
% 2.49/1.86 inference(quant_inst,[status(thm)],[])).
% 2.49/1.86 tff(162,plain,
% 2.49/1.86 ((~![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(h1(f)), ok)) | value(in(n1, and2(h1(f))), n0) | (~value(out(n1, and2(h1(f))), n0)) | value(in(n2, and2(h1(f))), n0) | (~type(and2(h1(f)), and))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[161, 160])).
% 2.49/1.86 tff(163,plain,
% 2.49/1.86 ((~mode(and2(h1(f)), ok)) | value(in(n1, and2(h1(f))), n0) | (~value(out(n1, and2(h1(f))), n0)) | value(in(n2, and2(h1(f))), n0)),
% 2.49/1.86 inference(unit_resolution,[status(thm)],[162, 156, 89])).
% 2.49/1.86 tff(164,plain,
% 2.49/1.86 (~value(out(n1, and2(h1(f))), n0)),
% 2.49/1.86 inference(unit_resolution,[status(thm)],[163, 146, 106, 78])).
% 2.49/1.86 tff(165,plain,
% 2.49/1.86 (^[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)))))),
% 2.49/1.86 inference(bind,[status(th)],[])).
% 2.49/1.86 tff(166,plain,
% 2.49/1.86 (![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))))),
% 2.49/1.86 inference(quant_intro,[status(thm)],[165])).
% 2.49/1.86 tff(167,plain,
% 2.49/1.86 (![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))))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(168,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')).
% 2.49/1.86 tff(169,plain,
% 2.49/1.86 (![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[168, 167])).
% 2.49/1.86 tff(170,plain,(
% 2.49/1.86 ![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 2.49/1.86 inference(skolemize,[status(sab)],[169])).
% 2.49/1.86 tff(171,plain,
% 2.49/1.86 (![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[170, 166])).
% 2.49/1.86 tff(172,plain,
% 2.49/1.86 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h1(f), halfadder)) | connection(out(c, h1(f)), out(n1, and2(h1(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h1(f), halfadder)) | connection(out(c, h1(f)), out(n1, and2(h1(f)))))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(173,plain,
% 2.49/1.86 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h1(f), halfadder)) | connection(out(c, h1(f)), out(n1, and2(h1(f)))))),
% 2.49/1.86 inference(quant_inst,[status(thm)],[])).
% 2.49/1.86 tff(174,plain,
% 2.49/1.86 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h1(f), halfadder)) | connection(out(c, h1(f)), out(n1, and2(h1(f))))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[173, 172])).
% 2.49/1.86 tff(175,plain,
% 2.49/1.86 (connection(out(c, h1(f)), out(n1, and2(h1(f))))),
% 2.49/1.86 inference(unit_resolution,[status(thm)],[174, 171, 60])).
% 2.49/1.86 tff(176,plain,
% 2.49/1.86 (^[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))))),
% 2.49/1.86 inference(bind,[status(th)],[])).
% 2.49/1.86 tff(177,plain,
% 2.49/1.86 (![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)))),
% 2.49/1.86 inference(quant_intro,[status(thm)],[176])).
% 2.49/1.86 tff(178,plain,
% 2.49/1.86 (![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)))),
% 2.49/1.86 inference(rewrite,[status(thm)],[])).
% 2.49/1.86 tff(179,plain,
% 2.49/1.86 (^[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))))),
% 2.49/1.86 inference(bind,[status(th)],[])).
% 2.49/1.86 tff(180,plain,
% 2.49/1.86 (![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)))),
% 2.49/1.86 inference(quant_intro,[status(thm)],[179])).
% 2.49/1.86 tff(181,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')).
% 2.49/1.86 tff(182,plain,
% 2.49/1.86 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[181, 180])).
% 2.49/1.86 tff(183,plain,
% 2.49/1.86 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[182, 178])).
% 2.49/1.86 tff(184,plain,(
% 2.49/1.86 ![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 2.49/1.86 inference(skolemize,[status(sab)],[183])).
% 2.49/1.86 tff(185,plain,
% 2.49/1.86 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 2.49/1.86 inference(modus_ponens,[status(thm)],[184, 177])).
% 2.49/1.86 tff(186,plain,
% 2.49/1.86 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and2(h1(f))), n0) | (~value(out(c, h1(f)), n0)) | (~connection(out(c, h1(f)), out(n1, and2(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, and2(h1(f))), n0) | (~value(out(c, h1(f)), n0)) | (~connection(out(c, h1(f)), out(n1, and2(h1(f))))))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(187,plain,
% 2.49/1.87 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and2(h1(f))), n0) | (~value(out(c, h1(f)), n0)) | (~connection(out(c, h1(f)), out(n1, and2(h1(f))))))),
% 2.49/1.87 inference(quant_inst,[status(thm)],[])).
% 2.49/1.87 tff(188,plain,
% 2.49/1.87 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, and2(h1(f))), n0) | (~value(out(c, h1(f)), n0)) | (~connection(out(c, h1(f)), out(n1, and2(h1(f)))))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[187, 186])).
% 2.49/1.87 tff(189,plain,
% 2.49/1.87 ($false),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[188, 185, 175, 164, 1])).
% 2.49/1.87 tff(190,plain,(~value(out(c, h1(f)), n0)), inference(lemma,lemma(discharge,[]))).
% 2.49/1.87 tff(191,plain,
% 2.49/1.87 (^[X: $i] : refl(((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X)))) <=> ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X)))))),
% 2.49/1.87 inference(bind,[status(th)],[])).
% 2.49/1.87 tff(192,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 2.49/1.87 inference(quant_intro,[status(thm)],[191])).
% 2.49/1.87 tff(193,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(194,axiom,(![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_connection_outch1_in2or1')).
% 2.49/1.87 tff(195,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[194, 193])).
% 2.49/1.87 tff(196,plain,(
% 2.49/1.87 ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 2.49/1.87 inference(skolemize,[status(sab)],[195])).
% 2.49/1.87 tff(197,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[196, 192])).
% 2.49/1.87 tff(198,plain,
% 2.49/1.87 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))) | ((~type(f, fulladder)) | connection(out(c, h1(f)), in(n2, or1(f))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))) | (~type(f, fulladder)) | connection(out(c, h1(f)), in(n2, or1(f))))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(199,plain,
% 2.49/1.87 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))) | ((~type(f, fulladder)) | connection(out(c, h1(f)), in(n2, or1(f))))),
% 2.49/1.87 inference(quant_inst,[status(thm)],[])).
% 2.49/1.87 tff(200,plain,
% 2.49/1.87 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))) | (~type(f, fulladder)) | connection(out(c, h1(f)), in(n2, or1(f)))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[199, 198])).
% 2.49/1.87 tff(201,plain,
% 2.49/1.87 (connection(out(c, h1(f)), in(n2, or1(f)))),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[200, 197, 4])).
% 2.49/1.87 tff(202,plain,
% 2.49/1.87 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n2, or1(f)), n0)) | (~connection(out(c, h1(f)), in(n2, or1(f)))) | value(out(c, h1(f)), n0))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, or1(f)), n0)) | (~connection(out(c, h1(f)), in(n2, or1(f)))) | value(out(c, h1(f)), n0))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(203,plain,
% 2.49/1.87 ((value(out(c, h1(f)), n0) | (~connection(out(c, h1(f)), in(n2, or1(f)))) | (~value(in(n2, or1(f)), n0))) <=> ((~value(in(n2, or1(f)), n0)) | (~connection(out(c, h1(f)), in(n2, or1(f)))) | value(out(c, h1(f)), n0))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(204,plain,
% 2.49/1.87 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h1(f)), n0) | (~connection(out(c, h1(f)), in(n2, or1(f)))) | (~value(in(n2, or1(f)), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n2, or1(f)), n0)) | (~connection(out(c, h1(f)), in(n2, or1(f)))) | value(out(c, h1(f)), n0)))),
% 2.49/1.87 inference(monotonicity,[status(thm)],[203])).
% 2.49/1.87 tff(205,plain,
% 2.49/1.87 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h1(f)), n0) | (~connection(out(c, h1(f)), in(n2, or1(f)))) | (~value(in(n2, or1(f)), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, or1(f)), n0)) | (~connection(out(c, h1(f)), in(n2, or1(f)))) | value(out(c, h1(f)), n0))),
% 2.49/1.87 inference(transitivity,[status(thm)],[204, 202])).
% 2.49/1.87 tff(206,plain,
% 2.49/1.87 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h1(f)), n0) | (~connection(out(c, h1(f)), in(n2, or1(f)))) | (~value(in(n2, or1(f)), n0)))),
% 2.49/1.87 inference(quant_inst,[status(thm)],[])).
% 2.49/1.87 tff(207,plain,
% 2.49/1.87 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, or1(f)), n0)) | (~connection(out(c, h1(f)), in(n2, or1(f)))) | value(out(c, h1(f)), n0)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[206, 205])).
% 2.49/1.87 tff(208,plain,
% 2.49/1.87 ((~value(in(n2, or1(f)), n0)) | value(out(c, h1(f)), n0)),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[207, 45, 201])).
% 2.49/1.87 tff(209,plain,
% 2.49/1.87 (~value(in(n2, or1(f)), n0)),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[208, 190])).
% 2.49/1.87 tff(210,assumption,(~value(out(n1, or1(f)), n0)), introduced(assumption)).
% 2.49/1.87 tff(211,plain,
% 2.49/1.87 (^[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)))))),
% 2.49/1.87 inference(bind,[status(th)],[])).
% 2.49/1.87 tff(212,plain,
% 2.49/1.87 (![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))))),
% 2.49/1.87 inference(quant_intro,[status(thm)],[211])).
% 2.49/1.87 tff(213,plain,
% 2.49/1.87 (![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))))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(214,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')).
% 2.49/1.87 tff(215,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[214, 213])).
% 2.49/1.87 tff(216,plain,(
% 2.49/1.87 ![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 2.49/1.87 inference(skolemize,[status(sab)],[215])).
% 2.49/1.87 tff(217,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[216, 212])).
% 2.49/1.87 tff(218,plain,
% 2.49/1.87 (((~![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))))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(219,plain,
% 2.49/1.87 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | ((~type(f, fulladder)) | connection(out(c, f), out(n1, or1(f))))),
% 2.49/1.87 inference(quant_inst,[status(thm)],[])).
% 2.49/1.87 tff(220,plain,
% 2.49/1.87 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | (~type(f, fulladder)) | connection(out(c, f), out(n1, or1(f)))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[219, 218])).
% 2.49/1.87 tff(221,plain,
% 2.49/1.87 (connection(out(c, f), out(n1, or1(f)))),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[220, 217, 4])).
% 2.49/1.87 tff(222,plain,
% 2.49/1.87 (value(out(c, f), n0) <=> value(out(c, f), n0)),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(223,axiom,(value(out(c, f), n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','outc_0')).
% 2.49/1.87 tff(224,plain,
% 2.49/1.87 (value(out(c, f), n0)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[223, 222])).
% 2.49/1.87 tff(225,plain,
% 2.49/1.87 (((~![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))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(226,plain,
% 2.49/1.87 ((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))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(227,plain,
% 2.49/1.87 (((~![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)))),
% 2.49/1.87 inference(monotonicity,[status(thm)],[226])).
% 2.49/1.87 tff(228,plain,
% 2.49/1.87 (((~![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))),
% 2.49/1.87 inference(transitivity,[status(thm)],[227, 225])).
% 2.49/1.87 tff(229,plain,
% 2.49/1.87 ((~![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)))))),
% 2.49/1.87 inference(quant_inst,[status(thm)],[])).
% 2.49/1.87 tff(230,plain,
% 2.49/1.87 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))) | value(out(n1, or1(f)), n0)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[229, 228])).
% 2.49/1.87 tff(231,plain,
% 2.49/1.87 ($false),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[230, 185, 224, 221, 210])).
% 2.49/1.87 tff(232,plain,(value(out(n1, or1(f)), n0)), inference(lemma,lemma(discharge,[]))).
% 2.49/1.87 tff(233,plain,
% 2.49/1.87 (^[X: $i] : refl(((~type(X, fulladder)) | type(or1(X), or)) <=> ((~type(X, fulladder)) | type(or1(X), or)))),
% 2.49/1.87 inference(bind,[status(th)],[])).
% 2.49/1.87 tff(234,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 2.49/1.87 inference(quant_intro,[status(thm)],[233])).
% 2.49/1.87 tff(235,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(236,axiom,(![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_or1')).
