TSTP Solution File: HWV008-1.002 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV008-1.002 : TPTP v8.1.0. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 02:10:30 EDT 2022
% Result : Unsatisfiable 18.15s 11.87s
% Output : Proof 18.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : HWV008-1.002 : TPTP v8.1.0. Bugfixed v2.2.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n022.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Aug 31 22:00:25 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36 Usage: tptp [options] [-file:]file
% 0.15/0.36 -h, -? prints this message.
% 0.15/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.36 -m, -model generate model.
% 0.15/0.36 -p, -proof generate proof.
% 0.15/0.36 -c, -core generate unsat core of named formulas.
% 0.15/0.36 -st, -statistics display statistics.
% 0.15/0.36 -t:timeout set timeout (in second).
% 0.15/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36 -<param>:<value> configuration parameter and value.
% 0.15/0.36 -o:<output-file> file to place output in.
% 18.15/11.87 % SZS status Unsatisfiable
% 18.15/11.87 % SZS output start Proof
% 18.15/11.87 tff(value_type, type, (
% 18.15/11.87 value: ( $i * $i ) > $o)).
% 18.15/11.87 tff(n0_type, type, (
% 18.15/11.87 n0: $i)).
% 18.15/11.87 tff(out_type, type, (
% 18.15/11.87 out: ( $i * $i ) > $i)).
% 18.15/11.87 tff(h2_type, type, (
% 18.15/11.87 h2: $i > $i)).
% 18.15/11.87 tff(f_type, type, (
% 18.15/11.87 f: ( $i * $i ) > $i)).
% 18.15/11.87 tff(a_type, type, (
% 18.15/11.87 a: $i)).
% 18.15/11.87 tff(n2_type, type, (
% 18.15/11.87 n2: $i)).
% 18.15/11.87 tff(c_type, type, (
% 18.15/11.87 c: $i)).
% 18.15/11.87 tff(and2_type, type, (
% 18.15/11.87 and2: $i > $i)).
% 18.15/11.87 tff(n1_type, type, (
% 18.15/11.87 n1: $i)).
% 18.15/11.87 tff(in_type, type, (
% 18.15/11.87 in: ( $i * $i ) > $i)).
% 18.15/11.87 tff(connection_type, type, (
% 18.15/11.87 connection: ( $i * $i ) > $o)).
% 18.15/11.87 tff(a2_type, type, (
% 18.15/11.87 a2: $i)).
% 18.15/11.87 tff(type_type, type, (
% 18.15/11.87 type: ( $i * $i ) > $o)).
% 18.15/11.87 tff(nbit_adder_type, type, (
% 18.15/11.87 nbit_adder: $i > $i)).
% 18.15/11.87 tff(fulladder_type, type, (
% 18.15/11.87 fulladder: $i)).
% 18.15/11.87 tff(halfadder_type, type, (
% 18.15/11.87 halfadder: $i)).
% 18.15/11.87 tff(mode_type, type, (
% 18.15/11.87 mode: ( $i * $i ) > $o)).
% 18.15/11.87 tff(ok_type, type, (
% 18.15/11.87 ok: $i)).
% 18.15/11.87 tff(and_type, type, (
% 18.15/11.87 and: $i)).
% 18.15/11.87 tff(abnormal_type, type, (
% 18.15/11.87 abnormal: $i)).
% 18.15/11.87 tff(or1_type, type, (
% 18.15/11.87 or1: $i > $i)).
% 18.15/11.87 tff(h1_type, type, (
% 18.15/11.87 h1: $i > $i)).
% 18.15/11.87 tff(b2_type, type, (
% 18.15/11.87 b2: $i)).
% 18.15/11.87 tff(equal_value_type, type, (
% 18.15/11.87 equal_value: ( $i * $i ) > $o)).
% 18.15/11.87 tff(or_type, type, (
% 18.15/11.87 or: $i)).
% 18.15/11.87 tff(1,assumption,(~value(in(n1, and2(h2(f(n2, a)))), n0)), introduced(assumption)).
% 18.15/11.87 tff(2,assumption,(~value(in(n1, f(n2, a)), n0)), introduced(assumption)).
% 18.15/11.87 tff(3,plain,
% 18.15/11.87 (type(a, nbit_adder(n2)) <=> type(a, nbit_adder(n2))),
% 18.15/11.87 inference(rewrite,[status(thm)],[])).
% 18.15/11.87 tff(4,axiom,(type(a, nbit_adder(n2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_isa_2bit_adder')).
% 18.15/11.87 tff(5,plain,
% 18.15/11.87 (type(a, nbit_adder(n2))),
% 18.15/11.87 inference(modus_ponens,[status(thm)],[4, 3])).
% 18.15/11.87 tff(6,plain,
% 18.15/11.87 (^[X: $i] : refl(((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X)))) <=> ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X)))))),
% 18.15/11.87 inference(bind,[status(th)],[])).
% 18.15/11.87 tff(7,plain,
% 18.15/11.87 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))),
% 18.15/11.87 inference(quant_intro,[status(thm)],[6])).
% 18.15/11.87 tff(8,plain,
% 18.15/11.87 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))),
% 18.15/11.87 inference(rewrite,[status(thm)],[])).
% 18.15/11.87 tff(9,axiom,(![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nbit_adder_connection_ina2_in1f2')).
% 18.15/11.87 tff(10,plain,
% 18.15/11.87 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))),
% 18.15/11.87 inference(modus_ponens,[status(thm)],[9, 8])).
% 18.15/11.87 tff(11,plain,(
% 18.15/11.87 ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))),
% 18.15/11.87 inference(skolemize,[status(sab)],[10])).
% 18.15/11.87 tff(12,plain,
% 18.15/11.87 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))),
% 18.15/11.87 inference(modus_ponens,[status(thm)],[11, 7])).
% 18.15/11.87 tff(13,plain,
% 18.15/11.87 (((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))) | ((~type(a, nbit_adder(n2))) | connection(in(a2, a), in(n1, f(n2, a))))) <=> ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))) | (~type(a, nbit_adder(n2))) | connection(in(a2, a), in(n1, f(n2, a))))),
% 18.15/11.87 inference(rewrite,[status(thm)],[])).
% 18.15/11.87 tff(14,plain,
% 18.15/11.87 ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))) | ((~type(a, nbit_adder(n2))) | connection(in(a2, a), in(n1, f(n2, a))))),
% 18.15/11.87 inference(quant_inst,[status(thm)],[])).
% 18.15/11.87 tff(15,plain,
% 18.15/11.87 ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))) | (~type(a, nbit_adder(n2))) | connection(in(a2, a), in(n1, f(n2, a)))),
% 18.15/11.87 inference(modus_ponens,[status(thm)],[14, 13])).
% 18.15/11.87 tff(16,plain,
% 18.15/11.87 (connection(in(a2, a), in(n1, f(n2, a)))),
% 18.15/11.87 inference(unit_resolution,[status(thm)],[15, 12, 5])).
% 18.15/11.87 tff(17,plain,
% 18.15/11.87 (value(in(a2, a), n0) <=> value(in(a2, a), n0)),
% 18.15/11.87 inference(rewrite,[status(thm)],[])).
% 18.15/11.87 tff(18,axiom,(value(in(a2, a), n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ina2_0')).
% 18.15/11.87 tff(19,plain,
% 18.15/11.87 (value(in(a2, a), n0)),
% 18.15/11.87 inference(modus_ponens,[status(thm)],[18, 17])).
% 18.15/11.87 tff(20,plain,
% 18.15/11.87 (^[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))))),
% 18.15/11.87 inference(bind,[status(th)],[])).
% 18.15/11.87 tff(21,plain,
% 18.15/11.87 (![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)))),
% 18.15/11.87 inference(quant_intro,[status(thm)],[20])).
% 18.15/11.87 tff(22,plain,
% 18.15/11.87 (![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)))),
% 18.15/11.87 inference(rewrite,[status(thm)],[])).
% 18.15/11.87 tff(23,plain,
% 18.15/11.87 (^[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))))),
% 18.15/11.87 inference(bind,[status(th)],[])).
% 18.15/11.87 tff(24,plain,
% 18.15/11.87 (![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)))),
% 18.15/11.87 inference(quant_intro,[status(thm)],[23])).
% 18.15/11.87 tff(25,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')).
% 18.15/11.87 tff(26,plain,
% 18.15/11.87 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 18.15/11.87 inference(modus_ponens,[status(thm)],[25, 24])).
% 18.15/11.87 tff(27,plain,
% 18.15/11.87 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 18.15/11.87 inference(modus_ponens,[status(thm)],[26, 22])).
% 18.15/11.87 tff(28,plain,(
% 18.15/11.87 ![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 18.15/11.87 inference(skolemize,[status(sab)],[27])).
% 18.15/11.87 tff(29,plain,
% 18.15/11.87 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 18.15/11.87 inference(modus_ponens,[status(thm)],[28, 21])).
% 18.15/11.87 tff(30,plain,
% 18.15/11.87 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(a2, a), n0)) | (~connection(in(a2, a), in(n1, f(n2, a)))) | value(in(n1, f(n2, a)), n0))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(a2, a), n0)) | (~connection(in(a2, a), in(n1, f(n2, a)))) | value(in(n1, f(n2, a)), n0))),
% 18.15/11.87 inference(rewrite,[status(thm)],[])).
% 18.15/11.87 tff(31,plain,
% 18.15/11.87 ((value(in(n1, f(n2, a)), n0) | (~value(in(a2, a), n0)) | (~connection(in(a2, a), in(n1, f(n2, a))))) <=> ((~value(in(a2, a), n0)) | (~connection(in(a2, a), in(n1, f(n2, a)))) | value(in(n1, f(n2, a)), n0))),
% 18.15/11.87 inference(rewrite,[status(thm)],[])).
% 18.15/11.87 tff(32,plain,
% 18.15/11.87 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, f(n2, a)), n0) | (~value(in(a2, a), n0)) | (~connection(in(a2, a), in(n1, f(n2, a)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(a2, a), n0)) | (~connection(in(a2, a), in(n1, f(n2, a)))) | value(in(n1, f(n2, a)), n0)))),
% 18.15/11.87 inference(monotonicity,[status(thm)],[31])).
% 18.15/11.87 tff(33,plain,
% 18.15/11.87 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, f(n2, a)), n0) | (~value(in(a2, a), n0)) | (~connection(in(a2, a), in(n1, f(n2, a)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(a2, a), n0)) | (~connection(in(a2, a), in(n1, f(n2, a)))) | value(in(n1, f(n2, a)), n0))),
% 18.15/11.87 inference(transitivity,[status(thm)],[32, 30])).
% 18.15/11.87 tff(34,plain,
% 18.15/11.87 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, f(n2, a)), n0) | (~value(in(a2, a), n0)) | (~connection(in(a2, a), in(n1, f(n2, a)))))),
% 18.15/11.87 inference(quant_inst,[status(thm)],[])).