% 2.49/1.87 tff(237,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[236, 235])).
% 2.49/1.87 tff(238,plain,(
% 2.49/1.87 ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 2.49/1.87 inference(skolemize,[status(sab)],[237])).
% 2.49/1.87 tff(239,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[238, 234])).
% 2.49/1.87 tff(240,plain,
% 2.49/1.87 (((~![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))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(241,plain,
% 2.49/1.87 ((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | ((~type(f, fulladder)) | type(or1(f), or))),
% 2.49/1.87 inference(quant_inst,[status(thm)],[])).
% 2.49/1.87 tff(242,plain,
% 2.49/1.87 ((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | (~type(f, fulladder)) | type(or1(f), or)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[241, 240])).
% 2.49/1.87 tff(243,plain,
% 2.49/1.87 (type(or1(f), or)),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[242, 239, 4])).
% 2.49/1.87 tff(244,plain,
% 2.49/1.87 (^[K: $i] : refl(((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or))) <=> ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or))))),
% 2.49/1.87 inference(bind,[status(th)],[])).
% 2.49/1.87 tff(245,plain,
% 2.49/1.87 (![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or))) <=> ![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 2.49/1.87 inference(quant_intro,[status(thm)],[244])).
% 2.49/1.87 tff(246,plain,
% 2.49/1.87 (![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or))) <=> ![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(247,plain,
% 2.49/1.87 (^[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(n2, K), n0)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n0)) | (~type(K, or))) | value(in(n2, K), n0)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n0)) | (~type(K, or))) | value(in(n2, K), n0)) <=> ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))), (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) | value(in(n2, K), n0)) <=> ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))))),
% 2.49/1.87 inference(bind,[status(th)],[])).
% 2.49/1.87 tff(248,plain,
% 2.49/1.87 (![K: $i] : ((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) | value(in(n2, K), n0)) <=> ![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 2.49/1.87 inference(quant_intro,[status(thm)],[247])).
% 2.49/1.87 tff(249,axiom,(![K: $i] : ((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) | value(in(n2, K), n0))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','or_0_01')).
% 2.49/1.87 tff(250,plain,
% 2.49/1.87 (![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[249, 248])).
% 2.49/1.87 tff(251,plain,
% 2.49/1.87 (![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[250, 246])).
% 2.49/1.87 tff(252,plain,(
% 2.49/1.87 ![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 2.49/1.87 inference(skolemize,[status(sab)],[251])).
% 2.49/1.87 tff(253,plain,
% 2.49/1.87 (![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[252, 245])).
% 2.49/1.87 tff(254,plain,
% 2.49/1.87 (((~![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n2, or1(f)), n0) | (~type(or1(f), or)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | (~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n2, or1(f)), n0) | (~type(or1(f), or)))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(255,plain,
% 2.49/1.87 (((~mode(or1(f), ok)) | value(in(n2, 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(n2, or1(f)), n0) | (~type(or1(f), or)))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(256,plain,
% 2.49/1.87 (((~![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(f), ok)) | value(in(n2, or1(f)), n0) | (~value(out(n1, or1(f)), n0)) | (~type(or1(f), or)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n2, or1(f)), n0) | (~type(or1(f), or))))),
% 2.49/1.87 inference(monotonicity,[status(thm)],[255])).
% 2.49/1.87 tff(257,plain,
% 2.49/1.87 (((~![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(f), ok)) | value(in(n2, or1(f)), n0) | (~value(out(n1, or1(f)), n0)) | (~type(or1(f), or)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | (~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n2, or1(f)), n0) | (~type(or1(f), or)))),
% 2.49/1.87 inference(transitivity,[status(thm)],[256, 254])).
% 2.49/1.87 tff(258,plain,
% 2.49/1.87 ((~![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(f), ok)) | value(in(n2, or1(f)), n0) | (~value(out(n1, or1(f)), n0)) | (~type(or1(f), or)))),
% 2.49/1.87 inference(quant_inst,[status(thm)],[])).
% 2.49/1.87 tff(259,plain,
% 2.49/1.87 ((~![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | (~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n2, or1(f)), n0) | (~type(or1(f), or))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[258, 257])).
% 2.49/1.87 tff(260,plain,
% 2.49/1.87 ((~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n2, or1(f)), n0)),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[259, 253, 243])).
% 2.49/1.87 tff(261,plain,
% 2.49/1.87 ((~mode(or1(f), ok)) | value(in(n2, or1(f)), n0)),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[260, 232])).
% 2.49/1.87 tff(262,plain,
% 2.49/1.87 (~mode(or1(f), ok)),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[261, 209])).
% 2.49/1.87 tff(263,plain,
% 2.49/1.87 (((~![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)))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(264,plain,
% 2.49/1.87 ((~![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)))),
% 2.49/1.87 inference(quant_inst,[status(thm)],[])).
% 2.49/1.87 tff(265,plain,
% 2.49/1.87 ((~![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))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[264, 263])).
% 2.49/1.87 tff(266,plain,
% 2.49/1.87 (mode(or1(f), abnormal) | mode(or1(f), ok)),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[265, 102, 243])).
% 2.49/1.87 tff(267,plain,
% 2.49/1.87 (mode(or1(f), abnormal)),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[266, 262])).
% 2.49/1.87 tff(268,plain,
% 2.49/1.87 (((~mode(or1(f), abnormal)) | (~mode(or1(h2(f)), abnormal))) <=> ((~mode(or1(f), abnormal)) | (~mode(or1(h2(f)), abnormal)))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(269,axiom,((~mode(or1(f), abnormal)) | (~mode(or1(h2(f)), abnormal))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_or1_or1h2')).
% 2.49/1.87 tff(270,plain,
% 2.49/1.87 ((~mode(or1(f), abnormal)) | (~mode(or1(h2(f)), abnormal))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[269, 268])).
% 2.49/1.87 tff(271,plain,
% 2.49/1.87 (~mode(or1(h2(f)), abnormal)),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[270, 267])).
% 2.49/1.87 tff(272,plain,
% 2.49/1.87 (^[X: $i] : refl(((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ((~type(X, fulladder)) | type(h2(X), halfadder)))),
% 2.49/1.87 inference(bind,[status(th)],[])).
% 2.49/1.87 tff(273,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 2.49/1.87 inference(quant_intro,[status(thm)],[272])).
% 2.49/1.87 tff(274,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(275,axiom,(![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_halfadder2')).
% 2.49/1.87 tff(276,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[275, 274])).
% 2.49/1.87 tff(277,plain,(
% 2.49/1.87 ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 2.49/1.87 inference(skolemize,[status(sab)],[276])).
% 2.49/1.87 tff(278,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[277, 273])).
% 2.49/1.87 tff(279,plain,
% 2.49/1.87 (((~![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))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(280,plain,
% 2.49/1.87 ((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | ((~type(f, fulladder)) | type(h2(f), halfadder))),
% 2.49/1.87 inference(quant_inst,[status(thm)],[])).
% 2.49/1.87 tff(281,plain,
% 2.49/1.87 ((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | (~type(f, fulladder)) | type(h2(f), halfadder)),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[280, 279])).
% 2.49/1.87 tff(282,plain,
% 2.49/1.87 (type(h2(f), halfadder)),
% 2.49/1.87 inference(unit_resolution,[status(thm)],[281, 278, 4])).
% 2.49/1.87 tff(283,plain,
% 2.49/1.87 (^[X: $i] : refl(((~type(X, halfadder)) | type(or1(X), or)) <=> ((~type(X, halfadder)) | type(or1(X), or)))),
% 2.49/1.87 inference(bind,[status(th)],[])).
% 2.49/1.87 tff(284,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, halfadder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))),
% 2.49/1.87 inference(quant_intro,[status(thm)],[283])).
% 2.49/1.87 tff(285,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, halfadder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.87 tff(286,axiom,(![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_or1')).
% 2.49/1.87 tff(287,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[286, 285])).
% 2.49/1.87 tff(288,plain,(
% 2.49/1.87 ![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))),
% 2.49/1.87 inference(skolemize,[status(sab)],[287])).
% 2.49/1.87 tff(289,plain,
% 2.49/1.87 (![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))),
% 2.49/1.87 inference(modus_ponens,[status(thm)],[288, 284])).
% 2.49/1.87 tff(290,plain,
% 2.49/1.87 (((~![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))) | ((~type(h2(f), halfadder)) | type(or1(h2(f)), or))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))) | (~type(h2(f), halfadder)) | type(or1(h2(f)), or))),
% 2.49/1.87 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(291,plain,
% 2.49/1.88 ((~![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))) | ((~type(h2(f), halfadder)) | type(or1(h2(f)), or))),
% 2.49/1.88 inference(quant_inst,[status(thm)],[])).
% 2.49/1.88 tff(292,plain,
% 2.49/1.88 ((~![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))) | (~type(h2(f), halfadder)) | type(or1(h2(f)), or)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[291, 290])).
% 2.49/1.88 tff(293,plain,
% 2.49/1.88 (type(or1(h2(f)), or)),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[292, 289, 282])).
% 2.49/1.88 tff(294,plain,
% 2.49/1.88 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(or1(h2(f)), abnormal) | mode(or1(h2(f)), ok) | (~type(or1(h2(f)), or)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(or1(h2(f)), abnormal) | mode(or1(h2(f)), ok) | (~type(or1(h2(f)), or)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(295,plain,
% 2.49/1.88 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(or1(h2(f)), abnormal) | mode(or1(h2(f)), ok) | (~type(or1(h2(f)), or)))),
% 2.49/1.88 inference(quant_inst,[status(thm)],[])).
% 2.49/1.88 tff(296,plain,
% 2.49/1.88 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(or1(h2(f)), abnormal) | mode(or1(h2(f)), ok) | (~type(or1(h2(f)), or))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[295, 294])).
% 2.49/1.88 tff(297,plain,
% 2.49/1.88 (mode(or1(h2(f)), abnormal) | mode(or1(h2(f)), ok)),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[296, 102, 293])).
% 2.49/1.88 tff(298,plain,
% 2.49/1.88 (mode(or1(h2(f)), ok)),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[297, 271])).
% 2.49/1.88 tff(299,assumption,(~value(out(n1, or1(h2(f))), n1)), introduced(assumption)).
% 2.49/1.88 tff(300,plain,
% 2.49/1.88 (((~mode(or1(f), abnormal)) | (~mode(and1(h2(f)), abnormal))) <=> ((~mode(or1(f), abnormal)) | (~mode(and1(h2(f)), abnormal)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(301,axiom,((~mode(or1(f), abnormal)) | (~mode(and1(h2(f)), abnormal))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_or1_and1h2')).
% 2.49/1.88 tff(302,plain,
% 2.49/1.88 ((~mode(or1(f), abnormal)) | (~mode(and1(h2(f)), abnormal))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[301, 300])).
% 2.49/1.88 tff(303,plain,
% 2.49/1.88 (~mode(and1(h2(f)), abnormal)),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[302, 267])).
% 2.49/1.88 tff(304,plain,
% 2.49/1.88 (^[X: $i] : refl(((~type(X, halfadder)) | type(and1(X), and)) <=> ((~type(X, halfadder)) | type(and1(X), and)))),
% 2.49/1.88 inference(bind,[status(th)],[])).
% 2.49/1.88 tff(305,plain,
% 2.49/1.88 (![X: $i] : ((~type(X, halfadder)) | type(and1(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))),
% 2.49/1.88 inference(quant_intro,[status(thm)],[304])).
% 2.49/1.88 tff(306,plain,
% 2.49/1.88 (![X: $i] : ((~type(X, halfadder)) | type(and1(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(307,axiom,(![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_and1')).
% 2.49/1.88 tff(308,plain,
% 2.49/1.88 (![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[307, 306])).
% 2.49/1.88 tff(309,plain,(
% 2.49/1.88 ![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))),
% 2.49/1.88 inference(skolemize,[status(sab)],[308])).
% 2.49/1.88 tff(310,plain,
% 2.49/1.88 (![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[309, 305])).
% 2.49/1.88 tff(311,plain,
% 2.49/1.88 (((~![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))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(312,plain,
% 2.49/1.88 ((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | ((~type(h2(f), halfadder)) | type(and1(h2(f)), and))),
% 2.49/1.88 inference(quant_inst,[status(thm)],[])).
% 2.49/1.88 tff(313,plain,
% 2.49/1.88 ((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | (~type(h2(f), halfadder)) | type(and1(h2(f)), and)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[312, 311])).
% 2.49/1.88 tff(314,plain,
% 2.49/1.88 (type(and1(h2(f)), and)),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[313, 310, 282])).
% 2.49/1.88 tff(315,plain,
% 2.49/1.88 (((~![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)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(316,plain,
% 2.49/1.88 ((~![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)))),
% 2.49/1.88 inference(quant_inst,[status(thm)],[])).
% 2.49/1.88 tff(317,plain,
% 2.49/1.88 ((~![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))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[316, 315])).
% 2.49/1.88 tff(318,plain,
% 2.49/1.88 (mode(and1(h2(f)), abnormal) | mode(and1(h2(f)), ok)),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[317, 102, 314])).
% 2.49/1.88 tff(319,plain,
% 2.49/1.88 (mode(and1(h2(f)), ok)),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[318, 303])).
% 2.49/1.88 tff(320,plain,
% 2.49/1.88 (^[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)))))),
% 2.49/1.88 inference(bind,[status(th)],[])).
% 2.49/1.88 tff(321,plain,
% 2.49/1.88 (![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))))),
% 2.49/1.88 inference(quant_intro,[status(thm)],[320])).
% 2.49/1.88 tff(322,plain,
% 2.49/1.88 (![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))))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(323,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')).
% 2.49/1.88 tff(324,plain,
% 2.49/1.88 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[323, 322])).
% 2.49/1.88 tff(325,plain,(
% 2.49/1.88 ![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))),
% 2.49/1.88 inference(skolemize,[status(sab)],[324])).
% 2.49/1.88 tff(326,plain,
% 2.49/1.88 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[325, 321])).
% 2.49/1.88 tff(327,plain,
% 2.49/1.88 (((~![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))))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(328,plain,
% 2.49/1.88 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))) | ((~type(f, fulladder)) | connection(out(s, f), out(s, h2(f))))),
% 2.49/1.88 inference(quant_inst,[status(thm)],[])).
% 2.49/1.88 tff(329,plain,
% 2.49/1.88 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))) | (~type(f, fulladder)) | connection(out(s, f), out(s, h2(f)))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[328, 327])).
% 2.49/1.88 tff(330,plain,
% 2.49/1.88 (connection(out(s, f), out(s, h2(f)))),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[329, 326, 4])).
% 2.49/1.88 tff(331,plain,
% 2.49/1.88 (value(out(s, f), n1) <=> value(out(s, f), n1)),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(332,axiom,(value(out(s, f), n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','outs_1')).
% 2.49/1.88 tff(333,plain,
% 2.49/1.88 (value(out(s, f), n1)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[332, 331])).
% 2.49/1.88 tff(334,plain,
% 2.49/1.88 (((~![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))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(335,plain,
% 2.49/1.88 ((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))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(336,plain,
% 2.49/1.88 (((~![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)))),
% 2.49/1.88 inference(monotonicity,[status(thm)],[335])).
% 2.49/1.88 tff(337,plain,
% 2.49/1.88 (((~![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))),
% 2.49/1.88 inference(transitivity,[status(thm)],[336, 334])).
% 2.49/1.88 tff(338,plain,
% 2.49/1.88 ((~![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)))))),
% 2.49/1.88 inference(quant_inst,[status(thm)],[])).
% 2.49/1.88 tff(339,plain,
% 2.49/1.88 ((~![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)),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[338, 337])).
% 2.49/1.88 tff(340,plain,
% 2.49/1.88 (value(out(s, h2(f)), n1)),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[339, 185, 333, 330])).
% 2.49/1.88 tff(341,assumption,(~value(out(n1, and1(h2(f))), n1)), introduced(assumption)).
% 2.49/1.88 tff(342,plain,
% 2.49/1.88 (^[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)))))),
% 2.49/1.88 inference(bind,[status(th)],[])).
% 2.49/1.88 tff(343,plain,
% 2.49/1.88 (![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))))),
% 2.49/1.88 inference(quant_intro,[status(thm)],[342])).
% 2.49/1.88 tff(344,plain,
% 2.49/1.88 (![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))))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(345,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')).
% 2.49/1.88 tff(346,plain,
% 2.49/1.88 (![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[345, 344])).
% 2.49/1.88 tff(347,plain,(
% 2.49/1.88 ![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))),
% 2.49/1.88 inference(skolemize,[status(sab)],[346])).
% 2.49/1.88 tff(348,plain,
% 2.49/1.88 (![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[347, 343])).
% 2.49/1.88 tff(349,plain,
% 2.49/1.88 (((~![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)))))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(350,plain,
% 2.49/1.88 ((~![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)))))),
% 2.49/1.88 inference(quant_inst,[status(thm)],[])).
% 2.49/1.88 tff(351,plain,
% 2.49/1.88 ((~![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))))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[350, 349])).
% 2.49/1.88 tff(352,plain,
% 2.49/1.88 (connection(out(s, h2(f)), out(n1, and1(h2(f))))),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[351, 348, 282])).
% 2.49/1.88 tff(353,plain,
% 2.49/1.88 (((~![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)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(354,plain,
% 2.49/1.88 ((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)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(355,plain,
% 2.49/1.88 (((~![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))))),
% 2.49/1.88 inference(monotonicity,[status(thm)],[354])).
% 2.49/1.88 tff(356,plain,
% 2.49/1.88 (((~![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)))),
% 2.49/1.88 inference(transitivity,[status(thm)],[355, 353])).
% 2.49/1.88 tff(357,plain,
% 2.49/1.88 ((~![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))))))),
% 2.49/1.88 inference(quant_inst,[status(thm)],[])).
% 2.49/1.88 tff(358,plain,
% 2.49/1.88 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~connection(out(s, h2(f)), out(n1, and1(h2(f))))) | value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[357, 356])).
% 2.49/1.88 tff(359,plain,
% 2.49/1.88 ($false),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[358, 185, 352, 341, 340])).
% 2.49/1.88 tff(360,plain,(value(out(n1, and1(h2(f))), n1)), inference(lemma,lemma(discharge,[]))).
% 2.49/1.88 tff(361,plain,
% 2.49/1.88 (^[K: $i] : refl(((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1)))),
% 2.49/1.88 inference(bind,[status(th)],[])).
% 2.49/1.88 tff(362,plain,
% 2.49/1.88 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 2.49/1.88 inference(quant_intro,[status(thm)],[361])).
% 2.49/1.88 tff(363,plain,
% 2.49/1.88 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(364,plain,
% 2.49/1.88 (^[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(n1, K), n1)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and))) | value(in(n1, K), n1)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and))) | value(in(n1, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))))),
% 2.49/1.88 inference(bind,[status(th)],[])).
% 2.49/1.88 tff(365,plain,
% 2.49/1.88 (![K: $i] : ((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 2.49/1.88 inference(quant_intro,[status(thm)],[364])).
% 2.49/1.88 tff(366,axiom,(![K: $i] : ((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','and_1_1x')).
% 2.49/1.88 tff(367,plain,
% 2.49/1.88 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[366, 365])).
% 2.49/1.88 tff(368,plain,
% 2.49/1.88 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[367, 363])).
% 2.49/1.88 tff(369,plain,(
% 2.49/1.88 ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 2.49/1.88 inference(skolemize,[status(sab)],[368])).
% 2.49/1.88 tff(370,plain,
% 2.49/1.88 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[369, 362])).
% 2.49/1.88 tff(371,plain,
% 2.49/1.88 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n1, and1(h2(f))), n1) | (~type(and1(h2(f)), and)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | (~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n1, and1(h2(f))), n1) | (~type(and1(h2(f)), and)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(372,plain,
% 2.49/1.88 (((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | (~type(and1(h2(f)), and)) | value(in(n1, and1(h2(f))), n1)) <=> ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n1, and1(h2(f))), n1) | (~type(and1(h2(f)), and)))),
% 2.49/1.88 inference(rewrite,[status(thm)],[])).
% 2.49/1.88 tff(373,plain,
% 2.49/1.88 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | (~type(and1(h2(f)), and)) | value(in(n1, and1(h2(f))), n1))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n1, and1(h2(f))), n1) | (~type(and1(h2(f)), and))))),
% 2.49/1.88 inference(monotonicity,[status(thm)],[372])).
% 2.49/1.88 tff(374,plain,
% 2.49/1.88 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | (~type(and1(h2(f)), and)) | value(in(n1, and1(h2(f))), n1))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | (~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n1, and1(h2(f))), n1) | (~type(and1(h2(f)), and)))),
% 2.49/1.88 inference(transitivity,[status(thm)],[373, 371])).
% 2.49/1.88 tff(375,plain,
% 2.49/1.88 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | (~type(and1(h2(f)), and)) | value(in(n1, and1(h2(f))), n1))),
% 2.49/1.88 inference(quant_inst,[status(thm)],[])).
% 2.49/1.88 tff(376,plain,
% 2.49/1.88 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | (~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n1, and1(h2(f))), n1) | (~type(and1(h2(f)), and))),
% 2.49/1.88 inference(modus_ponens,[status(thm)],[375, 374])).
% 2.49/1.88 tff(377,plain,
% 2.49/1.88 ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n1, and1(h2(f))), n1)),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[376, 370, 314])).
% 2.49/1.88 tff(378,plain,
% 2.49/1.88 (value(in(n1, and1(h2(f))), n1)),
% 2.49/1.88 inference(unit_resolution,[status(thm)],[377, 360, 319])).
% 2.49/1.88 tff(379,plain,
% 2.49/1.88 (^[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)))))),
% 2.49/1.89 inference(bind,[status(th)],[])).
% 2.49/1.89 tff(380,plain,
% 2.49/1.89 (![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))))),
% 2.49/1.89 inference(quant_intro,[status(thm)],[379])).
% 2.49/1.89 tff(381,plain,
% 2.49/1.89 (![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))))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(382,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')).
% 2.49/1.89 tff(383,plain,
% 2.49/1.89 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[382, 381])).
% 2.49/1.89 tff(384,plain,(
% 2.49/1.89 ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))),
% 2.49/1.89 inference(skolemize,[status(sab)],[383])).
% 2.49/1.89 tff(385,plain,
% 2.49/1.89 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[384, 380])).
% 2.49/1.89 tff(386,plain,
% 2.49/1.89 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))) | ((~type(h2(f), halfadder)) | connection(out(n1, or1(h2(f))), in(n1, and1(h2(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))) | (~type(h2(f), halfadder)) | connection(out(n1, or1(h2(f))), in(n1, and1(h2(f)))))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(387,plain,
% 2.49/1.89 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))) | ((~type(h2(f), halfadder)) | connection(out(n1, or1(h2(f))), in(n1, and1(h2(f)))))),
% 2.49/1.89 inference(quant_inst,[status(thm)],[])).
% 2.49/1.89 tff(388,plain,
% 2.49/1.89 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))) | (~type(h2(f), halfadder)) | connection(out(n1, or1(h2(f))), in(n1, and1(h2(f))))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[387, 386])).
% 2.49/1.89 tff(389,plain,
% 2.49/1.89 (connection(out(n1, or1(h2(f))), in(n1, and1(h2(f))))),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[388, 385, 282])).
% 2.49/1.89 tff(390,plain,
% 2.49/1.89 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n1, and1(h2(f))), n1)) | value(out(n1, or1(h2(f))), n1) | (~connection(out(n1, or1(h2(f))), in(n1, and1(h2(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, and1(h2(f))), n1)) | value(out(n1, or1(h2(f))), n1) | (~connection(out(n1, or1(h2(f))), in(n1, and1(h2(f))))))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(391,plain,
% 2.49/1.89 ((value(out(n1, or1(h2(f))), n1) | (~connection(out(n1, or1(h2(f))), in(n1, and1(h2(f))))) | (~value(in(n1, and1(h2(f))), n1))) <=> ((~value(in(n1, and1(h2(f))), n1)) | value(out(n1, or1(h2(f))), n1) | (~connection(out(n1, or1(h2(f))), in(n1, and1(h2(f))))))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(392,plain,
% 2.49/1.89 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, or1(h2(f))), n1) | (~connection(out(n1, or1(h2(f))), in(n1, and1(h2(f))))) | (~value(in(n1, and1(h2(f))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n1, and1(h2(f))), n1)) | value(out(n1, or1(h2(f))), n1) | (~connection(out(n1, or1(h2(f))), in(n1, and1(h2(f)))))))),
% 2.49/1.89 inference(monotonicity,[status(thm)],[391])).