% 18.15/11.87 tff(35,plain,
% 18.15/11.87 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(a2, a), n0)) | (~connection(in(a2, a), in(n1, f(n2, a)))) | value(in(n1, f(n2, a)), n0)),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[34, 33])).
% 18.15/11.88 tff(36,plain,
% 18.15/11.88 ($false),
% 18.15/11.88 inference(unit_resolution,[status(thm)],[35, 29, 19, 16, 2])).
% 18.15/11.88 tff(37,plain,(value(in(n1, f(n2, a)), n0)), inference(lemma,lemma(discharge,[]))).
% 18.15/11.88 tff(38,plain,
% 18.15/11.88 (^[X: $i] : refl(((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder)) <=> ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder)))),
% 18.15/11.88 inference(bind,[status(th)],[])).
% 18.15/11.88 tff(39,plain,
% 18.15/11.88 (![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder)) <=> ![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))),
% 18.15/11.88 inference(quant_intro,[status(thm)],[38])).
% 18.15/11.88 tff(40,plain,
% 18.15/11.88 (![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder)) <=> ![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.88 tff(41,axiom,(![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nbit_adder_fulladder2')).
% 18.15/11.88 tff(42,plain,
% 18.15/11.88 (![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[41, 40])).
% 18.15/11.88 tff(43,plain,(
% 18.15/11.88 ![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))),
% 18.15/11.88 inference(skolemize,[status(sab)],[42])).
% 18.15/11.88 tff(44,plain,
% 18.15/11.88 (![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[43, 39])).
% 18.15/11.88 tff(45,plain,
% 18.15/11.88 (((~![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))) | ((~type(a, nbit_adder(n2))) | type(f(n2, a), fulladder))) <=> ((~![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))) | (~type(a, nbit_adder(n2))) | type(f(n2, a), fulladder))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.88 tff(46,plain,
% 18.15/11.88 ((~![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))) | ((~type(a, nbit_adder(n2))) | type(f(n2, a), fulladder))),
% 18.15/11.88 inference(quant_inst,[status(thm)],[])).
% 18.15/11.88 tff(47,plain,
% 18.15/11.88 ((~![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))) | (~type(a, nbit_adder(n2))) | type(f(n2, a), fulladder)),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[46, 45])).
% 18.15/11.88 tff(48,plain,
% 18.15/11.88 (type(f(n2, a), fulladder)),
% 18.15/11.88 inference(unit_resolution,[status(thm)],[47, 44, 5])).
% 18.15/11.88 tff(49,plain,
% 18.15/11.88 (^[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)))))),
% 18.15/11.88 inference(bind,[status(th)],[])).
% 18.15/11.88 tff(50,plain,
% 18.15/11.88 (![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))))),
% 18.15/11.88 inference(quant_intro,[status(thm)],[49])).
% 18.15/11.88 tff(51,plain,
% 18.15/11.88 (![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))))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.88 tff(52,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')).
% 18.15/11.88 tff(53,plain,
% 18.15/11.88 (![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[52, 51])).
% 18.15/11.88 tff(54,plain,(
% 18.15/11.88 ![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 18.15/11.88 inference(skolemize,[status(sab)],[53])).
% 18.15/11.88 tff(55,plain,
% 18.15/11.88 (![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[54, 50])).
% 18.15/11.88 tff(56,plain,
% 18.15/11.88 (((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | ((~type(f(n2, a), fulladder)) | connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a)))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | (~type(f(n2, a), fulladder)) | connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a)))))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.88 tff(57,plain,
% 18.15/11.88 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | ((~type(f(n2, a), fulladder)) | connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a)))))),
% 18.15/11.88 inference(quant_inst,[status(thm)],[])).
% 18.15/11.88 tff(58,plain,
% 18.15/11.88 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | (~type(f(n2, a), fulladder)) | connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[57, 56])).
% 18.15/11.88 tff(59,plain,
% 18.15/11.88 (connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))),
% 18.15/11.88 inference(unit_resolution,[status(thm)],[58, 55, 48])).
% 18.15/11.88 tff(60,plain,
% 18.15/11.88 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(n1, f(n2, a)), n0)) | value(in(n1, h2(f(n2, a))), n0) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n1, f(n2, a)), n0)) | value(in(n1, h2(f(n2, a))), n0) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.88 tff(61,plain,
% 18.15/11.88 ((value(in(n1, h2(f(n2, a))), n0) | (~value(in(n1, f(n2, a)), n0)) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a)))))) <=> ((~value(in(n1, f(n2, a)), n0)) | value(in(n1, h2(f(n2, a))), n0) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.88 tff(62,plain,
% 18.15/11.88 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, h2(f(n2, a))), n0) | (~value(in(n1, f(n2, a)), n0)) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(n1, f(n2, a)), n0)) | value(in(n1, h2(f(n2, a))), n0) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a)))))))),
% 18.15/11.88 inference(monotonicity,[status(thm)],[61])).
% 18.15/11.88 tff(63,plain,
% 18.15/11.88 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, h2(f(n2, a))), n0) | (~value(in(n1, f(n2, a)), n0)) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n1, f(n2, a)), n0)) | value(in(n1, h2(f(n2, a))), n0) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))))),
% 18.15/11.88 inference(transitivity,[status(thm)],[62, 60])).
% 18.15/11.88 tff(64,plain,
% 18.15/11.88 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, h2(f(n2, a))), n0) | (~value(in(n1, f(n2, a)), n0)) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))))),
% 18.15/11.88 inference(quant_inst,[status(thm)],[])).
% 18.15/11.88 tff(65,plain,
% 18.15/11.88 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n1, f(n2, a)), n0)) | value(in(n1, h2(f(n2, a))), n0) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a)))))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[64, 63])).
% 18.15/11.88 tff(66,plain,
% 18.15/11.88 (value(in(n1, h2(f(n2, a))), n0)),
% 18.15/11.88 inference(unit_resolution,[status(thm)],[65, 29, 59, 37])).
% 18.15/11.88 tff(67,plain,
% 18.15/11.88 (^[X: $i] : refl(((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ((~type(X, fulladder)) | type(h2(X), halfadder)))),
% 18.15/11.88 inference(bind,[status(th)],[])).
% 18.15/11.88 tff(68,plain,
% 18.15/11.88 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 18.15/11.88 inference(quant_intro,[status(thm)],[67])).
% 18.15/11.88 tff(69,plain,
% 18.15/11.88 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.88 tff(70,axiom,(![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_halfadder2')).
% 18.15/11.88 tff(71,plain,
% 18.15/11.88 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[70, 69])).
% 18.15/11.88 tff(72,plain,(
% 18.15/11.88 ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 18.15/11.88 inference(skolemize,[status(sab)],[71])).
% 18.15/11.88 tff(73,plain,
% 18.15/11.88 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[72, 68])).
% 18.15/11.88 tff(74,plain,
% 18.15/11.88 (((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | ((~type(f(n2, a), fulladder)) | type(h2(f(n2, a)), halfadder))) <=> ((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | (~type(f(n2, a), fulladder)) | type(h2(f(n2, a)), halfadder))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.88 tff(75,plain,
% 18.15/11.88 ((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | ((~type(f(n2, a), fulladder)) | type(h2(f(n2, a)), halfadder))),
% 18.15/11.88 inference(quant_inst,[status(thm)],[])).
% 18.15/11.88 tff(76,plain,
% 18.15/11.88 ((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | (~type(f(n2, a), fulladder)) | type(h2(f(n2, a)), halfadder)),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[75, 74])).
% 18.15/11.88 tff(77,plain,
% 18.15/11.88 (type(h2(f(n2, a)), halfadder)),
% 18.15/11.88 inference(unit_resolution,[status(thm)],[76, 73, 48])).
% 18.15/11.88 tff(78,plain,
% 18.15/11.88 (^[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)))))),
% 18.15/11.88 inference(bind,[status(th)],[])).
% 18.15/11.88 tff(79,plain,
% 18.15/11.88 (![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))))),
% 18.15/11.88 inference(quant_intro,[status(thm)],[78])).
% 18.15/11.88 tff(80,plain,
% 18.15/11.88 (![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))))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.88 tff(81,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')).
% 18.15/11.88 tff(82,plain,
% 18.15/11.88 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[81, 80])).
% 18.15/11.88 tff(83,plain,(
% 18.15/11.88 ![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 18.15/11.88 inference(skolemize,[status(sab)],[82])).
% 18.15/11.88 tff(84,plain,
% 18.15/11.88 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[83, 79])).
% 18.15/11.88 tff(85,plain,
% 18.15/11.88 (((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h2(f(n2, a)), halfadder)) | connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a))))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h2(f(n2, a)), halfadder)) | connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a))))))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.88 tff(86,plain,
% 18.15/11.88 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h2(f(n2, a)), halfadder)) | connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a))))))),
% 18.15/11.88 inference(quant_inst,[status(thm)],[])).
% 18.15/11.88 tff(87,plain,
% 18.15/11.88 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h2(f(n2, a)), halfadder)) | connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[86, 85])).
% 18.15/11.88 tff(88,plain,
% 18.15/11.88 ((~type(h2(f(n2, a)), halfadder)) | connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))),
% 18.15/11.88 inference(unit_resolution,[status(thm)],[87, 84])).
% 18.15/11.88 tff(89,plain,
% 18.15/11.88 (connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))),
% 18.15/11.88 inference(unit_resolution,[status(thm)],[88, 77])).
% 18.15/11.88 tff(90,plain,
% 18.15/11.88 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(n1, h2(f(n2, a))), n0)) | value(in(n1, and2(h2(f(n2, a)))), n0) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n1, h2(f(n2, a))), n0)) | value(in(n1, and2(h2(f(n2, a)))), n0) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.88 tff(91,plain,
% 18.15/11.88 ((value(in(n1, and2(h2(f(n2, a)))), n0) | (~value(in(n1, h2(f(n2, a))), n0)) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a))))))) <=> ((~value(in(n1, h2(f(n2, a))), n0)) | value(in(n1, and2(h2(f(n2, a)))), n0) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.88 tff(92,plain,
% 18.15/11.88 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, and2(h2(f(n2, a)))), n0) | (~value(in(n1, h2(f(n2, a))), n0)) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(n1, h2(f(n2, a))), n0)) | value(in(n1, and2(h2(f(n2, a)))), n0) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a))))))))),
% 18.15/11.88 inference(monotonicity,[status(thm)],[91])).
% 18.15/11.88 tff(93,plain,
% 18.15/11.88 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, and2(h2(f(n2, a)))), n0) | (~value(in(n1, h2(f(n2, a))), n0)) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n1, h2(f(n2, a))), n0)) | value(in(n1, and2(h2(f(n2, a)))), n0) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))))),
% 18.15/11.88 inference(transitivity,[status(thm)],[92, 90])).
% 18.15/11.88 tff(94,plain,
% 18.15/11.88 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, and2(h2(f(n2, a)))), n0) | (~value(in(n1, h2(f(n2, a))), n0)) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))))),
% 18.15/11.88 inference(quant_inst,[status(thm)],[])).