% 2.49/1.89 tff(393,plain,
% 2.49/1.89 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, or1(h2(f))), n1) | (~connection(out(n1, or1(h2(f))), in(n1, and1(h2(f))))) | (~value(in(n1, and1(h2(f))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, and1(h2(f))), n1)) | value(out(n1, or1(h2(f))), n1) | (~connection(out(n1, or1(h2(f))), in(n1, and1(h2(f))))))),
% 2.49/1.89 inference(transitivity,[status(thm)],[392, 390])).
% 2.49/1.89 tff(394,plain,
% 2.49/1.89 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, or1(h2(f))), n1) | (~connection(out(n1, or1(h2(f))), in(n1, and1(h2(f))))) | (~value(in(n1, and1(h2(f))), n1)))),
% 2.49/1.89 inference(quant_inst,[status(thm)],[])).
% 2.49/1.89 tff(395,plain,
% 2.49/1.89 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, and1(h2(f))), n1)) | value(out(n1, or1(h2(f))), n1) | (~connection(out(n1, or1(h2(f))), in(n1, and1(h2(f)))))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[394, 393])).
% 2.49/1.89 tff(396,plain,
% 2.49/1.89 ($false),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[395, 45, 389, 378, 299])).
% 2.49/1.89 tff(397,plain,(value(out(n1, or1(h2(f))), n1)), inference(lemma,lemma(discharge,[]))).
% 2.49/1.89 tff(398,plain,
% 2.49/1.89 (^[X: $i] : refl(((~type(X, halfadder)) | connection(in(n1, X), in(n1, or1(X)))) <=> ((~type(X, halfadder)) | connection(in(n1, X), in(n1, or1(X)))))),
% 2.49/1.89 inference(bind,[status(th)],[])).
% 2.49/1.89 tff(399,plain,
% 2.49/1.89 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, or1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, or1(X))))),
% 2.49/1.89 inference(quant_intro,[status(thm)],[398])).
% 2.49/1.89 tff(400,plain,
% 2.49/1.89 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, or1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, or1(X))))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(401,axiom,(![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, or1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_connection_in1_in1or1')).
% 2.49/1.89 tff(402,plain,
% 2.49/1.89 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, or1(X))))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[401, 400])).
% 2.49/1.89 tff(403,plain,(
% 2.49/1.89 ![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, or1(X))))),
% 2.49/1.89 inference(skolemize,[status(sab)],[402])).
% 2.49/1.89 tff(404,plain,
% 2.49/1.89 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, or1(X))))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[403, 399])).
% 2.49/1.89 tff(405,plain,
% 2.49/1.89 (((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, or1(X))))) | ((~type(h2(f), halfadder)) | connection(in(n1, h2(f)), in(n1, or1(h2(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, or1(X))))) | (~type(h2(f), halfadder)) | connection(in(n1, h2(f)), in(n1, or1(h2(f)))))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(406,plain,
% 2.49/1.89 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, or1(X))))) | ((~type(h2(f), halfadder)) | connection(in(n1, h2(f)), in(n1, or1(h2(f)))))),
% 2.49/1.89 inference(quant_inst,[status(thm)],[])).
% 2.49/1.89 tff(407,plain,
% 2.49/1.89 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, or1(X))))) | (~type(h2(f), halfadder)) | connection(in(n1, h2(f)), in(n1, or1(h2(f))))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[406, 405])).
% 2.49/1.89 tff(408,plain,
% 2.49/1.89 (connection(in(n1, h2(f)), in(n1, or1(h2(f))))),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[407, 404, 282])).
% 2.49/1.89 tff(409,plain,
% 2.49/1.89 (^[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)))))),
% 2.49/1.89 inference(bind,[status(th)],[])).
% 2.49/1.89 tff(410,plain,
% 2.49/1.89 (![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))))),
% 2.49/1.89 inference(quant_intro,[status(thm)],[409])).
% 2.49/1.89 tff(411,plain,
% 2.49/1.89 (![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))))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(412,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')).
% 2.49/1.89 tff(413,plain,
% 2.49/1.89 (![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[412, 411])).
% 2.49/1.89 tff(414,plain,(
% 2.49/1.89 ![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 2.49/1.89 inference(skolemize,[status(sab)],[413])).
% 2.49/1.89 tff(415,plain,
% 2.49/1.89 (![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[414, 410])).
% 2.49/1.89 tff(416,plain,
% 2.49/1.89 (((~![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))))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(417,plain,
% 2.49/1.89 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | ((~type(f, fulladder)) | connection(in(n1, f), in(n1, h2(f))))),
% 2.49/1.89 inference(quant_inst,[status(thm)],[])).
% 2.49/1.89 tff(418,plain,
% 2.49/1.89 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | (~type(f, fulladder)) | connection(in(n1, f), in(n1, h2(f)))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[417, 416])).
% 2.49/1.89 tff(419,plain,
% 2.49/1.89 (connection(in(n1, f), in(n1, h2(f)))),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[418, 415, 4])).
% 2.49/1.89 tff(420,plain,
% 2.49/1.89 (value(in(n1, f), n0) <=> value(in(n1, f), n0)),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(421,axiom,(value(in(n1, f), n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','in1_1')).
% 2.49/1.89 tff(422,plain,
% 2.49/1.89 (value(in(n1, f), n0)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[421, 420])).
% 2.49/1.89 tff(423,plain,
% 2.49/1.89 ((~equal_value(n1, n0)) <=> (~equal_value(n1, n0))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(424,axiom,(~equal_value(n1, n0)), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','equal_value2')).
% 2.49/1.89 tff(425,plain,
% 2.49/1.89 (~equal_value(n1, n0)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[424, 423])).
% 2.49/1.89 tff(426,plain,
% 2.49/1.89 (((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n1, n0) | (~value(in(n1, f), n0)) | (~value(in(n1, f), n1)))) <=> ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n1, n0) | (~value(in(n1, f), n0)) | (~value(in(n1, f), n1)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(427,plain,
% 2.49/1.89 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n1, n0) | (~value(in(n1, f), n0)) | (~value(in(n1, f), n1)))),
% 2.49/1.89 inference(quant_inst,[status(thm)],[])).
% 2.49/1.89 tff(428,plain,
% 2.49/1.89 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n1, n0) | (~value(in(n1, f), n0)) | (~value(in(n1, f), n1))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[427, 426])).
% 2.49/1.89 tff(429,plain,
% 2.49/1.89 (~value(in(n1, f), n1)),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[428, 31, 425, 422])).
% 2.49/1.89 tff(430,plain,
% 2.49/1.89 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, f), n1) | (~connection(in(n1, f), in(n1, h2(f)))) | (~value(in(n1, h2(f)), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, f), n1) | (~connection(in(n1, f), in(n1, h2(f)))) | (~value(in(n1, h2(f)), n1)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(431,plain,
% 2.49/1.89 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, f), n1) | (~connection(in(n1, f), in(n1, h2(f)))) | (~value(in(n1, h2(f)), n1)))),
% 2.49/1.89 inference(quant_inst,[status(thm)],[])).
% 2.49/1.89 tff(432,plain,
% 2.49/1.89 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, f), n1) | (~connection(in(n1, f), in(n1, h2(f)))) | (~value(in(n1, h2(f)), n1))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[431, 430])).
% 2.49/1.89 tff(433,plain,
% 2.49/1.89 (~value(in(n1, h2(f)), n1)),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[432, 45, 429, 419])).
% 2.49/1.89 tff(434,plain,
% 2.49/1.89 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h2(f)), n1) | (~connection(in(n1, h2(f)), in(n1, or1(h2(f))))) | (~value(in(n1, or1(h2(f))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h2(f)), n1) | (~connection(in(n1, h2(f)), in(n1, or1(h2(f))))) | (~value(in(n1, or1(h2(f))), n1)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(435,plain,
% 2.49/1.89 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h2(f)), n1) | (~connection(in(n1, h2(f)), in(n1, or1(h2(f))))) | (~value(in(n1, or1(h2(f))), n1)))),
% 2.49/1.89 inference(quant_inst,[status(thm)],[])).
% 2.49/1.89 tff(436,plain,
% 2.49/1.89 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h2(f)), n1) | (~connection(in(n1, h2(f)), in(n1, or1(h2(f))))) | (~value(in(n1, or1(h2(f))), n1))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[435, 434])).
% 2.49/1.89 tff(437,plain,
% 2.49/1.89 (~value(in(n1, or1(h2(f))), n1)),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[436, 45, 433, 408])).
% 2.49/1.89 tff(438,plain,
% 2.49/1.89 (^[K: $i] : refl(((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or))))),
% 2.49/1.89 inference(bind,[status(th)],[])).
% 2.49/1.89 tff(439,plain,
% 2.49/1.89 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or))) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 2.49/1.89 inference(quant_intro,[status(thm)],[438])).
% 2.49/1.89 tff(440,plain,
% 2.49/1.89 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or))) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(441,plain,
% 2.49/1.89 (^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, or)))), (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, or))) | value(in(n1, K), n1)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, or))) | value(in(n1, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n1) | (~type(K, or)))), (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n1) | (~type(K, or))))), ((((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) | value(in(n2, K), n1)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n1) | (~type(K, or))) | value(in(n2, K), n1)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n1) | (~type(K, or))) | value(in(n2, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))), ((((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) | value(in(n2, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))))),
% 2.49/1.89 inference(bind,[status(th)],[])).
% 2.49/1.89 tff(442,plain,
% 2.49/1.89 (![K: $i] : (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) | value(in(n2, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 2.49/1.89 inference(quant_intro,[status(thm)],[441])).
% 2.49/1.89 tff(443,axiom,(![K: $i] : (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) | value(in(n2, K), n1))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','or_1_11')).
% 2.49/1.89 tff(444,plain,
% 2.49/1.89 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[443, 442])).
% 2.49/1.89 tff(445,plain,
% 2.49/1.89 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[444, 440])).
% 2.49/1.89 tff(446,plain,(
% 2.49/1.89 ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 2.49/1.89 inference(skolemize,[status(sab)],[445])).
% 2.49/1.89 tff(447,plain,
% 2.49/1.89 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[446, 439])).
% 2.49/1.89 tff(448,plain,
% 2.49/1.89 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))) | (value(in(n1, or1(h2(f))), n1) | (~mode(or1(h2(f)), ok)) | (~value(out(n1, or1(h2(f))), n1)) | (~type(or1(h2(f)), or)) | value(in(n2, or1(h2(f))), n1))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))) | value(in(n1, or1(h2(f))), n1) | (~mode(or1(h2(f)), ok)) | (~value(out(n1, or1(h2(f))), n1)) | (~type(or1(h2(f)), or)) | value(in(n2, or1(h2(f))), n1))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(449,plain,
% 2.49/1.89 (((~mode(or1(h2(f)), ok)) | (~value(out(n1, or1(h2(f))), n1)) | value(in(n2, or1(h2(f))), n1) | value(in(n1, or1(h2(f))), n1) | (~type(or1(h2(f)), or))) <=> (value(in(n1, or1(h2(f))), n1) | (~mode(or1(h2(f)), ok)) | (~value(out(n1, or1(h2(f))), n1)) | (~type(or1(h2(f)), or)) | value(in(n2, or1(h2(f))), n1))),
% 2.49/1.89 inference(rewrite,[status(thm)],[])).
% 2.49/1.89 tff(450,plain,
% 2.49/1.89 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))) | ((~mode(or1(h2(f)), ok)) | (~value(out(n1, or1(h2(f))), n1)) | value(in(n2, or1(h2(f))), n1) | value(in(n1, or1(h2(f))), n1) | (~type(or1(h2(f)), or)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))) | (value(in(n1, or1(h2(f))), n1) | (~mode(or1(h2(f)), ok)) | (~value(out(n1, or1(h2(f))), n1)) | (~type(or1(h2(f)), or)) | value(in(n2, or1(h2(f))), n1)))),
% 2.49/1.89 inference(monotonicity,[status(thm)],[449])).
% 2.49/1.89 tff(451,plain,
% 2.49/1.89 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))) | ((~mode(or1(h2(f)), ok)) | (~value(out(n1, or1(h2(f))), n1)) | value(in(n2, or1(h2(f))), n1) | value(in(n1, or1(h2(f))), n1) | (~type(or1(h2(f)), or)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))) | value(in(n1, or1(h2(f))), n1) | (~mode(or1(h2(f)), ok)) | (~value(out(n1, or1(h2(f))), n1)) | (~type(or1(h2(f)), or)) | value(in(n2, or1(h2(f))), n1))),
% 2.49/1.89 inference(transitivity,[status(thm)],[450, 448])).