% 18.15/11.88 tff(95,plain,
% 18.15/11.88 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n1, h2(f(n2, a))), n0)) | value(in(n1, and2(h2(f(n2, a)))), n0) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a))))))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[94, 93])).
% 18.15/11.88 tff(96,plain,
% 18.15/11.88 ($false),
% 18.15/11.88 inference(unit_resolution,[status(thm)],[95, 29, 89, 66, 1])).
% 18.15/11.88 tff(97,plain,(value(in(n1, and2(h2(f(n2, a)))), n0)), inference(lemma,lemma(discharge,[]))).
% 18.15/11.88 tff(98,plain,
% 18.15/11.88 (^[X: $i] : refl(((~type(X, halfadder)) | type(and2(X), and)) <=> ((~type(X, halfadder)) | type(and2(X), and)))),
% 18.15/11.88 inference(bind,[status(th)],[])).
% 18.15/11.88 tff(99,plain,
% 18.15/11.88 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 18.15/11.88 inference(quant_intro,[status(thm)],[98])).
% 18.15/11.88 tff(100,plain,
% 18.15/11.88 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.88 tff(101,axiom,(![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_and2')).
% 18.15/11.88 tff(102,plain,
% 18.15/11.88 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[101, 100])).
% 18.15/11.88 tff(103,plain,(
% 18.15/11.88 ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 18.15/11.88 inference(skolemize,[status(sab)],[102])).
% 18.15/11.88 tff(104,plain,
% 18.15/11.88 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[103, 99])).
% 18.15/11.88 tff(105,plain,
% 18.15/11.88 (((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h2(f(n2, a)), halfadder)) | type(and2(h2(f(n2, a))), and))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h2(f(n2, a)), halfadder)) | type(and2(h2(f(n2, a))), and))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.88 tff(106,plain,
% 18.15/11.88 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h2(f(n2, a)), halfadder)) | type(and2(h2(f(n2, a))), and))),
% 18.15/11.88 inference(quant_inst,[status(thm)],[])).
% 18.15/11.88 tff(107,plain,
% 18.15/11.88 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h2(f(n2, a)), halfadder)) | type(and2(h2(f(n2, a))), and)),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[106, 105])).
% 18.15/11.88 tff(108,plain,
% 18.15/11.88 ((~type(h2(f(n2, a)), halfadder)) | type(and2(h2(f(n2, a))), and)),
% 18.15/11.88 inference(unit_resolution,[status(thm)],[107, 104])).
% 18.15/11.88 tff(109,plain,
% 18.15/11.88 (type(and2(h2(f(n2, a))), and)),
% 18.15/11.88 inference(unit_resolution,[status(thm)],[108, 77])).
% 18.15/11.88 tff(110,plain,
% 18.15/11.88 ((~mode(and2(h2(f(n2, a))), abnormal)) <=> (~mode(and2(h2(f(n2, a))), abnormal))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.88 tff(111,axiom,(~mode(and2(h2(f(n2, a))), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_and2h1f2a')).
% 18.15/11.88 tff(112,plain,
% 18.15/11.88 (~mode(and2(h2(f(n2, a))), abnormal)),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[111, 110])).
% 18.15/11.88 tff(113,plain,
% 18.15/11.88 (^[Any: $i, K: $i] : refl((mode(K, abnormal) | mode(K, ok) | (~type(K, Any))) <=> (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))))),
% 18.15/11.88 inference(bind,[status(th)],[])).
% 18.15/11.88 tff(114,plain,
% 18.15/11.88 (![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)))),
% 18.15/11.88 inference(quant_intro,[status(thm)],[113])).
% 18.15/11.88 tff(115,plain,
% 18.15/11.88 (![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)))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.88 tff(116,plain,
% 18.15/11.88 (^[Any: $i, K: $i] : rewrite((((~type(K, Any)) | mode(K, ok)) | mode(K, abnormal)) <=> (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))))),
% 18.15/11.88 inference(bind,[status(th)],[])).
% 18.15/11.88 tff(117,plain,
% 18.15/11.88 (![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)))),
% 18.15/11.88 inference(quant_intro,[status(thm)],[116])).
% 18.15/11.88 tff(118,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')).
% 18.15/11.88 tff(119,plain,
% 18.15/11.88 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[118, 117])).
% 18.15/11.88 tff(120,plain,
% 18.15/11.88 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[119, 115])).
% 18.15/11.88 tff(121,plain,(
% 18.15/11.88 ![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 18.15/11.88 inference(skolemize,[status(sab)],[120])).
% 18.15/11.88 tff(122,plain,
% 18.15/11.88 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[121, 114])).
% 18.15/11.88 tff(123,plain,
% 18.15/11.88 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h2(f(n2, a))), abnormal) | mode(and2(h2(f(n2, a))), ok) | (~type(and2(h2(f(n2, a))), and)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h2(f(n2, a))), abnormal) | mode(and2(h2(f(n2, a))), ok) | (~type(and2(h2(f(n2, a))), and)))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.88 tff(124,plain,
% 18.15/11.88 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h2(f(n2, a))), abnormal) | mode(and2(h2(f(n2, a))), ok) | (~type(and2(h2(f(n2, a))), and)))),
% 18.15/11.88 inference(quant_inst,[status(thm)],[])).
% 18.15/11.88 tff(125,plain,
% 18.15/11.88 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h2(f(n2, a))), abnormal) | mode(and2(h2(f(n2, a))), ok) | (~type(and2(h2(f(n2, a))), and))),
% 18.15/11.88 inference(modus_ponens,[status(thm)],[124, 123])).
% 18.15/11.88 tff(126,plain,
% 18.15/11.88 (mode(and2(h2(f(n2, a))), ok)),
% 18.15/11.88 inference(unit_resolution,[status(thm)],[125, 122, 112, 109])).
% 18.15/11.88 tff(127,plain,
% 18.15/11.88 (^[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))))),
% 18.15/11.88 inference(bind,[status(th)],[])).
% 18.15/11.88 tff(128,plain,
% 18.15/11.88 (![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)))),
% 18.15/11.88 inference(quant_intro,[status(thm)],[127])).
% 18.15/11.88 tff(129,plain,
% 18.15/11.88 (![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)))),
% 18.15/11.88 inference(rewrite,[status(thm)],[])).
% 18.15/11.89 tff(130,plain,
% 18.15/11.89 (^[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)))))),
% 18.15/11.89 inference(bind,[status(th)],[])).
% 18.15/11.89 tff(131,plain,
% 18.15/11.89 (![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)))),
% 18.15/11.89 inference(quant_intro,[status(thm)],[130])).
% 18.15/11.89 tff(132,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')).
% 18.15/11.89 tff(133,plain,
% 18.15/11.89 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[132, 131])).
% 18.15/11.89 tff(134,plain,
% 18.15/11.89 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[133, 129])).
% 18.15/11.89 tff(135,plain,(
% 18.15/11.89 ![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 18.15/11.89 inference(skolemize,[status(sab)],[134])).
% 18.15/11.89 tff(136,plain,
% 18.15/11.89 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[135, 128])).
% 18.15/11.89 tff(137,plain,
% 18.15/11.89 (((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h2(f(n2, a))), ok)) | value(out(n1, and2(h2(f(n2, a)))), n0) | (~type(and2(h2(f(n2, a))), and)) | (~value(in(n1, and2(h2(f(n2, a)))), n0)))) <=> ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | (~mode(and2(h2(f(n2, a))), ok)) | value(out(n1, and2(h2(f(n2, a)))), n0) | (~type(and2(h2(f(n2, a))), and)) | (~value(in(n1, and2(h2(f(n2, a)))), n0)))),
% 18.15/11.89 inference(rewrite,[status(thm)],[])).
% 18.15/11.89 tff(138,plain,
% 18.15/11.89 (((~mode(and2(h2(f(n2, a))), ok)) | value(out(n1, and2(h2(f(n2, a)))), n0) | (~value(in(n1, and2(h2(f(n2, a)))), n0)) | (~type(and2(h2(f(n2, a))), and))) <=> ((~mode(and2(h2(f(n2, a))), ok)) | value(out(n1, and2(h2(f(n2, a)))), n0) | (~type(and2(h2(f(n2, a))), and)) | (~value(in(n1, and2(h2(f(n2, a)))), n0)))),
% 18.15/11.89 inference(rewrite,[status(thm)],[])).
% 18.15/11.89 tff(139,plain,
% 18.15/11.89 (((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h2(f(n2, a))), ok)) | value(out(n1, and2(h2(f(n2, a)))), n0) | (~value(in(n1, and2(h2(f(n2, a)))), n0)) | (~type(and2(h2(f(n2, a))), and)))) <=> ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h2(f(n2, a))), ok)) | value(out(n1, and2(h2(f(n2, a)))), n0) | (~type(and2(h2(f(n2, a))), and)) | (~value(in(n1, and2(h2(f(n2, a)))), n0))))),
% 18.15/11.89 inference(monotonicity,[status(thm)],[138])).
% 18.15/11.89 tff(140,plain,
% 18.15/11.89 (((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h2(f(n2, a))), ok)) | value(out(n1, and2(h2(f(n2, a)))), n0) | (~value(in(n1, and2(h2(f(n2, a)))), n0)) | (~type(and2(h2(f(n2, a))), and)))) <=> ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | (~mode(and2(h2(f(n2, a))), ok)) | value(out(n1, and2(h2(f(n2, a)))), n0) | (~type(and2(h2(f(n2, a))), and)) | (~value(in(n1, and2(h2(f(n2, a)))), n0)))),
% 18.15/11.89 inference(transitivity,[status(thm)],[139, 137])).
% 18.15/11.89 tff(141,plain,
% 18.15/11.89 ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h2(f(n2, a))), ok)) | value(out(n1, and2(h2(f(n2, a)))), n0) | (~value(in(n1, and2(h2(f(n2, a)))), n0)) | (~type(and2(h2(f(n2, a))), and)))),
% 18.15/11.89 inference(quant_inst,[status(thm)],[])).
% 18.15/11.89 tff(142,plain,
% 18.15/11.89 ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | (~mode(and2(h2(f(n2, a))), ok)) | value(out(n1, and2(h2(f(n2, a)))), n0) | (~type(and2(h2(f(n2, a))), and)) | (~value(in(n1, and2(h2(f(n2, a)))), n0))),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[141, 140])).
% 18.15/11.89 tff(143,plain,
% 18.15/11.89 ((~mode(and2(h2(f(n2, a))), ok)) | value(out(n1, and2(h2(f(n2, a)))), n0) | (~value(in(n1, and2(h2(f(n2, a)))), n0))),
% 18.15/11.89 inference(unit_resolution,[status(thm)],[142, 136, 109])).