% 2.49/1.89 tff(452,plain,
% 2.49/1.89 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))) | ((~mode(or1(h2(f)), ok)) | (~value(out(n1, or1(h2(f))), n1)) | value(in(n2, or1(h2(f))), n1) | value(in(n1, or1(h2(f))), n1) | (~type(or1(h2(f)), or)))),
% 2.49/1.89 inference(quant_inst,[status(thm)],[])).
% 2.49/1.89 tff(453,plain,
% 2.49/1.89 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))) | value(in(n1, or1(h2(f))), n1) | (~mode(or1(h2(f)), ok)) | (~value(out(n1, or1(h2(f))), n1)) | (~type(or1(h2(f)), or)) | value(in(n2, or1(h2(f))), n1)),
% 2.49/1.89 inference(modus_ponens,[status(thm)],[452, 451])).
% 2.49/1.89 tff(454,plain,
% 2.49/1.89 ((~mode(or1(h2(f)), ok)) | (~value(out(n1, or1(h2(f))), n1)) | value(in(n2, or1(h2(f))), n1)),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[453, 447, 293, 437])).
% 2.49/1.89 tff(455,plain,
% 2.49/1.89 (value(in(n2, or1(h2(f))), n1)),
% 2.49/1.89 inference(unit_resolution,[status(thm)],[454, 397, 298])).
% 2.49/1.89 tff(456,plain,
% 2.49/1.89 (^[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)))))),
% 2.49/1.89 inference(bind,[status(th)],[])).
% 2.49/1.89 tff(457,plain,
% 2.49/1.89 (![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))))),
% 2.49/1.89 inference(quant_intro,[status(thm)],[456])).
% 2.49/1.89 tff(458,plain,
% 2.49/1.90 (![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))))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(459,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')).
% 2.49/1.90 tff(460,plain,
% 2.49/1.90 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[459, 458])).
% 2.49/1.90 tff(461,plain,(
% 2.49/1.90 ![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))),
% 2.49/1.90 inference(skolemize,[status(sab)],[460])).
% 2.49/1.90 tff(462,plain,
% 2.49/1.90 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[461, 457])).
% 2.49/1.90 tff(463,plain,
% 2.49/1.90 (((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))) | ((~type(h2(f), halfadder)) | connection(in(n2, h2(f)), in(n2, or1(h2(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))) | (~type(h2(f), halfadder)) | connection(in(n2, h2(f)), in(n2, or1(h2(f)))))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(464,plain,
% 2.49/1.90 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))) | ((~type(h2(f), halfadder)) | connection(in(n2, h2(f)), in(n2, or1(h2(f)))))),
% 2.49/1.90 inference(quant_inst,[status(thm)],[])).
% 2.49/1.90 tff(465,plain,
% 2.49/1.90 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))) | (~type(h2(f), halfadder)) | connection(in(n2, h2(f)), in(n2, or1(h2(f))))),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[464, 463])).
% 2.49/1.90 tff(466,plain,
% 2.49/1.90 (connection(in(n2, h2(f)), in(n2, or1(h2(f))))),
% 2.49/1.90 inference(unit_resolution,[status(thm)],[465, 462, 282])).
% 2.49/1.90 tff(467,plain,
% 2.49/1.90 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h2(f)), n1) | (~value(in(n2, or1(h2(f))), n1)) | (~connection(in(n2, h2(f)), in(n2, or1(h2(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n2, h2(f)), n1) | (~value(in(n2, or1(h2(f))), n1)) | (~connection(in(n2, h2(f)), in(n2, or1(h2(f))))))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(468,plain,
% 2.49/1.90 ((value(in(n2, h2(f)), n1) | (~connection(in(n2, h2(f)), in(n2, or1(h2(f))))) | (~value(in(n2, or1(h2(f))), n1))) <=> (value(in(n2, h2(f)), n1) | (~value(in(n2, or1(h2(f))), n1)) | (~connection(in(n2, h2(f)), in(n2, or1(h2(f))))))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(469,plain,
% 2.49/1.90 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h2(f)), n1) | (~connection(in(n2, h2(f)), in(n2, or1(h2(f))))) | (~value(in(n2, or1(h2(f))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h2(f)), n1) | (~value(in(n2, or1(h2(f))), n1)) | (~connection(in(n2, h2(f)), in(n2, or1(h2(f)))))))),
% 2.49/1.90 inference(monotonicity,[status(thm)],[468])).
% 2.49/1.90 tff(470,plain,
% 2.49/1.90 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h2(f)), n1) | (~connection(in(n2, h2(f)), in(n2, or1(h2(f))))) | (~value(in(n2, or1(h2(f))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n2, h2(f)), n1) | (~value(in(n2, or1(h2(f))), n1)) | (~connection(in(n2, h2(f)), in(n2, or1(h2(f))))))),
% 2.49/1.90 inference(transitivity,[status(thm)],[469, 467])).
% 2.49/1.90 tff(471,plain,
% 2.49/1.90 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h2(f)), n1) | (~connection(in(n2, h2(f)), in(n2, or1(h2(f))))) | (~value(in(n2, or1(h2(f))), n1)))),
% 2.49/1.90 inference(quant_inst,[status(thm)],[])).
% 2.49/1.90 tff(472,plain,
% 2.49/1.90 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n2, h2(f)), n1) | (~value(in(n2, or1(h2(f))), n1)) | (~connection(in(n2, h2(f)), in(n2, or1(h2(f)))))),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[471, 470])).
% 2.49/1.90 tff(473,plain,
% 2.49/1.90 (value(in(n2, h2(f)), n1)),
% 2.49/1.90 inference(unit_resolution,[status(thm)],[472, 45, 466, 455])).
% 2.49/1.90 tff(474,plain,
% 2.49/1.90 (^[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)))))),
% 2.49/1.90 inference(bind,[status(th)],[])).
% 2.49/1.90 tff(475,plain,
% 2.49/1.90 (![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))))),
% 2.49/1.90 inference(quant_intro,[status(thm)],[474])).
% 2.49/1.90 tff(476,plain,
% 2.49/1.90 (![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))))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(477,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')).
% 2.49/1.90 tff(478,plain,
% 2.49/1.90 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[477, 476])).
% 2.49/1.90 tff(479,plain,(
% 2.49/1.90 ![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))),
% 2.49/1.90 inference(skolemize,[status(sab)],[478])).
% 2.49/1.90 tff(480,plain,
% 2.49/1.90 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[479, 475])).
% 2.49/1.90 tff(481,plain,
% 2.49/1.90 (((~![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))))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(482,plain,
% 2.49/1.90 ((~![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))))),
% 2.49/1.90 inference(quant_inst,[status(thm)],[])).
% 2.49/1.90 tff(483,plain,
% 2.49/1.90 ((~![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)))),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[482, 481])).
% 2.49/1.90 tff(484,plain,
% 2.49/1.90 (connection(out(s, h1(f)), in(n2, h2(f)))),
% 2.49/1.90 inference(unit_resolution,[status(thm)],[483, 480, 4])).
% 2.49/1.90 tff(485,plain,
% 2.49/1.90 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n2, h2(f)), n1)) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | value(out(s, h1(f)), n1))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, h2(f)), n1)) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | value(out(s, h1(f)), n1))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(486,plain,
% 2.49/1.90 ((value(out(s, h1(f)), n1) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | (~value(in(n2, h2(f)), n1))) <=> ((~value(in(n2, h2(f)), n1)) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | value(out(s, h1(f)), n1))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(487,plain,
% 2.49/1.90 (((~![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)), in(n2, h2(f)))) | (~value(in(n2, h2(f)), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n2, h2(f)), n1)) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | value(out(s, h1(f)), n1)))),
% 2.49/1.90 inference(monotonicity,[status(thm)],[486])).
% 2.49/1.90 tff(488,plain,
% 2.49/1.90 (((~![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)), in(n2, h2(f)))) | (~value(in(n2, h2(f)), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, h2(f)), n1)) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | value(out(s, h1(f)), n1))),
% 2.49/1.90 inference(transitivity,[status(thm)],[487, 485])).
% 2.49/1.90 tff(489,plain,
% 2.49/1.90 ((~![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)), in(n2, h2(f)))) | (~value(in(n2, h2(f)), n1)))),
% 2.49/1.90 inference(quant_inst,[status(thm)],[])).
% 2.49/1.90 tff(490,plain,
% 2.49/1.90 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, h2(f)), n1)) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | value(out(s, h1(f)), n1)),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[489, 488])).
% 2.49/1.90 tff(491,plain,
% 2.49/1.90 (value(out(s, h1(f)), n1)),
% 2.49/1.90 inference(unit_resolution,[status(thm)],[490, 45, 484, 473])).
% 2.49/1.90 tff(492,plain,
% 2.49/1.90 (((~mode(or1(f), abnormal)) | (~mode(and1(h1(f)), abnormal))) <=> ((~mode(or1(f), abnormal)) | (~mode(and1(h1(f)), abnormal)))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(493,axiom,((~mode(or1(f), abnormal)) | (~mode(and1(h1(f)), abnormal))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_or1_and1h1')).
% 2.49/1.90 tff(494,plain,
% 2.49/1.90 ((~mode(or1(f), abnormal)) | (~mode(and1(h1(f)), abnormal))),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[493, 492])).
% 2.49/1.90 tff(495,plain,
% 2.49/1.90 (~mode(and1(h1(f)), abnormal)),
% 2.49/1.90 inference(unit_resolution,[status(thm)],[494, 267])).
% 2.49/1.90 tff(496,plain,
% 2.49/1.90 (((~![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))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(497,plain,
% 2.49/1.90 ((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | ((~type(h1(f), halfadder)) | type(and1(h1(f)), and))),
% 2.49/1.90 inference(quant_inst,[status(thm)],[])).
% 2.49/1.90 tff(498,plain,
% 2.49/1.90 ((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | (~type(h1(f), halfadder)) | type(and1(h1(f)), and)),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[497, 496])).
% 2.49/1.90 tff(499,plain,
% 2.49/1.90 (type(and1(h1(f)), and)),
% 2.49/1.90 inference(unit_resolution,[status(thm)],[498, 310, 60])).
% 2.49/1.90 tff(500,plain,
% 2.49/1.90 (((~![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)))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(501,plain,
% 2.49/1.90 ((~![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)))),
% 2.49/1.90 inference(quant_inst,[status(thm)],[])).
% 2.49/1.90 tff(502,plain,
% 2.49/1.90 ((~![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))),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[501, 500])).
% 2.49/1.90 tff(503,plain,
% 2.49/1.90 (mode(and1(h1(f)), abnormal) | mode(and1(h1(f)), ok)),
% 2.49/1.90 inference(unit_resolution,[status(thm)],[502, 102, 499])).
% 2.49/1.90 tff(504,plain,
% 2.49/1.90 (mode(and1(h1(f)), ok)),
% 2.49/1.90 inference(unit_resolution,[status(thm)],[503, 495])).
% 2.49/1.90 tff(505,plain,
% 2.49/1.90 (((~mode(or1(f), abnormal)) | (~mode(not1(h1(f)), abnormal))) <=> ((~mode(or1(f), abnormal)) | (~mode(not1(h1(f)), abnormal)))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(506,axiom,((~mode(or1(f), abnormal)) | (~mode(not1(h1(f)), abnormal))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_or1_not1h1')).
% 2.49/1.90 tff(507,plain,
% 2.49/1.90 ((~mode(or1(f), abnormal)) | (~mode(not1(h1(f)), abnormal))),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[506, 505])).
% 2.49/1.90 tff(508,plain,
% 2.49/1.90 (~mode(not1(h1(f)), abnormal)),
% 2.49/1.90 inference(unit_resolution,[status(thm)],[507, 267])).
% 2.49/1.90 tff(509,plain,
% 2.49/1.90 (^[X: $i] : refl(((~type(X, halfadder)) | type(not1(X), not)) <=> ((~type(X, halfadder)) | type(not1(X), not)))),
% 2.49/1.90 inference(bind,[status(th)],[])).
% 2.49/1.90 tff(510,plain,
% 2.49/1.90 (![X: $i] : ((~type(X, halfadder)) | type(not1(X), not)) <=> ![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))),
% 2.49/1.90 inference(quant_intro,[status(thm)],[509])).
% 2.49/1.90 tff(511,plain,
% 2.49/1.90 (![X: $i] : ((~type(X, halfadder)) | type(not1(X), not)) <=> ![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(512,axiom,(![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_not1')).