% 18.15/11.89 tff(144,plain,
% 18.15/11.89 (value(out(n1, and2(h2(f(n2, a)))), n0) | (~value(in(n1, and2(h2(f(n2, a)))), n0))),
% 18.15/11.89 inference(unit_resolution,[status(thm)],[143, 126])).
% 18.15/11.89 tff(145,plain,
% 18.15/11.89 (value(out(n1, and2(h2(f(n2, a)))), n0)),
% 18.15/11.89 inference(unit_resolution,[status(thm)],[144, 97])).
% 18.15/11.89 tff(146,plain,
% 18.15/11.89 (^[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)))))),
% 18.15/11.89 inference(bind,[status(th)],[])).
% 18.15/11.89 tff(147,plain,
% 18.15/11.89 (![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))))),
% 18.15/11.89 inference(quant_intro,[status(thm)],[146])).
% 18.15/11.89 tff(148,plain,
% 18.15/11.89 (![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))))),
% 18.15/11.89 inference(rewrite,[status(thm)],[])).
% 18.15/11.89 tff(149,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')).
% 18.15/11.89 tff(150,plain,
% 18.15/11.89 (![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[149, 148])).
% 18.15/11.89 tff(151,plain,(
% 18.15/11.89 ![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 18.15/11.89 inference(skolemize,[status(sab)],[150])).
% 18.15/11.89 tff(152,plain,
% 18.15/11.89 (![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[151, 147])).
% 18.15/11.89 tff(153,plain,
% 18.15/11.89 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h2(f(n2, a)), halfadder)) | connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a))))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h2(f(n2, a)), halfadder)) | connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a))))))),
% 18.15/11.89 inference(rewrite,[status(thm)],[])).
% 18.15/11.89 tff(154,plain,
% 18.15/11.89 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h2(f(n2, a)), halfadder)) | connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a))))))),
% 18.15/11.89 inference(quant_inst,[status(thm)],[])).
% 18.15/11.89 tff(155,plain,
% 18.15/11.89 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h2(f(n2, a)), halfadder)) | connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a)))))),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[154, 153])).
% 18.15/11.89 tff(156,plain,
% 18.15/11.89 ((~type(h2(f(n2, a)), halfadder)) | connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a)))))),
% 18.15/11.89 inference(unit_resolution,[status(thm)],[155, 152])).
% 18.15/11.89 tff(157,plain,
% 18.15/11.89 (connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a)))))),
% 18.15/11.89 inference(unit_resolution,[status(thm)],[156, 77])).
% 18.15/11.89 tff(158,plain,
% 18.15/11.89 (^[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))))),
% 18.15/11.89 inference(bind,[status(th)],[])).
% 18.15/11.89 tff(159,plain,
% 18.15/11.89 (![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)))),
% 18.15/11.89 inference(quant_intro,[status(thm)],[158])).
% 18.15/11.89 tff(160,plain,
% 18.15/11.89 (![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)))),
% 18.15/11.89 inference(rewrite,[status(thm)],[])).
% 18.15/11.89 tff(161,plain,
% 18.15/11.89 (^[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))))),
% 18.15/11.89 inference(bind,[status(th)],[])).
% 18.15/11.89 tff(162,plain,
% 18.15/11.89 (![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)))),
% 18.15/11.89 inference(quant_intro,[status(thm)],[161])).
% 18.15/11.89 tff(163,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')).
% 18.15/11.89 tff(164,plain,
% 18.15/11.89 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[163, 162])).
% 18.15/11.89 tff(165,plain,
% 18.15/11.89 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[164, 160])).
% 18.15/11.89 tff(166,plain,(
% 18.15/11.89 ![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 18.15/11.89 inference(skolemize,[status(sab)],[165])).
% 18.15/11.89 tff(167,plain,
% 18.15/11.89 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[166, 159])).
% 18.15/11.89 tff(168,plain,
% 18.15/11.89 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(out(n1, and2(h2(f(n2, a)))), n0)) | value(out(c, h2(f(n2, a))), n0) | (~connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a)))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and2(h2(f(n2, a)))), n0)) | value(out(c, h2(f(n2, a))), n0) | (~connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a)))))))),
% 18.15/11.89 inference(rewrite,[status(thm)],[])).
% 18.15/11.89 tff(169,plain,
% 18.15/11.89 ((value(out(c, h2(f(n2, a))), n0) | (~connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a)))))) | (~value(out(n1, and2(h2(f(n2, a)))), n0))) <=> ((~value(out(n1, and2(h2(f(n2, a)))), n0)) | value(out(c, h2(f(n2, a))), n0) | (~connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a)))))))),
% 18.15/11.89 inference(rewrite,[status(thm)],[])).
% 18.15/11.89 tff(170,plain,
% 18.15/11.89 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(f(n2, a))), n0) | (~connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a)))))) | (~value(out(n1, and2(h2(f(n2, a)))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(out(n1, and2(h2(f(n2, a)))), n0)) | value(out(c, h2(f(n2, a))), n0) | (~connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a))))))))),
% 18.15/11.89 inference(monotonicity,[status(thm)],[169])).
% 18.15/11.89 tff(171,plain,
% 18.15/11.89 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(f(n2, a))), n0) | (~connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a)))))) | (~value(out(n1, and2(h2(f(n2, a)))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and2(h2(f(n2, a)))), n0)) | value(out(c, h2(f(n2, a))), n0) | (~connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a)))))))),
% 18.15/11.89 inference(transitivity,[status(thm)],[170, 168])).
% 18.15/11.89 tff(172,plain,
% 18.15/11.89 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(f(n2, a))), n0) | (~connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a)))))) | (~value(out(n1, and2(h2(f(n2, a)))), n0)))),
% 18.15/11.89 inference(quant_inst,[status(thm)],[])).
% 18.15/11.89 tff(173,plain,
% 18.15/11.89 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and2(h2(f(n2, a)))), n0)) | value(out(c, h2(f(n2, a))), n0) | (~connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a))))))),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[172, 171])).
% 18.15/11.89 tff(174,plain,
% 18.15/11.89 (value(out(c, h2(f(n2, a))), n0)),
% 18.15/11.89 inference(unit_resolution,[status(thm)],[173, 167, 157, 145])).
% 18.15/11.89 tff(175,assumption,(~value(in(n1, and2(h1(f(n2, a)))), n0)), introduced(assumption)).
% 18.15/11.89 tff(176,assumption,(~value(in(n1, h1(f(n2, a))), n0)), introduced(assumption)).
% 18.15/11.89 tff(177,plain,
% 18.15/11.89 (^[X: $i] : refl(((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X)))) <=> ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X)))))),
% 18.15/11.89 inference(bind,[status(th)],[])).
% 18.15/11.89 tff(178,plain,
% 18.15/11.89 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))),
% 18.15/11.89 inference(quant_intro,[status(thm)],[177])).
% 18.15/11.89 tff(179,plain,
% 18.15/11.89 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))),
% 18.15/11.89 inference(rewrite,[status(thm)],[])).
% 18.15/11.89 tff(180,axiom,(![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nbit_adder_connection_inb2_in2f2')).
% 18.15/11.89 tff(181,plain,
% 18.15/11.89 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[180, 179])).
% 18.15/11.89 tff(182,plain,(
% 18.15/11.89 ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))),
% 18.15/11.89 inference(skolemize,[status(sab)],[181])).
% 18.15/11.89 tff(183,plain,
% 18.15/11.89 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[182, 178])).
% 18.15/11.89 tff(184,plain,
% 18.15/11.89 (((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))) | ((~type(a, nbit_adder(n2))) | connection(in(b2, a), in(n2, f(n2, a))))) <=> ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))) | (~type(a, nbit_adder(n2))) | connection(in(b2, a), in(n2, f(n2, a))))),
% 18.15/11.89 inference(rewrite,[status(thm)],[])).
% 18.15/11.89 tff(185,plain,
% 18.15/11.89 ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))) | ((~type(a, nbit_adder(n2))) | connection(in(b2, a), in(n2, f(n2, a))))),
% 18.15/11.89 inference(quant_inst,[status(thm)],[])).
% 18.15/11.89 tff(186,plain,
% 18.15/11.89 ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))) | (~type(a, nbit_adder(n2))) | connection(in(b2, a), in(n2, f(n2, a)))),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[185, 184])).
% 18.15/11.89 tff(187,plain,
% 18.15/11.89 (connection(in(b2, a), in(n2, f(n2, a)))),
% 18.15/11.89 inference(unit_resolution,[status(thm)],[186, 183, 5])).
% 18.15/11.89 tff(188,plain,
% 18.15/11.89 (value(in(b2, a), n0) <=> value(in(b2, a), n0)),
% 18.15/11.89 inference(rewrite,[status(thm)],[])).
% 18.15/11.89 tff(189,axiom,(value(in(b2, a), n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','inb2_0')).
% 18.15/11.89 tff(190,plain,
% 18.15/11.89 (value(in(b2, a), n0)),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[189, 188])).
% 18.15/11.89 tff(191,plain,
% 18.15/11.89 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(b2, a), n0)) | (~connection(in(b2, a), in(n2, f(n2, a)))) | value(in(n2, f(n2, a)), n0))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(b2, a), n0)) | (~connection(in(b2, a), in(n2, f(n2, a)))) | value(in(n2, f(n2, a)), n0))),
% 18.15/11.89 inference(rewrite,[status(thm)],[])).
% 18.15/11.89 tff(192,plain,
% 18.15/11.89 ((value(in(n2, f(n2, a)), n0) | (~value(in(b2, a), n0)) | (~connection(in(b2, a), in(n2, f(n2, a))))) <=> ((~value(in(b2, a), n0)) | (~connection(in(b2, a), in(n2, f(n2, a)))) | value(in(n2, f(n2, a)), n0))),
% 18.15/11.89 inference(rewrite,[status(thm)],[])).
% 18.15/11.89 tff(193,plain,
% 18.15/11.89 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, f(n2, a)), n0) | (~value(in(b2, a), n0)) | (~connection(in(b2, a), in(n2, f(n2, a)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(b2, a), n0)) | (~connection(in(b2, a), in(n2, f(n2, a)))) | value(in(n2, f(n2, a)), n0)))),
% 18.15/11.89 inference(monotonicity,[status(thm)],[192])).
% 18.15/11.89 tff(194,plain,
% 18.15/11.89 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, f(n2, a)), n0) | (~value(in(b2, a), n0)) | (~connection(in(b2, a), in(n2, f(n2, a)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(b2, a), n0)) | (~connection(in(b2, a), in(n2, f(n2, a)))) | value(in(n2, f(n2, a)), n0))),
% 18.15/11.89 inference(transitivity,[status(thm)],[193, 191])).
% 18.15/11.89 tff(195,plain,
% 18.15/11.89 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, f(n2, a)), n0) | (~value(in(b2, a), n0)) | (~connection(in(b2, a), in(n2, f(n2, a)))))),
% 18.15/11.89 inference(quant_inst,[status(thm)],[])).
% 18.15/11.89 tff(196,plain,
% 18.15/11.89 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(b2, a), n0)) | (~connection(in(b2, a), in(n2, f(n2, a)))) | value(in(n2, f(n2, a)), n0)),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[195, 194])).
% 18.15/11.89 tff(197,plain,
% 18.15/11.89 (value(in(n2, f(n2, a)), n0)),
% 18.15/11.89 inference(unit_resolution,[status(thm)],[196, 29, 190, 187])).
% 18.15/11.89 tff(198,plain,
% 18.15/11.89 (^[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)))))),
% 18.15/11.89 inference(bind,[status(th)],[])).
% 18.15/11.89 tff(199,plain,
% 18.15/11.89 (![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))))),
% 18.15/11.89 inference(quant_intro,[status(thm)],[198])).
% 18.15/11.89 tff(200,plain,
% 18.15/11.89 (![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))))),
% 18.15/11.89 inference(rewrite,[status(thm)],[])).
% 18.15/11.89 tff(201,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')).
% 18.15/11.89 tff(202,plain,
% 18.15/11.89 (![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[201, 200])).
% 18.15/11.89 tff(203,plain,(
% 18.15/11.89 ![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 18.15/11.89 inference(skolemize,[status(sab)],[202])).
% 18.15/11.89 tff(204,plain,
% 18.15/11.89 (![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[203, 199])).
% 18.15/11.89 tff(205,plain,
% 18.15/11.89 (((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | ((~type(f(n2, a), fulladder)) | connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a)))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | (~type(f(n2, a), fulladder)) | connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a)))))),
% 18.15/11.89 inference(rewrite,[status(thm)],[])).
% 18.15/11.89 tff(206,plain,
% 18.15/11.89 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | ((~type(f(n2, a), fulladder)) | connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a)))))),
% 18.15/11.89 inference(quant_inst,[status(thm)],[])).
% 18.15/11.89 tff(207,plain,
% 18.15/11.89 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | (~type(f(n2, a), fulladder)) | connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))),
% 18.15/11.89 inference(modus_ponens,[status(thm)],[206, 205])).
% 18.15/11.89 tff(208,plain,
% 18.15/11.89 (connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))),
% 18.15/11.89 inference(unit_resolution,[status(thm)],[207, 204, 48])).
% 18.15/11.89 tff(209,plain,
% 18.15/11.89 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(n2, f(n2, a)), n0)) | value(in(n1, h1(f(n2, a))), n0) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n2, f(n2, a)), n0)) | value(in(n1, h1(f(n2, a))), n0) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))))),
% 18.15/11.90 inference(rewrite,[status(thm)],[])).
% 18.15/11.90 tff(210,plain,
% 18.15/11.90 ((value(in(n1, h1(f(n2, a))), n0) | (~value(in(n2, f(n2, a)), n0)) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a)))))) <=> ((~value(in(n2, f(n2, a)), n0)) | value(in(n1, h1(f(n2, a))), n0) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))))),
% 18.15/11.90 inference(rewrite,[status(thm)],[])).
% 18.15/11.90 tff(211,plain,
% 18.15/11.90 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, h1(f(n2, a))), n0) | (~value(in(n2, f(n2, a)), n0)) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(n2, f(n2, a)), n0)) | value(in(n1, h1(f(n2, a))), n0) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a)))))))),
% 18.15/11.90 inference(monotonicity,[status(thm)],[210])).
% 18.15/11.90 tff(212,plain,
% 18.15/11.90 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, h1(f(n2, a))), n0) | (~value(in(n2, f(n2, a)), n0)) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n2, f(n2, a)), n0)) | value(in(n1, h1(f(n2, a))), n0) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))))),
% 18.15/11.90 inference(transitivity,[status(thm)],[211, 209])).
% 18.15/11.90 tff(213,plain,
% 18.15/11.90 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, h1(f(n2, a))), n0) | (~value(in(n2, f(n2, a)), n0)) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))))),
% 18.15/11.90 inference(quant_inst,[status(thm)],[])).
% 18.15/11.90 tff(214,plain,
% 18.15/11.90 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n2, f(n2, a)), n0)) | value(in(n1, h1(f(n2, a))), n0) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a)))))),
% 18.15/11.90 inference(modus_ponens,[status(thm)],[213, 212])).
% 18.15/11.90 tff(215,plain,
% 18.15/11.90 ($false),
% 18.15/11.90 inference(unit_resolution,[status(thm)],[214, 29, 208, 197, 176])).
% 18.15/11.90 tff(216,plain,(value(in(n1, h1(f(n2, a))), n0)), inference(lemma,lemma(discharge,[]))).
% 18.15/11.90 tff(217,plain,
% 18.15/11.90 (^[X: $i] : refl(((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ((~type(X, fulladder)) | type(h1(X), halfadder)))),
% 18.15/11.90 inference(bind,[status(th)],[])).
% 18.15/11.90 tff(218,plain,
% 18.15/11.90 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 18.15/11.90 inference(quant_intro,[status(thm)],[217])).
% 18.15/11.90 tff(219,plain,
% 18.15/11.90 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 18.15/11.90 inference(rewrite,[status(thm)],[])).
% 18.15/11.90 tff(220,axiom,(![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_halfadder1')).
% 18.15/11.90 tff(221,plain,
% 18.15/11.90 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 18.15/11.90 inference(modus_ponens,[status(thm)],[220, 219])).
% 18.15/11.90 tff(222,plain,(
% 18.15/11.90 ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 18.15/11.90 inference(skolemize,[status(sab)],[221])).
% 18.15/11.90 tff(223,plain,
% 18.15/11.90 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 18.15/11.90 inference(modus_ponens,[status(thm)],[222, 218])).
% 18.15/11.90 tff(224,plain,
% 18.15/11.90 (((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | ((~type(f(n2, a), fulladder)) | type(h1(f(n2, a)), halfadder))) <=> ((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | (~type(f(n2, a), fulladder)) | type(h1(f(n2, a)), halfadder))),
% 18.15/11.90 inference(rewrite,[status(thm)],[])).
% 18.15/11.90 tff(225,plain,
% 18.15/11.90 ((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | ((~type(f(n2, a), fulladder)) | type(h1(f(n2, a)), halfadder))),
% 18.15/11.90 inference(quant_inst,[status(thm)],[])).
% 18.15/11.90 tff(226,plain,
% 18.15/11.90 ((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | (~type(f(n2, a), fulladder)) | type(h1(f(n2, a)), halfadder)),
% 18.15/11.90 inference(modus_ponens,[status(thm)],[225, 224])).
% 18.15/11.90 tff(227,plain,
% 18.15/11.90 (type(h1(f(n2, a)), halfadder)),
% 18.15/11.90 inference(unit_resolution,[status(thm)],[226, 223, 48])).
% 18.15/11.90 tff(228,plain,
% 18.15/11.90 (((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h1(f(n2, a)), halfadder)) | connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a))))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h1(f(n2, a)), halfadder)) | connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a))))))),
% 18.15/11.90 inference(rewrite,[status(thm)],[])).
% 18.15/11.90 tff(229,plain,
% 18.15/11.90 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h1(f(n2, a)), halfadder)) | connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a))))))),
% 18.15/11.90 inference(quant_inst,[status(thm)],[])).
% 18.15/11.90 tff(230,plain,
% 18.15/11.90 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h1(f(n2, a)), halfadder)) | connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))),
% 18.15/11.90 inference(modus_ponens,[status(thm)],[229, 228])).
% 18.15/11.90 tff(231,plain,
% 18.15/11.90 ((~type(h1(f(n2, a)), halfadder)) | connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))),
% 18.15/11.90 inference(unit_resolution,[status(thm)],[230, 84])).
% 18.15/11.90 tff(232,plain,
% 18.15/11.90 (connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))),
% 18.15/11.90 inference(unit_resolution,[status(thm)],[231, 227])).
% 18.15/11.90 tff(233,plain,
% 18.15/11.90 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(n1, h1(f(n2, a))), n0)) | value(in(n1, and2(h1(f(n2, a)))), n0) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n1, h1(f(n2, a))), n0)) | value(in(n1, and2(h1(f(n2, a)))), n0) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))))),
% 18.15/11.90 inference(rewrite,[status(thm)],[])).
% 18.15/11.90 tff(234,plain,
% 18.15/11.90 ((value(in(n1, and2(h1(f(n2, a)))), n0) | (~value(in(n1, h1(f(n2, a))), n0)) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a))))))) <=> ((~value(in(n1, h1(f(n2, a))), n0)) | value(in(n1, and2(h1(f(n2, a)))), n0) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))))),
% 18.15/11.90 inference(rewrite,[status(thm)],[])).
% 18.15/11.90 tff(235,plain,
% 18.15/11.90 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, and2(h1(f(n2, a)))), n0) | (~value(in(n1, h1(f(n2, a))), n0)) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(n1, h1(f(n2, a))), n0)) | value(in(n1, and2(h1(f(n2, a)))), n0) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a))))))))),
% 18.15/11.90 inference(monotonicity,[status(thm)],[234])).
% 18.15/11.90 tff(236,plain,
% 18.15/11.90 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, and2(h1(f(n2, a)))), n0) | (~value(in(n1, h1(f(n2, a))), n0)) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n1, h1(f(n2, a))), n0)) | value(in(n1, and2(h1(f(n2, a)))), n0) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))))),
% 18.15/11.90 inference(transitivity,[status(thm)],[235, 233])).
% 18.15/11.90 tff(237,plain,
% 18.15/11.90 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, and2(h1(f(n2, a)))), n0) | (~value(in(n1, h1(f(n2, a))), n0)) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))))),
% 18.15/11.90 inference(quant_inst,[status(thm)],[])).
% 18.15/11.90 tff(238,plain,
% 18.15/11.90 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n1, h1(f(n2, a))), n0)) | value(in(n1, and2(h1(f(n2, a)))), n0) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a))))))),
% 18.15/11.90 inference(modus_ponens,[status(thm)],[237, 236])).
% 18.15/11.90 tff(239,plain,
% 18.15/11.90 ($false),
% 18.15/11.90 inference(unit_resolution,[status(thm)],[238, 29, 232, 216, 175])).
% 18.15/11.90 tff(240,plain,(value(in(n1, and2(h1(f(n2, a)))), n0)), inference(lemma,lemma(discharge,[]))).
% 18.15/11.90 tff(241,plain,
% 18.15/11.90 (((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h1(f(n2, a)), halfadder)) | type(and2(h1(f(n2, a))), and))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h1(f(n2, a)), halfadder)) | type(and2(h1(f(n2, a))), and))),
% 18.15/11.90 inference(rewrite,[status(thm)],[])).
% 18.15/11.90 tff(242,plain,
% 18.15/11.90 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h1(f(n2, a)), halfadder)) | type(and2(h1(f(n2, a))), and))),
% 18.15/11.90 inference(quant_inst,[status(thm)],[])).