% 2.49/1.90 tff(513,plain,
% 2.49/1.90 (![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[512, 511])).
% 2.49/1.90 tff(514,plain,(
% 2.49/1.90 ![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))),
% 2.49/1.90 inference(skolemize,[status(sab)],[513])).
% 2.49/1.90 tff(515,plain,
% 2.49/1.90 (![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[514, 510])).
% 2.49/1.90 tff(516,plain,
% 2.49/1.90 (((~![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))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(517,plain,
% 2.49/1.90 ((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | ((~type(h1(f), halfadder)) | type(not1(h1(f)), not))),
% 2.49/1.90 inference(quant_inst,[status(thm)],[])).
% 2.49/1.90 tff(518,plain,
% 2.49/1.90 ((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | (~type(h1(f), halfadder)) | type(not1(h1(f)), not)),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[517, 516])).
% 2.49/1.90 tff(519,plain,
% 2.49/1.90 (type(not1(h1(f)), not)),
% 2.49/1.90 inference(unit_resolution,[status(thm)],[518, 515, 60])).
% 2.49/1.90 tff(520,plain,
% 2.49/1.90 (((~![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)))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(521,plain,
% 2.49/1.90 ((~![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)))),
% 2.49/1.90 inference(quant_inst,[status(thm)],[])).
% 2.49/1.90 tff(522,plain,
% 2.49/1.90 ((~![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))),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[521, 520])).
% 2.49/1.90 tff(523,plain,
% 2.49/1.90 (mode(not1(h1(f)), abnormal) | mode(not1(h1(f)), ok)),
% 2.49/1.90 inference(unit_resolution,[status(thm)],[522, 102, 519])).
% 2.49/1.90 tff(524,plain,
% 2.49/1.90 (mode(not1(h1(f)), ok)),
% 2.49/1.90 inference(unit_resolution,[status(thm)],[523, 508])).
% 2.49/1.90 tff(525,assumption,(~value(in(n1, not1(h1(f))), n1)), introduced(assumption)).
% 2.49/1.90 tff(526,assumption,(~value(in(n1, h1(f)), n1)), introduced(assumption)).
% 2.49/1.90 tff(527,plain,
% 2.49/1.90 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(n2, f), n1)) | (~connection(in(n2, f), in(n1, h1(f)))) | value(in(n1, h1(f)), n1))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n2, f), n1)) | (~connection(in(n2, f), in(n1, h1(f)))) | value(in(n1, h1(f)), n1))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(528,plain,
% 2.49/1.90 ((value(in(n1, h1(f)), n1) | (~value(in(n2, f), n1)) | (~connection(in(n2, f), in(n1, h1(f))))) <=> ((~value(in(n2, f), n1)) | (~connection(in(n2, f), in(n1, h1(f)))) | value(in(n1, h1(f)), n1))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(529,plain,
% 2.49/1.90 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, h1(f)), n1) | (~value(in(n2, f), n1)) | (~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), n1)) | (~connection(in(n2, f), in(n1, h1(f)))) | value(in(n1, h1(f)), n1)))),
% 2.49/1.90 inference(monotonicity,[status(thm)],[528])).
% 2.49/1.90 tff(530,plain,
% 2.49/1.90 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, h1(f)), n1) | (~value(in(n2, f), n1)) | (~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), n1)) | (~connection(in(n2, f), in(n1, h1(f)))) | value(in(n1, h1(f)), n1))),
% 2.49/1.90 inference(transitivity,[status(thm)],[529, 527])).
% 2.49/1.90 tff(531,plain,
% 2.49/1.90 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, h1(f)), n1) | (~value(in(n2, f), n1)) | (~connection(in(n2, f), in(n1, h1(f)))))),
% 2.49/1.90 inference(quant_inst,[status(thm)],[])).
% 2.49/1.90 tff(532,plain,
% 2.49/1.90 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n2, f), n1)) | (~connection(in(n2, f), in(n1, h1(f)))) | value(in(n1, h1(f)), n1)),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[531, 530])).
% 2.49/1.90 tff(533,plain,
% 2.49/1.90 ($false),
% 2.49/1.90 inference(unit_resolution,[status(thm)],[532, 185, 120, 117, 526])).
% 2.49/1.90 tff(534,plain,(value(in(n1, h1(f)), n1)), inference(lemma,lemma(discharge,[]))).
% 2.49/1.90 tff(535,assumption,(~value(in(n1, and2(h1(f))), n1)), introduced(assumption)).
% 2.49/1.90 tff(536,plain,
% 2.49/1.90 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, and2(h1(f))), n1) | (~value(in(n1, h1(f)), n1)) | (~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))), n1) | (~value(in(n1, h1(f)), n1)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(537,plain,
% 2.49/1.90 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, and2(h1(f))), n1) | (~value(in(n1, h1(f)), n1)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))))),
% 2.49/1.90 inference(quant_inst,[status(thm)],[])).
% 2.49/1.90 tff(538,plain,
% 2.49/1.90 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(in(n1, and2(h1(f))), n1) | (~value(in(n1, h1(f)), n1)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f)))))),
% 2.49/1.90 inference(modus_ponens,[status(thm)],[537, 536])).
% 2.49/1.90 tff(539,plain,
% 2.49/1.90 ($false),
% 2.49/1.90 inference(unit_resolution,[status(thm)],[538, 185, 139, 535, 534])).
% 2.49/1.90 tff(540,plain,(value(in(n1, and2(h1(f))), n1)), inference(lemma,lemma(discharge,[]))).
% 2.49/1.90 tff(541,assumption,(~value(in(n2, h1(f)), n1)), introduced(assumption)).
% 2.49/1.90 tff(542,plain,
% 2.49/1.90 (((~![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))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(543,plain,
% 2.49/1.90 ((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))),
% 2.49/1.90 inference(rewrite,[status(thm)],[])).
% 2.49/1.90 tff(544,plain,
% 2.49/1.90 (((~![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)))),
% 2.49/1.90 inference(monotonicity,[status(thm)],[543])).
% 2.49/1.90 tff(545,plain,
% 2.49/1.90 (((~![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))),
% 2.49/1.90 inference(transitivity,[status(thm)],[544, 542])).
% 2.49/1.90 tff(546,plain,
% 2.49/1.90 ((~![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)))))),
% 2.49/1.90 inference(quant_inst,[status(thm)],[])).
% 2.49/1.90 tff(547,plain,
% 2.49/1.90 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(c, f), n1)) | (~connection(in(c, f), in(n2, h1(f)))) | value(in(n2, h1(f)), n1)),
% 2.49/1.91 inference(modus_ponens,[status(thm)],[546, 545])).
% 2.49/1.91 tff(548,plain,
% 2.49/1.91 ($false),
% 2.49/1.91 inference(unit_resolution,[status(thm)],[547, 185, 18, 15, 541])).
% 2.49/1.91 tff(549,plain,(value(in(n2, h1(f)), n1)), inference(lemma,lemma(discharge,[]))).
% 2.49/1.91 tff(550,assumption,(~value(in(n2, and2(h1(f))), n1)), introduced(assumption)).
% 2.49/1.91 tff(551,plain,
% 2.49/1.91 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, and2(h1(f))), n1) | (~value(in(n2, h1(f)), n1)) | (~connection(in(n2, h1(f)), in(n2, and2(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(in(n2, and2(h1(f))), n1) | (~value(in(n2, h1(f)), n1)) | (~connection(in(n2, h1(f)), in(n2, and2(h1(f))))))),
% 2.49/1.91 inference(rewrite,[status(thm)],[])).
% 2.49/1.91 tff(552,plain,
% 2.49/1.91 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, and2(h1(f))), n1) | (~value(in(n2, h1(f)), n1)) | (~connection(in(n2, h1(f)), in(n2, and2(h1(f))))))),
% 2.49/1.91 inference(quant_inst,[status(thm)],[])).
% 2.49/1.91 tff(553,plain,
% 2.49/1.91 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(in(n2, and2(h1(f))), n1) | (~value(in(n2, h1(f)), n1)) | (~connection(in(n2, h1(f)), in(n2, and2(h1(f)))))),
% 2.49/1.91 inference(modus_ponens,[status(thm)],[552, 551])).
% 2.49/1.91 tff(554,plain,
% 2.49/1.91 ($false),
% 2.49/1.91 inference(unit_resolution,[status(thm)],[553, 185, 71, 550, 549])).
% 2.49/1.91 tff(555,plain,(value(in(n2, and2(h1(f))), n1)), inference(lemma,lemma(discharge,[]))).
% 2.49/1.91 tff(556,plain,
% 2.49/1.91 (^[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))))),
% 2.49/1.91 inference(bind,[status(th)],[])).
% 2.49/1.91 tff(557,plain,
% 2.49/1.91 (![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)))),
% 2.49/1.91 inference(quant_intro,[status(thm)],[556])).
% 2.49/1.91 tff(558,plain,
% 2.49/1.91 (![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)))),
% 2.49/1.91 inference(rewrite,[status(thm)],[])).
% 2.49/1.91 tff(559,plain,
% 2.49/1.91 (^[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)))))),
% 2.49/1.91 inference(bind,[status(th)],[])).
% 2.49/1.91 tff(560,plain,
% 2.49/1.91 (![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)))),
% 2.49/1.91 inference(quant_intro,[status(thm)],[559])).
% 2.49/1.91 tff(561,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')).
% 2.49/1.91 tff(562,plain,
% 2.49/1.91 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))),
% 2.49/1.91 inference(modus_ponens,[status(thm)],[561, 560])).
% 2.49/1.91 tff(563,plain,
% 2.49/1.91 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))),
% 2.49/1.91 inference(modus_ponens,[status(thm)],[562, 558])).
% 2.49/1.91 tff(564,plain,(
% 2.49/1.91 ![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))),
% 2.49/1.91 inference(skolemize,[status(sab)],[563])).
% 2.49/1.91 tff(565,plain,
% 2.49/1.91 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))),
% 2.49/1.91 inference(modus_ponens,[status(thm)],[564, 557])).
% 2.49/1.91 tff(566,plain,
% 2.49/1.91 (((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))) | ((~mode(and2(h1(f)), ok)) | value(out(n1, and2(h1(f))), n1) | (~value(in(n1, and2(h1(f))), n1)) | (~type(and2(h1(f)), and)) | (~value(in(n2, and2(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(and2(h1(f)), ok)) | value(out(n1, and2(h1(f))), n1) | (~value(in(n1, and2(h1(f))), n1)) | (~type(and2(h1(f)), and)) | (~value(in(n2, and2(h1(f))), n1)))),
% 2.49/1.91 inference(rewrite,[status(thm)],[])).
% 2.49/1.91 tff(567,plain,
% 2.49/1.91 (((~mode(and2(h1(f)), ok)) | (~type(and2(h1(f)), and)) | value(out(n1, and2(h1(f))), n1) | (~value(in(n2, and2(h1(f))), n1)) | (~value(in(n1, and2(h1(f))), n1))) <=> ((~mode(and2(h1(f)), ok)) | value(out(n1, and2(h1(f))), n1) | (~value(in(n1, and2(h1(f))), n1)) | (~type(and2(h1(f)), and)) | (~value(in(n2, and2(h1(f))), n1)))),
% 2.49/1.91 inference(rewrite,[status(thm)],[])).
% 2.49/1.91 tff(568,plain,
% 2.49/1.91 (((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))) | ((~mode(and2(h1(f)), ok)) | (~type(and2(h1(f)), and)) | value(out(n1, and2(h1(f))), n1) | (~value(in(n2, and2(h1(f))), n1)) | (~value(in(n1, and2(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(and2(h1(f)), ok)) | value(out(n1, and2(h1(f))), n1) | (~value(in(n1, and2(h1(f))), n1)) | (~type(and2(h1(f)), and)) | (~value(in(n2, and2(h1(f))), n1))))),
% 2.49/1.91 inference(monotonicity,[status(thm)],[567])).
% 2.49/1.91 tff(569,plain,
% 2.49/1.91 (((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))) | ((~mode(and2(h1(f)), ok)) | (~type(and2(h1(f)), and)) | value(out(n1, and2(h1(f))), n1) | (~value(in(n2, and2(h1(f))), n1)) | (~value(in(n1, and2(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(and2(h1(f)), ok)) | value(out(n1, and2(h1(f))), n1) | (~value(in(n1, and2(h1(f))), n1)) | (~type(and2(h1(f)), and)) | (~value(in(n2, and2(h1(f))), n1)))),
% 2.49/1.91 inference(transitivity,[status(thm)],[568, 566])).