% 18.15/11.90 tff(243,plain,
% 18.15/11.90 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h1(f(n2, a)), halfadder)) | type(and2(h1(f(n2, a))), and)),
% 18.15/11.90 inference(modus_ponens,[status(thm)],[242, 241])).
% 18.15/11.90 tff(244,plain,
% 18.15/11.90 ((~type(h1(f(n2, a)), halfadder)) | type(and2(h1(f(n2, a))), and)),
% 18.15/11.90 inference(unit_resolution,[status(thm)],[243, 104])).
% 18.15/11.90 tff(245,plain,
% 18.15/11.90 (type(and2(h1(f(n2, a))), and)),
% 18.15/11.90 inference(unit_resolution,[status(thm)],[244, 227])).
% 18.15/11.90 tff(246,plain,
% 18.15/11.90 ((~mode(and2(h1(f(n2, a))), abnormal)) <=> (~mode(and2(h1(f(n2, a))), abnormal))),
% 18.15/11.90 inference(rewrite,[status(thm)],[])).
% 18.15/11.90 tff(247,axiom,(~mode(and2(h1(f(n2, a))), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_and2h2f2a')).
% 18.15/11.90 tff(248,plain,
% 18.15/11.90 (~mode(and2(h1(f(n2, a))), abnormal)),
% 18.15/11.90 inference(modus_ponens,[status(thm)],[247, 246])).
% 18.15/11.90 tff(249,plain,
% 18.15/11.90 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h1(f(n2, a))), abnormal) | mode(and2(h1(f(n2, a))), ok) | (~type(and2(h1(f(n2, a))), and)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h1(f(n2, a))), abnormal) | mode(and2(h1(f(n2, a))), ok) | (~type(and2(h1(f(n2, a))), and)))),
% 18.15/11.90 inference(rewrite,[status(thm)],[])).
% 18.15/11.90 tff(250,plain,
% 18.15/11.90 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h1(f(n2, a))), abnormal) | mode(and2(h1(f(n2, a))), ok) | (~type(and2(h1(f(n2, a))), and)))),
% 18.15/11.90 inference(quant_inst,[status(thm)],[])).
% 18.15/11.90 tff(251,plain,
% 18.15/11.90 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h1(f(n2, a))), abnormal) | mode(and2(h1(f(n2, a))), ok) | (~type(and2(h1(f(n2, a))), and))),
% 18.15/11.90 inference(modus_ponens,[status(thm)],[250, 249])).
% 18.15/11.90 tff(252,plain,
% 18.15/11.90 (mode(and2(h1(f(n2, a))), ok)),
% 18.15/11.90 inference(unit_resolution,[status(thm)],[251, 122, 248, 245])).
% 18.15/11.90 tff(253,plain,
% 18.15/11.90 (((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h1(f(n2, a))), ok)) | value(out(n1, and2(h1(f(n2, a)))), n0) | (~type(and2(h1(f(n2, a))), and)) | (~value(in(n1, and2(h1(f(n2, a)))), n0)))) <=> ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | (~mode(and2(h1(f(n2, a))), ok)) | value(out(n1, and2(h1(f(n2, a)))), n0) | (~type(and2(h1(f(n2, a))), and)) | (~value(in(n1, and2(h1(f(n2, a)))), n0)))),
% 18.15/11.90 inference(rewrite,[status(thm)],[])).
% 18.15/11.90 tff(254,plain,
% 18.15/11.90 (((~mode(and2(h1(f(n2, a))), ok)) | value(out(n1, and2(h1(f(n2, a)))), n0) | (~value(in(n1, and2(h1(f(n2, a)))), n0)) | (~type(and2(h1(f(n2, a))), and))) <=> ((~mode(and2(h1(f(n2, a))), ok)) | value(out(n1, and2(h1(f(n2, a)))), n0) | (~type(and2(h1(f(n2, a))), and)) | (~value(in(n1, and2(h1(f(n2, a)))), n0)))),
% 18.15/11.90 inference(rewrite,[status(thm)],[])).
% 18.15/11.90 tff(255,plain,
% 18.15/11.90 (((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h1(f(n2, a))), ok)) | value(out(n1, and2(h1(f(n2, a)))), n0) | (~value(in(n1, and2(h1(f(n2, a)))), n0)) | (~type(and2(h1(f(n2, a))), and)))) <=> ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h1(f(n2, a))), ok)) | value(out(n1, and2(h1(f(n2, a)))), n0) | (~type(and2(h1(f(n2, a))), and)) | (~value(in(n1, and2(h1(f(n2, a)))), n0))))),
% 18.15/11.90 inference(monotonicity,[status(thm)],[254])).
% 18.15/11.90 tff(256,plain,
% 18.15/11.90 (((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h1(f(n2, a))), ok)) | value(out(n1, and2(h1(f(n2, a)))), n0) | (~value(in(n1, and2(h1(f(n2, a)))), n0)) | (~type(and2(h1(f(n2, a))), and)))) <=> ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | (~mode(and2(h1(f(n2, a))), ok)) | value(out(n1, and2(h1(f(n2, a)))), n0) | (~type(and2(h1(f(n2, a))), and)) | (~value(in(n1, and2(h1(f(n2, a)))), n0)))),
% 18.15/11.90 inference(transitivity,[status(thm)],[255, 253])).
% 18.15/11.90 tff(257,plain,
% 18.15/11.90 ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h1(f(n2, a))), ok)) | value(out(n1, and2(h1(f(n2, a)))), n0) | (~value(in(n1, and2(h1(f(n2, a)))), n0)) | (~type(and2(h1(f(n2, a))), and)))),
% 18.15/11.90 inference(quant_inst,[status(thm)],[])).
% 18.15/11.90 tff(258,plain,
% 18.15/11.90 ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | (~mode(and2(h1(f(n2, a))), ok)) | value(out(n1, and2(h1(f(n2, a)))), n0) | (~type(and2(h1(f(n2, a))), and)) | (~value(in(n1, and2(h1(f(n2, a)))), n0))),
% 18.15/11.90 inference(modus_ponens,[status(thm)],[257, 256])).
% 18.15/11.90 tff(259,plain,
% 18.15/11.90 ((~mode(and2(h1(f(n2, a))), ok)) | value(out(n1, and2(h1(f(n2, a)))), n0) | (~value(in(n1, and2(h1(f(n2, a)))), n0))),
% 18.15/11.90 inference(unit_resolution,[status(thm)],[258, 136, 245])).
% 18.15/11.90 tff(260,plain,
% 18.15/11.90 (value(out(n1, and2(h1(f(n2, a)))), n0) | (~value(in(n1, and2(h1(f(n2, a)))), n0))),
% 18.15/11.90 inference(unit_resolution,[status(thm)],[259, 252])).
% 18.15/11.90 tff(261,plain,
% 18.15/11.90 (value(out(n1, and2(h1(f(n2, a)))), n0)),
% 18.15/11.90 inference(unit_resolution,[status(thm)],[260, 240])).
% 18.15/11.90 tff(262,plain,
% 18.15/11.90 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h1(f(n2, a)), halfadder)) | connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a))))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h1(f(n2, a)), halfadder)) | connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a))))))),
% 18.15/11.90 inference(rewrite,[status(thm)],[])).
% 18.15/11.90 tff(263,plain,
% 18.15/11.90 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h1(f(n2, a)), halfadder)) | connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a))))))),
% 18.15/11.90 inference(quant_inst,[status(thm)],[])).
% 18.15/11.90 tff(264,plain,
% 18.15/11.90 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h1(f(n2, a)), halfadder)) | connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))),
% 18.15/11.90 inference(modus_ponens,[status(thm)],[263, 262])).
% 18.15/11.90 tff(265,plain,
% 18.15/11.90 ((~type(h1(f(n2, a)), halfadder)) | connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))),
% 18.15/11.90 inference(unit_resolution,[status(thm)],[264, 152])).
% 18.15/11.90 tff(266,plain,
% 18.15/11.90 (connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))),
% 18.15/11.90 inference(unit_resolution,[status(thm)],[265, 227])).
% 18.15/11.90 tff(267,plain,
% 18.15/11.90 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(out(n1, and2(h1(f(n2, a)))), n0)) | (~connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))) | value(out(c, h1(f(n2, a))), n0))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and2(h1(f(n2, a)))), n0)) | (~connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))) | value(out(c, h1(f(n2, a))), n0))),
% 18.15/11.90 inference(rewrite,[status(thm)],[])).
% 18.15/11.90 tff(268,plain,
% 18.15/11.90 ((value(out(c, h1(f(n2, a))), n0) | (~connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))) | (~value(out(n1, and2(h1(f(n2, a)))), n0))) <=> ((~value(out(n1, and2(h1(f(n2, a)))), n0)) | (~connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))) | value(out(c, h1(f(n2, a))), n0))),
% 18.15/11.90 inference(rewrite,[status(thm)],[])).
% 18.15/11.90 tff(269,plain,
% 18.15/11.90 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h1(f(n2, a))), n0) | (~connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))) | (~value(out(n1, and2(h1(f(n2, a)))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(out(n1, and2(h1(f(n2, a)))), n0)) | (~connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))) | value(out(c, h1(f(n2, a))), n0)))),
% 18.15/11.91 inference(monotonicity,[status(thm)],[268])).
% 18.15/11.91 tff(270,plain,
% 18.15/11.91 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h1(f(n2, a))), n0) | (~connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))) | (~value(out(n1, and2(h1(f(n2, a)))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and2(h1(f(n2, a)))), n0)) | (~connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))) | value(out(c, h1(f(n2, a))), n0))),
% 18.15/11.91 inference(transitivity,[status(thm)],[269, 267])).
% 18.15/11.91 tff(271,plain,
% 18.15/11.91 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h1(f(n2, a))), n0) | (~connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))) | (~value(out(n1, and2(h1(f(n2, a)))), n0)))),
% 18.15/11.91 inference(quant_inst,[status(thm)],[])).
% 18.15/11.91 tff(272,plain,
% 18.15/11.91 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and2(h1(f(n2, a)))), n0)) | (~connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))) | value(out(c, h1(f(n2, a))), n0)),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[271, 270])).
% 18.15/11.91 tff(273,plain,
% 18.15/11.91 (value(out(c, h1(f(n2, a))), n0)),
% 18.15/11.91 inference(unit_resolution,[status(thm)],[272, 167, 266, 261])).
% 18.15/11.91 tff(274,plain,
% 18.15/11.91 (^[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)))))),
% 18.15/11.91 inference(bind,[status(th)],[])).
% 18.15/11.91 tff(275,plain,
% 18.15/11.91 (![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))))),
% 18.15/11.91 inference(quant_intro,[status(thm)],[274])).
% 18.15/11.91 tff(276,plain,
% 18.15/11.91 (![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))))),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(277,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')).
% 18.15/11.91 tff(278,plain,
% 18.15/11.91 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[277, 276])).