% 2.49/1.91 tff(570,plain,
% 2.49/1.91 ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))) | ((~mode(and2(h1(f)), ok)) | (~type(and2(h1(f)), and)) | value(out(n1, and2(h1(f))), n1) | (~value(in(n2, and2(h1(f))), n1)) | (~value(in(n1, and2(h1(f))), n1)))),
% 2.49/1.91 inference(quant_inst,[status(thm)],[])).
% 2.49/1.91 tff(571,plain,
% 2.49/1.91 ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(out(n1, K), n1) | (~value(in(n2, K), n1)) | (~value(in(n1, K), n1)))) | (~mode(and2(h1(f)), ok)) | value(out(n1, and2(h1(f))), n1) | (~value(in(n1, and2(h1(f))), n1)) | (~type(and2(h1(f)), and)) | (~value(in(n2, and2(h1(f))), n1))),
% 2.58/1.91 inference(modus_ponens,[status(thm)],[570, 569])).
% 2.58/1.91 tff(572,plain,
% 2.58/1.91 ((~mode(and2(h1(f)), ok)) | value(out(n1, and2(h1(f))), n1) | (~value(in(n1, and2(h1(f))), n1)) | (~value(in(n2, and2(h1(f))), n1))),
% 2.58/1.91 inference(unit_resolution,[status(thm)],[571, 565, 89])).
% 2.58/1.91 tff(573,plain,
% 2.58/1.91 (value(out(n1, and2(h1(f))), n1) | (~value(in(n1, and2(h1(f))), n1)) | (~value(in(n2, and2(h1(f))), n1))),
% 2.58/1.91 inference(unit_resolution,[status(thm)],[572, 106])).
% 2.58/1.91 tff(574,plain,
% 2.58/1.91 (value(out(n1, and2(h1(f))), n1) | (~value(in(n1, and2(h1(f))), n1))),
% 2.58/1.91 inference(unit_resolution,[status(thm)],[573, 555])).
% 2.58/1.91 tff(575,plain,
% 2.58/1.91 (value(out(n1, and2(h1(f))), n1)),
% 2.58/1.91 inference(unit_resolution,[status(thm)],[574, 540])).
% 2.58/1.91 tff(576,plain,
% 2.58/1.91 (^[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)))))),
% 2.58/1.91 inference(bind,[status(th)],[])).
% 2.58/1.91 tff(577,plain,
% 2.58/1.91 (![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))))),
% 2.58/1.91 inference(quant_intro,[status(thm)],[576])).
% 2.58/1.91 tff(578,plain,
% 2.58/1.91 (![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))))),
% 2.58/1.91 inference(rewrite,[status(thm)],[])).
% 2.58/1.91 tff(579,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')).
% 2.58/1.91 tff(580,plain,
% 2.58/1.91 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))),
% 2.58/1.91 inference(modus_ponens,[status(thm)],[579, 578])).
% 2.58/1.91 tff(581,plain,(
% 2.58/1.91 ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))),
% 2.58/1.91 inference(skolemize,[status(sab)],[580])).
% 2.58/1.91 tff(582,plain,
% 2.58/1.91 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))),
% 2.58/1.91 inference(modus_ponens,[status(thm)],[581, 577])).
% 2.58/1.91 tff(583,plain,
% 2.58/1.91 (((~![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)))))),
% 2.58/1.91 inference(rewrite,[status(thm)],[])).
% 2.58/1.91 tff(584,plain,
% 2.58/1.91 ((~![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)))))),
% 2.58/1.91 inference(quant_inst,[status(thm)],[])).
% 2.58/1.91 tff(585,plain,
% 2.58/1.91 ((~![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))))),
% 2.58/1.91 inference(modus_ponens,[status(thm)],[584, 583])).
% 2.58/1.91 tff(586,plain,
% 2.58/1.91 (connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))),
% 2.58/1.91 inference(unit_resolution,[status(thm)],[585, 582, 60])).
% 2.58/1.91 tff(587,plain,
% 2.58/1.91 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(out(n1, and2(h1(f))), n1)) | value(in(n1, not1(h1(f))), n1) | (~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(out(n1, and2(h1(f))), n1)) | value(in(n1, not1(h1(f))), n1) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))))),
% 2.58/1.91 inference(rewrite,[status(thm)],[])).
% 2.58/1.91 tff(588,plain,
% 2.58/1.91 ((value(in(n1, not1(h1(f))), n1) | (~value(out(n1, and2(h1(f))), n1)) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f)))))) <=> ((~value(out(n1, and2(h1(f))), n1)) | value(in(n1, not1(h1(f))), n1) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))))),
% 2.58/1.91 inference(rewrite,[status(thm)],[])).
% 2.58/1.91 tff(589,plain,
% 2.58/1.91 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, not1(h1(f))), n1) | (~value(out(n1, and2(h1(f))), n1)) | (~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(out(n1, and2(h1(f))), n1)) | value(in(n1, not1(h1(f))), n1) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f)))))))),
% 2.58/1.91 inference(monotonicity,[status(thm)],[588])).
% 2.58/1.91 tff(590,plain,
% 2.58/1.91 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, not1(h1(f))), n1) | (~value(out(n1, and2(h1(f))), n1)) | (~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(out(n1, and2(h1(f))), n1)) | value(in(n1, not1(h1(f))), n1) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))))),
% 2.58/1.91 inference(transitivity,[status(thm)],[589, 587])).
% 2.58/1.91 tff(591,plain,
% 2.58/1.91 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, not1(h1(f))), n1) | (~value(out(n1, and2(h1(f))), n1)) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))))),
% 2.58/1.91 inference(quant_inst,[status(thm)],[])).
% 2.58/1.91 tff(592,plain,
% 2.58/1.91 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(n1, and2(h1(f))), n1)) | value(in(n1, not1(h1(f))), n1) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f)))))),
% 2.58/1.91 inference(modus_ponens,[status(thm)],[591, 590])).
% 2.58/1.91 tff(593,plain,
% 2.58/1.91 ($false),
% 2.58/1.91 inference(unit_resolution,[status(thm)],[592, 185, 586, 575, 525])).
% 2.58/1.91 tff(594,plain,(value(in(n1, not1(h1(f))), n1)), inference(lemma,lemma(discharge,[]))).
% 2.58/1.91 tff(595,plain,
% 2.58/1.91 (^[K: $i] : refl(((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not))) <=> ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not))))),
% 2.58/1.91 inference(bind,[status(th)],[])).
% 2.58/1.91 tff(596,plain,
% 2.58/1.91 (![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not))) <=> ![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not)))),
% 2.58/1.91 inference(quant_intro,[status(thm)],[595])).
% 2.58/1.91 tff(597,plain,
% 2.58/1.91 (![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not))) <=> ![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not)))),
% 2.58/1.91 inference(rewrite,[status(thm)],[])).
% 2.58/1.91 tff(598,plain,
% 2.58/1.91 (^[K: $i] : trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, not))) | (~value(in(n1, K), n1))) <=> ((~mode(K, ok)) | (~value(in(n1, K), n1)) | (~type(K, not)))), (((((~mode(K, ok)) | (~type(K, not))) | (~value(in(n1, K), n1))) | value(out(n1, K), n0)) <=> (((~mode(K, ok)) | (~value(in(n1, K), n1)) | (~type(K, not))) | value(out(n1, K), n0)))), rewrite((((~mode(K, ok)) | (~value(in(n1, K), n1)) | (~type(K, not))) | value(out(n1, K), n0)) <=> ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not)))), (((((~mode(K, ok)) | (~type(K, not))) | (~value(in(n1, K), n1))) | value(out(n1, K), n0)) <=> ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not)))))),
% 2.58/1.91 inference(bind,[status(th)],[])).
% 2.58/1.91 tff(599,plain,
% 2.58/1.91 (![K: $i] : ((((~mode(K, ok)) | (~type(K, not))) | (~value(in(n1, K), n1))) | value(out(n1, K), n0)) <=> ![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not)))),
% 2.58/1.91 inference(quant_intro,[status(thm)],[598])).
% 2.58/1.91 tff(600,axiom,(![K: $i] : ((((~mode(K, ok)) | (~type(K, not))) | (~value(in(n1, K), n1))) | value(out(n1, K), n0))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','not_1_0_fw')).
% 2.58/1.91 tff(601,plain,
% 2.58/1.91 (![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not)))),
% 2.58/1.91 inference(modus_ponens,[status(thm)],[600, 599])).
% 2.58/1.91 tff(602,plain,
% 2.58/1.91 (![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not)))),
% 2.58/1.91 inference(modus_ponens,[status(thm)],[601, 597])).
% 2.58/1.91 tff(603,plain,(
% 2.58/1.91 ![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not)))),
% 2.58/1.91 inference(skolemize,[status(sab)],[602])).
% 2.58/1.91 tff(604,plain,
% 2.58/1.91 (![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not)))),
% 2.58/1.91 inference(modus_ponens,[status(thm)],[603, 596])).
% 2.58/1.91 tff(605,plain,
% 2.58/1.91 (((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not)))) | ((~mode(not1(h1(f)), ok)) | (~value(in(n1, not1(h1(f))), n1)) | (~type(not1(h1(f)), not)) | value(out(n1, not1(h1(f))), n0))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not)))) | (~mode(not1(h1(f)), ok)) | (~value(in(n1, not1(h1(f))), n1)) | (~type(not1(h1(f)), not)) | value(out(n1, not1(h1(f))), n0))),
% 2.58/1.91 inference(rewrite,[status(thm)],[])).
% 2.58/1.91 tff(606,plain,
% 2.58/1.91 (((~mode(not1(h1(f)), ok)) | value(out(n1, not1(h1(f))), n0) | (~value(in(n1, not1(h1(f))), n1)) | (~type(not1(h1(f)), not))) <=> ((~mode(not1(h1(f)), ok)) | (~value(in(n1, not1(h1(f))), n1)) | (~type(not1(h1(f)), not)) | value(out(n1, not1(h1(f))), n0))),
% 2.58/1.91 inference(rewrite,[status(thm)],[])).
% 2.58/1.91 tff(607,plain,
% 2.58/1.91 (((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not)))) | ((~mode(not1(h1(f)), ok)) | value(out(n1, not1(h1(f))), n0) | (~value(in(n1, not1(h1(f))), n1)) | (~type(not1(h1(f)), not)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not)))) | ((~mode(not1(h1(f)), ok)) | (~value(in(n1, not1(h1(f))), n1)) | (~type(not1(h1(f)), not)) | value(out(n1, not1(h1(f))), n0)))),
% 2.58/1.91 inference(monotonicity,[status(thm)],[606])).
% 2.58/1.91 tff(608,plain,
% 2.58/1.91 (((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not)))) | ((~mode(not1(h1(f)), ok)) | value(out(n1, not1(h1(f))), n0) | (~value(in(n1, not1(h1(f))), n1)) | (~type(not1(h1(f)), not)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not)))) | (~mode(not1(h1(f)), ok)) | (~value(in(n1, not1(h1(f))), n1)) | (~type(not1(h1(f)), not)) | value(out(n1, not1(h1(f))), n0))),
% 2.58/1.91 inference(transitivity,[status(thm)],[607, 605])).
% 2.58/1.91 tff(609,plain,
% 2.58/1.91 ((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not)))) | ((~mode(not1(h1(f)), ok)) | value(out(n1, not1(h1(f))), n0) | (~value(in(n1, not1(h1(f))), n1)) | (~type(not1(h1(f)), not)))),
% 2.58/1.91 inference(quant_inst,[status(thm)],[])).
% 2.58/1.91 tff(610,plain,
% 2.58/1.91 ((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(n1, K), n1)) | (~type(K, not)))) | (~mode(not1(h1(f)), ok)) | (~value(in(n1, not1(h1(f))), n1)) | (~type(not1(h1(f)), not)) | value(out(n1, not1(h1(f))), n0)),
% 2.58/1.91 inference(modus_ponens,[status(thm)],[609, 608])).
% 2.58/1.91 tff(611,plain,
% 2.58/1.91 ((~mode(not1(h1(f)), ok)) | (~value(in(n1, not1(h1(f))), n1)) | (~type(not1(h1(f)), not)) | value(out(n1, not1(h1(f))), n0)),
% 2.58/1.91 inference(unit_resolution,[status(thm)],[610, 604])).