% 18.15/11.91 tff(279,plain,(
% 18.15/11.91 ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 18.15/11.91 inference(skolemize,[status(sab)],[278])).
% 18.15/11.91 tff(280,plain,
% 18.15/11.91 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[279, 275])).
% 18.15/11.91 tff(281,plain,
% 18.15/11.91 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))) | ((~type(f(n2, a), fulladder)) | connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a)))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))) | (~type(f(n2, a), fulladder)) | connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a)))))),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(282,plain,
% 18.15/11.91 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))) | ((~type(f(n2, a), fulladder)) | connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a)))))),
% 18.15/11.91 inference(quant_inst,[status(thm)],[])).
% 18.15/11.91 tff(283,plain,
% 18.15/11.91 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))) | (~type(f(n2, a), fulladder)) | connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a))))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[282, 281])).
% 18.15/11.91 tff(284,plain,
% 18.15/11.91 (connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a))))),
% 18.15/11.91 inference(unit_resolution,[status(thm)],[283, 280, 48])).
% 18.15/11.91 tff(285,plain,
% 18.15/11.91 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, or1(f(n2, a))), n0) | (~value(out(c, h1(f(n2, a))), n0)) | (~connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(in(n2, or1(f(n2, a))), n0) | (~value(out(c, h1(f(n2, a))), n0)) | (~connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a))))))),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(286,plain,
% 18.15/11.91 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, or1(f(n2, a))), n0) | (~value(out(c, h1(f(n2, a))), n0)) | (~connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a))))))),
% 18.15/11.91 inference(quant_inst,[status(thm)],[])).
% 18.15/11.91 tff(287,plain,
% 18.15/11.91 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(in(n2, or1(f(n2, a))), n0) | (~value(out(c, h1(f(n2, a))), n0)) | (~connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a)))))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[286, 285])).
% 18.15/11.91 tff(288,plain,
% 18.15/11.91 (value(in(n2, or1(f(n2, a))), n0)),
% 18.15/11.91 inference(unit_resolution,[status(thm)],[287, 29, 284, 273])).
% 18.15/11.91 tff(289,plain,
% 18.15/11.91 (^[X: $i] : refl(((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X)))) <=> ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X)))))),
% 18.15/11.91 inference(bind,[status(th)],[])).
% 18.15/11.91 tff(290,plain,
% 18.15/11.91 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))),
% 18.15/11.91 inference(quant_intro,[status(thm)],[289])).
% 18.15/11.91 tff(291,plain,
% 18.15/11.91 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(292,axiom,(![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nbit_adder_connection_outc_outcf1')).
% 18.15/11.91 tff(293,plain,
% 18.15/11.91 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[292, 291])).
% 18.15/11.91 tff(294,plain,(
% 18.15/11.91 ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))),
% 18.15/11.91 inference(skolemize,[status(sab)],[293])).
% 18.15/11.91 tff(295,plain,
% 18.15/11.91 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[294, 290])).
% 18.15/11.91 tff(296,plain,
% 18.15/11.91 (((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))) | ((~type(a, nbit_adder(n2))) | connection(out(c, a), out(c, f(n2, a))))) <=> ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))) | (~type(a, nbit_adder(n2))) | connection(out(c, a), out(c, f(n2, a))))),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(297,plain,
% 18.15/11.91 ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))) | ((~type(a, nbit_adder(n2))) | connection(out(c, a), out(c, f(n2, a))))),
% 18.15/11.91 inference(quant_inst,[status(thm)],[])).
% 18.15/11.91 tff(298,plain,
% 18.15/11.91 ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))) | (~type(a, nbit_adder(n2))) | connection(out(c, a), out(c, f(n2, a)))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[297, 296])).
% 18.15/11.91 tff(299,plain,
% 18.15/11.91 (connection(out(c, a), out(c, f(n2, a)))),
% 18.15/11.91 inference(unit_resolution,[status(thm)],[298, 295, 5])).
% 18.15/11.91 tff(300,plain,
% 18.15/11.91 (value(out(c, a), n1) <=> value(out(c, a), n1)),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(301,axiom,(value(out(c, a), n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','outc_1')).
% 18.15/11.91 tff(302,plain,
% 18.15/11.91 (value(out(c, a), n1)),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[301, 300])).
% 18.15/11.91 tff(303,plain,
% 18.15/11.91 ((~equal_value(n0, n1)) <=> (~equal_value(n0, n1))),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(304,axiom,(~equal_value(n0, n1)), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','equal_value1')).
% 18.15/11.91 tff(305,plain,
% 18.15/11.91 (~equal_value(n0, n1)),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[304, 303])).
% 18.15/11.91 tff(306,plain,
% 18.15/11.91 (^[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))))),
% 18.15/11.91 inference(bind,[status(th)],[])).
% 18.15/11.91 tff(307,plain,
% 18.15/11.91 (![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)))),
% 18.15/11.91 inference(quant_intro,[status(thm)],[306])).
% 18.15/11.91 tff(308,plain,
% 18.15/11.91 (![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)))),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(309,plain,
% 18.15/11.91 (^[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)))))),
% 18.15/11.91 inference(bind,[status(th)],[])).
% 18.15/11.91 tff(310,plain,
% 18.15/11.91 (![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)))),
% 18.15/11.91 inference(quant_intro,[status(thm)],[309])).
% 18.15/11.91 tff(311,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')).
% 18.15/11.91 tff(312,plain,
% 18.15/11.91 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[311, 310])).
% 18.15/11.91 tff(313,plain,
% 18.15/11.91 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[312, 308])).
% 18.15/11.91 tff(314,plain,(
% 18.15/11.91 ![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 18.15/11.91 inference(skolemize,[status(sab)],[313])).
% 18.15/11.91 tff(315,plain,
% 18.15/11.91 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[314, 307])).
% 18.15/11.91 tff(316,plain,
% 18.15/11.91 (((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(out(c, a), n1)) | (~value(out(c, a), n0)))) <=> ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n0, n1) | (~value(out(c, a), n1)) | (~value(out(c, a), n0)))),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(317,plain,
% 18.15/11.91 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(out(c, a), n1)) | (~value(out(c, a), n0)))),
% 18.15/11.91 inference(quant_inst,[status(thm)],[])).
% 18.15/11.91 tff(318,plain,
% 18.15/11.91 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n0, n1) | (~value(out(c, a), n1)) | (~value(out(c, a), n0))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[317, 316])).
% 18.15/11.91 tff(319,plain,
% 18.15/11.91 (~value(out(c, a), n0)),
% 18.15/11.91 inference(unit_resolution,[status(thm)],[318, 315, 305, 302])).
% 18.15/11.91 tff(320,plain,
% 18.15/11.91 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, a), n0) | (~connection(out(c, a), out(c, f(n2, a)))) | (~value(out(c, f(n2, a)), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(c, a), n0) | (~connection(out(c, a), out(c, f(n2, a)))) | (~value(out(c, f(n2, a)), n0)))),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(321,plain,
% 18.15/11.91 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, a), n0) | (~connection(out(c, a), out(c, f(n2, a)))) | (~value(out(c, f(n2, a)), n0)))),
% 18.15/11.91 inference(quant_inst,[status(thm)],[])).
% 18.15/11.91 tff(322,plain,
% 18.15/11.91 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(c, a), n0) | (~connection(out(c, a), out(c, f(n2, a)))) | (~value(out(c, f(n2, a)), n0))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[321, 320])).
% 18.15/11.91 tff(323,plain,
% 18.15/11.91 (~value(out(c, f(n2, a)), n0)),
% 18.15/11.91 inference(unit_resolution,[status(thm)],[322, 167, 319, 299])).
% 18.15/11.91 tff(324,plain,
% 18.15/11.91 (^[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)))))),
% 18.15/11.91 inference(bind,[status(th)],[])).
% 18.15/11.91 tff(325,plain,
% 18.15/11.91 (![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))))),
% 18.15/11.91 inference(quant_intro,[status(thm)],[324])).
% 18.15/11.91 tff(326,plain,
% 18.15/11.91 (![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))))),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(327,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')).
% 18.15/11.91 tff(328,plain,
% 18.15/11.91 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[327, 326])).
% 18.15/11.91 tff(329,plain,(
% 18.15/11.91 ![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 18.15/11.91 inference(skolemize,[status(sab)],[328])).
% 18.15/11.91 tff(330,plain,
% 18.15/11.91 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[329, 325])).
% 18.15/11.91 tff(331,plain,
% 18.15/11.91 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | ((~type(f(n2, a), fulladder)) | connection(out(c, f(n2, a)), out(n1, or1(f(n2, a)))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | (~type(f(n2, a), fulladder)) | connection(out(c, f(n2, a)), out(n1, or1(f(n2, a)))))),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(332,plain,
% 18.15/11.91 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | ((~type(f(n2, a), fulladder)) | connection(out(c, f(n2, a)), out(n1, or1(f(n2, a)))))),
% 18.15/11.91 inference(quant_inst,[status(thm)],[])).
% 18.15/11.91 tff(333,plain,
% 18.15/11.91 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | (~type(f(n2, a), fulladder)) | connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[332, 331])).
% 18.15/11.91 tff(334,plain,
% 18.15/11.91 (connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))),
% 18.15/11.91 inference(unit_resolution,[status(thm)],[333, 330, 48])).
% 18.15/11.91 tff(335,plain,
% 18.15/11.91 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, f(n2, a)), n0) | (~value(out(n1, or1(f(n2, a))), n0)) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(c, f(n2, a)), n0) | (~value(out(n1, or1(f(n2, a))), n0)) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))))),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(336,plain,
% 18.15/11.91 ((value(out(c, f(n2, a)), n0) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))) | (~value(out(n1, or1(f(n2, a))), n0))) <=> (value(out(c, f(n2, a)), n0) | (~value(out(n1, or1(f(n2, a))), n0)) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))))),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(337,plain,
% 18.15/11.91 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, f(n2, a)), n0) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))) | (~value(out(n1, or1(f(n2, a))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, f(n2, a)), n0) | (~value(out(n1, or1(f(n2, a))), n0)) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a)))))))),
% 18.15/11.91 inference(monotonicity,[status(thm)],[336])).
% 18.15/11.91 tff(338,plain,
% 18.15/11.91 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, f(n2, a)), n0) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))) | (~value(out(n1, or1(f(n2, a))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(c, f(n2, a)), n0) | (~value(out(n1, or1(f(n2, a))), n0)) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))))),
% 18.15/11.91 inference(transitivity,[status(thm)],[337, 335])).
% 18.15/11.91 tff(339,plain,
% 18.15/11.91 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, f(n2, a)), n0) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))) | (~value(out(n1, or1(f(n2, a))), n0)))),
% 18.15/11.91 inference(quant_inst,[status(thm)],[])).
% 18.15/11.91 tff(340,plain,
% 18.15/11.91 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(c, f(n2, a)), n0) | (~value(out(n1, or1(f(n2, a))), n0)) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a)))))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[339, 338])).