% 2.58/1.91 tff(612,plain,
% 2.58/1.91 ((~mode(not1(h1(f)), ok)) | (~value(in(n1, not1(h1(f))), n1)) | value(out(n1, not1(h1(f))), n0)),
% 2.58/1.91 inference(unit_resolution,[status(thm)],[611, 519])).
% 2.58/1.91 tff(613,plain,
% 2.58/1.91 ((~mode(not1(h1(f)), ok)) | value(out(n1, not1(h1(f))), n0)),
% 2.58/1.91 inference(unit_resolution,[status(thm)],[612, 594])).
% 2.58/1.91 tff(614,plain,
% 2.58/1.91 (value(out(n1, not1(h1(f))), n0)),
% 2.58/1.91 inference(unit_resolution,[status(thm)],[613, 524])).
% 2.58/1.91 tff(615,assumption,(~value(in(n2, and1(h1(f))), n0)), introduced(assumption)).
% 2.58/1.91 tff(616,plain,
% 2.58/1.91 (^[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)))))),
% 2.58/1.91 inference(bind,[status(th)],[])).
% 2.58/1.91 tff(617,plain,
% 2.58/1.91 (![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))))),
% 2.58/1.92 inference(quant_intro,[status(thm)],[616])).
% 2.58/1.92 tff(618,plain,
% 2.58/1.92 (![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))))),
% 2.58/1.92 inference(rewrite,[status(thm)],[])).
% 2.58/1.92 tff(619,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')).
% 2.58/1.92 tff(620,plain,
% 2.58/1.92 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))),
% 2.58/1.92 inference(modus_ponens,[status(thm)],[619, 618])).
% 2.58/1.92 tff(621,plain,(
% 2.58/1.92 ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))),
% 2.58/1.92 inference(skolemize,[status(sab)],[620])).
% 2.58/1.92 tff(622,plain,
% 2.58/1.92 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))),
% 2.58/1.92 inference(modus_ponens,[status(thm)],[621, 617])).
% 2.58/1.92 tff(623,plain,
% 2.58/1.92 (((~![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)))))),
% 2.58/1.92 inference(rewrite,[status(thm)],[])).
% 2.58/1.92 tff(624,plain,
% 2.58/1.92 ((~![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)))))),
% 2.58/1.92 inference(quant_inst,[status(thm)],[])).
% 2.58/1.92 tff(625,plain,
% 2.58/1.92 ((~![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))))),
% 2.58/1.92 inference(modus_ponens,[status(thm)],[624, 623])).
% 2.58/1.92 tff(626,plain,
% 2.58/1.92 (connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))),
% 2.58/1.92 inference(unit_resolution,[status(thm)],[625, 622, 60])).
% 2.58/1.92 tff(627,assumption,(value(out(n1, not1(h1(f))), n0)), introduced(assumption)).
% 2.58/1.92 tff(628,plain,
% 2.58/1.92 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(out(n1, not1(h1(f))), n0)) | value(in(n2, and1(h1(f))), n0) | (~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))), n0)) | value(in(n2, and1(h1(f))), n0) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))))),
% 2.58/1.92 inference(rewrite,[status(thm)],[])).
% 2.58/1.92 tff(629,plain,
% 2.58/1.92 ((value(in(n2, and1(h1(f))), n0) | (~value(out(n1, not1(h1(f))), n0)) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f)))))) <=> ((~value(out(n1, not1(h1(f))), n0)) | value(in(n2, and1(h1(f))), n0) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))))),
% 2.58/1.92 inference(rewrite,[status(thm)],[])).
% 2.58/1.92 tff(630,plain,
% 2.58/1.92 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, and1(h1(f))), n0) | (~value(out(n1, not1(h1(f))), n0)) | (~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))), n0)) | value(in(n2, and1(h1(f))), n0) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f)))))))),
% 2.58/1.92 inference(monotonicity,[status(thm)],[629])).
% 2.58/1.92 tff(631,plain,
% 2.58/1.92 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, and1(h1(f))), n0) | (~value(out(n1, not1(h1(f))), n0)) | (~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))), n0)) | value(in(n2, and1(h1(f))), n0) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))))),
% 2.58/1.92 inference(transitivity,[status(thm)],[630, 628])).
% 2.58/1.92 tff(632,plain,
% 2.58/1.92 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, and1(h1(f))), n0) | (~value(out(n1, not1(h1(f))), n0)) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))))),
% 2.58/1.92 inference(quant_inst,[status(thm)],[])).
% 2.58/1.92 tff(633,plain,
% 2.58/1.92 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(n1, not1(h1(f))), n0)) | value(in(n2, and1(h1(f))), n0) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f)))))),
% 2.58/1.92 inference(modus_ponens,[status(thm)],[632, 631])).
% 2.58/1.92 tff(634,plain,
% 2.58/1.92 ($false),
% 2.58/1.92 inference(unit_resolution,[status(thm)],[633, 185, 627, 626, 615])).
% 2.58/1.92 tff(635,plain,(value(in(n2, and1(h1(f))), n0) | (~value(out(n1, not1(h1(f))), n0))), inference(lemma,lemma(discharge,[]))).
% 2.58/1.92 tff(636,plain,
% 2.58/1.92 (value(in(n2, and1(h1(f))), n0)),
% 2.58/1.92 inference(unit_resolution,[status(thm)],[635, 614])).
% 2.58/1.92 tff(637,plain,
% 2.58/1.92 (^[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))))),
% 2.58/1.92 inference(bind,[status(th)],[])).
% 2.58/1.92 tff(638,plain,
% 2.58/1.92 (![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)))),
% 2.58/1.92 inference(quant_intro,[status(thm)],[637])).
% 2.58/1.92 tff(639,plain,
% 2.58/1.92 (![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)))),
% 2.58/1.92 inference(rewrite,[status(thm)],[])).
% 2.58/1.92 tff(640,plain,
% 2.58/1.92 (^[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)))))),
% 2.58/1.92 inference(bind,[status(th)],[])).
% 2.58/1.92 tff(641,plain,
% 2.58/1.92 (![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)))),
% 2.58/1.92 inference(quant_intro,[status(thm)],[640])).
% 2.58/1.92 tff(642,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')).
% 2.58/1.92 tff(643,plain,
% 2.58/1.92 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 2.58/1.92 inference(modus_ponens,[status(thm)],[642, 641])).
% 2.58/1.92 tff(644,plain,
% 2.58/1.92 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 2.58/1.92 inference(modus_ponens,[status(thm)],[643, 639])).
% 2.58/1.92 tff(645,plain,(
% 2.58/1.92 ![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 2.58/1.92 inference(skolemize,[status(sab)],[644])).
% 2.58/1.92 tff(646,plain,
% 2.58/1.92 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 2.58/1.92 inference(modus_ponens,[status(thm)],[645, 638])).
% 2.58/1.92 tff(647,plain,
% 2.58/1.92 (((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and1(h1(f)), ok)) | value(out(n1, and1(h1(f))), n0) | (~value(in(n2, and1(h1(f))), n0)) | (~type(and1(h1(f)), and)))) <=> ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | (~mode(and1(h1(f)), ok)) | value(out(n1, and1(h1(f))), n0) | (~value(in(n2, and1(h1(f))), n0)) | (~type(and1(h1(f)), and)))),
% 2.58/1.92 inference(rewrite,[status(thm)],[])).
% 2.58/1.92 tff(648,plain,
% 2.58/1.92 ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and1(h1(f)), ok)) | value(out(n1, and1(h1(f))), n0) | (~value(in(n2, and1(h1(f))), n0)) | (~type(and1(h1(f)), and)))),
% 2.58/1.92 inference(quant_inst,[status(thm)],[])).
% 2.58/1.92 tff(649,plain,
% 2.58/1.92 ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | (~mode(and1(h1(f)), ok)) | value(out(n1, and1(h1(f))), n0) | (~value(in(n2, and1(h1(f))), n0)) | (~type(and1(h1(f)), and))),
% 2.58/1.92 inference(modus_ponens,[status(thm)],[648, 647])).
% 2.58/1.92 tff(650,plain,
% 2.58/1.92 ((~mode(and1(h1(f)), ok)) | value(out(n1, and1(h1(f))), n0) | (~value(in(n2, and1(h1(f))), n0))),
% 2.58/1.92 inference(unit_resolution,[status(thm)],[649, 646, 499])).
% 2.58/1.92 tff(651,plain,
% 2.58/1.92 (value(out(n1, and1(h1(f))), n0)),
% 2.58/1.92 inference(unit_resolution,[status(thm)],[650, 636, 504])).
% 2.58/1.92 tff(652,plain,
% 2.58/1.92 (((~![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)))))),
% 2.58/1.92 inference(rewrite,[status(thm)],[])).
% 2.58/1.92 tff(653,plain,
% 2.58/1.92 ((~![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)))))),
% 2.58/1.92 inference(quant_inst,[status(thm)],[])).
% 2.58/1.92 tff(654,plain,
% 2.58/1.92 ((~![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))))),
% 2.58/1.92 inference(modus_ponens,[status(thm)],[653, 652])).
% 2.58/1.92 tff(655,plain,
% 2.58/1.92 (connection(out(s, h1(f)), out(n1, and1(h1(f))))),
% 2.58/1.92 inference(unit_resolution,[status(thm)],[654, 348, 60])).
% 2.58/1.92 tff(656,plain,
% 2.58/1.92 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(out(n1, and1(h1(f))), n0)) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))) | value(out(s, h1(f)), n0))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and1(h1(f))), n0)) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))) | value(out(s, h1(f)), n0))),
% 2.58/1.92 inference(rewrite,[status(thm)],[])).
% 2.58/1.92 tff(657,plain,
% 2.58/1.92 ((value(out(s, h1(f)), n0) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))) | (~value(out(n1, and1(h1(f))), n0))) <=> ((~value(out(n1, and1(h1(f))), n0)) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))) | value(out(s, h1(f)), n0))),
% 2.58/1.92 inference(rewrite,[status(thm)],[])).
% 2.58/1.92 tff(658,plain,
% 2.58/1.92 (((~![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)), out(n1, and1(h1(f))))) | (~value(out(n1, and1(h1(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(out(n1, and1(h1(f))), n0)) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))) | value(out(s, h1(f)), n0)))),
% 2.58/1.92 inference(monotonicity,[status(thm)],[657])).
% 2.58/1.92 tff(659,plain,
% 2.58/1.92 (((~![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)), out(n1, and1(h1(f))))) | (~value(out(n1, and1(h1(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and1(h1(f))), n0)) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))) | value(out(s, h1(f)), n0))),
% 2.58/1.92 inference(transitivity,[status(thm)],[658, 656])).
% 2.58/1.92 tff(660,plain,
% 2.58/1.92 ((~![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)), out(n1, and1(h1(f))))) | (~value(out(n1, and1(h1(f))), n0)))),
% 2.58/1.92 inference(quant_inst,[status(thm)],[])).
% 2.58/1.92 tff(661,plain,
% 2.58/1.92 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and1(h1(f))), n0)) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))) | value(out(s, h1(f)), n0)),
% 2.58/1.92 inference(modus_ponens,[status(thm)],[660, 659])).
% 2.58/1.92 tff(662,plain,
% 2.58/1.92 (value(out(s, h1(f)), n0)),
% 2.58/1.92 inference(unit_resolution,[status(thm)],[661, 45, 655, 651])).
% 2.58/1.92 tff(663,plain,
% 2.58/1.92 (((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n1, n0) | (~value(out(s, h1(f)), n0)) | (~value(out(s, h1(f)), n1)))) <=> ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n1, n0) | (~value(out(s, h1(f)), n0)) | (~value(out(s, h1(f)), n1)))),
% 2.58/1.92 inference(rewrite,[status(thm)],[])).
% 2.58/1.92 tff(664,plain,
% 2.58/1.92 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n1, n0) | (~value(out(s, h1(f)), n0)) | (~value(out(s, h1(f)), n1)))),
% 2.58/1.92 inference(quant_inst,[status(thm)],[])).
% 2.58/1.92 tff(665,plain,
% 2.58/1.92 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n1, n0) | (~value(out(s, h1(f)), n0)) | (~value(out(s, h1(f)), n1))),
% 2.58/1.92 inference(modus_ponens,[status(thm)],[664, 663])).
% 2.58/1.92 tff(666,plain,
% 2.58/1.92 ($false),
% 2.58/1.92 inference(unit_resolution,[status(thm)],[665, 31, 425, 662, 491])).
% 2.58/1.92 % SZS output end Proof
%------------------------------------------------------------------------------