% 18.15/11.91 tff(341,plain,
% 18.15/11.91 (~value(out(n1, or1(f(n2, a))), n0)),
% 18.15/11.91 inference(unit_resolution,[status(thm)],[340, 167, 334, 323])).
% 18.15/11.91 tff(342,plain,
% 18.15/11.91 (^[X: $i] : refl(((~type(X, fulladder)) | type(or1(X), or)) <=> ((~type(X, fulladder)) | type(or1(X), or)))),
% 18.15/11.91 inference(bind,[status(th)],[])).
% 18.15/11.91 tff(343,plain,
% 18.15/11.91 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 18.15/11.91 inference(quant_intro,[status(thm)],[342])).
% 18.15/11.91 tff(344,plain,
% 18.15/11.91 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(345,axiom,(![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_or1')).
% 18.15/11.91 tff(346,plain,
% 18.15/11.91 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[345, 344])).
% 18.15/11.91 tff(347,plain,(
% 18.15/11.91 ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 18.15/11.91 inference(skolemize,[status(sab)],[346])).
% 18.15/11.91 tff(348,plain,
% 18.15/11.91 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[347, 343])).
% 18.15/11.91 tff(349,plain,
% 18.15/11.91 (((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | ((~type(f(n2, a), fulladder)) | type(or1(f(n2, a)), or))) <=> ((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | (~type(f(n2, a), fulladder)) | type(or1(f(n2, a)), or))),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(350,plain,
% 18.15/11.91 ((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | ((~type(f(n2, a), fulladder)) | type(or1(f(n2, a)), or))),
% 18.15/11.91 inference(quant_inst,[status(thm)],[])).
% 18.15/11.91 tff(351,plain,
% 18.15/11.91 ((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | (~type(f(n2, a), fulladder)) | type(or1(f(n2, a)), or)),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[350, 349])).
% 18.15/11.91 tff(352,plain,
% 18.15/11.91 (type(or1(f(n2, a)), or)),
% 18.15/11.91 inference(unit_resolution,[status(thm)],[351, 348, 48])).
% 18.15/11.91 tff(353,plain,
% 18.15/11.91 ((~mode(or1(f(n2, a)), abnormal)) <=> (~mode(or1(f(n2, a)), abnormal))),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(354,axiom,(~mode(or1(f(n2, a)), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_or1f2a')).
% 18.15/11.91 tff(355,plain,
% 18.15/11.91 (~mode(or1(f(n2, a)), abnormal)),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[354, 353])).
% 18.15/11.91 tff(356,plain,
% 18.15/11.91 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(or1(f(n2, a)), abnormal) | mode(or1(f(n2, a)), ok) | (~type(or1(f(n2, a)), or)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(or1(f(n2, a)), abnormal) | mode(or1(f(n2, a)), ok) | (~type(or1(f(n2, a)), or)))),
% 18.15/11.91 inference(rewrite,[status(thm)],[])).
% 18.15/11.91 tff(357,plain,
% 18.15/11.91 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(or1(f(n2, a)), abnormal) | mode(or1(f(n2, a)), ok) | (~type(or1(f(n2, a)), or)))),
% 18.15/11.91 inference(quant_inst,[status(thm)],[])).
% 18.15/11.91 tff(358,plain,
% 18.15/11.91 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(or1(f(n2, a)), abnormal) | mode(or1(f(n2, a)), ok) | (~type(or1(f(n2, a)), or))),
% 18.15/11.91 inference(modus_ponens,[status(thm)],[357, 356])).
% 18.15/11.91 tff(359,plain,
% 18.15/11.91 (mode(or1(f(n2, a)), ok)),
% 18.15/11.91 inference(unit_resolution,[status(thm)],[358, 122, 355, 352])).
% 18.15/11.92 tff(360,plain,
% 18.15/11.92 (^[K: $i] : refl(((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0))) <=> ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0))))),
% 18.15/11.92 inference(bind,[status(th)],[])).
% 18.15/11.92 tff(361,plain,
% 18.15/11.92 (![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0))) <=> ![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))),
% 18.15/11.92 inference(quant_intro,[status(thm)],[360])).
% 18.15/11.92 tff(362,plain,
% 18.15/11.92 (![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0))) <=> ![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))),
% 18.15/11.92 inference(rewrite,[status(thm)],[])).
% 18.15/11.92 tff(363,plain,
% 18.15/11.92 (^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, or))) | (~value(in(n1, K), n0))) <=> ((~mode(K, ok)) | (~type(K, or)) | (~value(in(n1, K), n0)))), (((((~mode(K, ok)) | (~type(K, or))) | (~value(in(n1, K), n0))) | (~value(in(n2, K), n0))) <=> (((~mode(K, ok)) | (~type(K, or)) | (~value(in(n1, K), n0))) | (~value(in(n2, K), n0))))), rewrite((((~mode(K, ok)) | (~type(K, or)) | (~value(in(n1, K), n0))) | (~value(in(n2, K), n0))) <=> ((~mode(K, ok)) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))), (((((~mode(K, ok)) | (~type(K, or))) | (~value(in(n1, K), n0))) | (~value(in(n2, K), n0))) <=> ((~mode(K, ok)) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0))))), ((((((~mode(K, ok)) | (~type(K, or))) | (~value(in(n1, K), n0))) | (~value(in(n2, K), n0))) | value(out(n1, K), n0)) <=> (((~mode(K, ok)) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0))) | value(out(n1, K), n0)))), rewrite((((~mode(K, ok)) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0))) | value(out(n1, K), n0)) <=> ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))), ((((((~mode(K, ok)) | (~type(K, or))) | (~value(in(n1, K), n0))) | (~value(in(n2, K), n0))) | value(out(n1, K), n0)) <=> ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))))),
% 18.15/11.92 inference(bind,[status(th)],[])).
% 18.15/11.92 tff(364,plain,
% 18.15/11.92 (![K: $i] : (((((~mode(K, ok)) | (~type(K, or))) | (~value(in(n1, K), n0))) | (~value(in(n2, K), n0))) | value(out(n1, K), n0)) <=> ![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))),
% 18.15/11.92 inference(quant_intro,[status(thm)],[363])).
% 18.15/11.92 tff(365,axiom,(![K: $i] : (((((~mode(K, ok)) | (~type(K, or))) | (~value(in(n1, K), n0))) | (~value(in(n2, K), n0))) | value(out(n1, K), n0))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','or_00_0')).
% 18.15/11.92 tff(366,plain,
% 18.15/11.92 (![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))),
% 18.15/11.92 inference(modus_ponens,[status(thm)],[365, 364])).
% 18.15/11.92 tff(367,plain,
% 18.15/11.92 (![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))),
% 18.15/11.92 inference(modus_ponens,[status(thm)],[366, 362])).
% 18.15/11.92 tff(368,plain,(
% 18.15/11.92 ![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))),
% 18.15/11.92 inference(skolemize,[status(sab)],[367])).
% 18.15/11.92 tff(369,plain,
% 18.15/11.92 (![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))),
% 18.15/11.92 inference(modus_ponens,[status(thm)],[368, 361])).
% 18.15/11.92 tff(370,plain,
% 18.15/11.92 (((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))) | ((~mode(or1(f(n2, a)), ok)) | (~type(or1(f(n2, a)), or)) | value(out(n1, or1(f(n2, a))), n0) | (~value(in(n1, or1(f(n2, a))), n0)) | (~value(in(n2, or1(f(n2, a))), n0)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))) | (~mode(or1(f(n2, a)), ok)) | (~type(or1(f(n2, a)), or)) | value(out(n1, or1(f(n2, a))), n0) | (~value(in(n1, or1(f(n2, a))), n0)) | (~value(in(n2, or1(f(n2, a))), n0)))),
% 18.15/11.92 inference(rewrite,[status(thm)],[])).
% 18.15/11.92 tff(371,plain,
% 18.15/11.92 (((~mode(or1(f(n2, a)), ok)) | value(out(n1, or1(f(n2, a))), n0) | (~type(or1(f(n2, a)), or)) | (~value(in(n2, or1(f(n2, a))), n0)) | (~value(in(n1, or1(f(n2, a))), n0))) <=> ((~mode(or1(f(n2, a)), ok)) | (~type(or1(f(n2, a)), or)) | value(out(n1, or1(f(n2, a))), n0) | (~value(in(n1, or1(f(n2, a))), n0)) | (~value(in(n2, or1(f(n2, a))), n0)))),
% 18.15/11.92 inference(rewrite,[status(thm)],[])).
% 18.15/11.92 tff(372,plain,
% 18.15/11.92 (((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))) | ((~mode(or1(f(n2, a)), ok)) | value(out(n1, or1(f(n2, a))), n0) | (~type(or1(f(n2, a)), or)) | (~value(in(n2, or1(f(n2, a))), n0)) | (~value(in(n1, or1(f(n2, a))), n0)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))) | ((~mode(or1(f(n2, a)), ok)) | (~type(or1(f(n2, a)), or)) | value(out(n1, or1(f(n2, a))), n0) | (~value(in(n1, or1(f(n2, a))), n0)) | (~value(in(n2, or1(f(n2, a))), n0))))),
% 18.15/11.92 inference(monotonicity,[status(thm)],[371])).
% 18.15/11.92 tff(373,plain,
% 18.15/11.92 (((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))) | ((~mode(or1(f(n2, a)), ok)) | value(out(n1, or1(f(n2, a))), n0) | (~type(or1(f(n2, a)), or)) | (~value(in(n2, or1(f(n2, a))), n0)) | (~value(in(n1, or1(f(n2, a))), n0)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))) | (~mode(or1(f(n2, a)), ok)) | (~type(or1(f(n2, a)), or)) | value(out(n1, or1(f(n2, a))), n0) | (~value(in(n1, or1(f(n2, a))), n0)) | (~value(in(n2, or1(f(n2, a))), n0)))),
% 18.15/11.92 inference(transitivity,[status(thm)],[372, 370])).
% 18.15/11.92 tff(374,plain,
% 18.15/11.92 ((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))) | ((~mode(or1(f(n2, a)), ok)) | value(out(n1, or1(f(n2, a))), n0) | (~type(or1(f(n2, a)), or)) | (~value(in(n2, or1(f(n2, a))), n0)) | (~value(in(n1, or1(f(n2, a))), n0)))),
% 18.15/11.92 inference(quant_inst,[status(thm)],[])).
% 18.15/11.92 tff(375,plain,
% 18.15/11.92 ((~![K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~type(K, or)) | (~value(in(n2, K), n0)) | (~value(in(n1, K), n0)))) | (~mode(or1(f(n2, a)), ok)) | (~type(or1(f(n2, a)), or)) | value(out(n1, or1(f(n2, a))), n0) | (~value(in(n1, or1(f(n2, a))), n0)) | (~value(in(n2, or1(f(n2, a))), n0))),
% 18.15/11.92 inference(modus_ponens,[status(thm)],[374, 373])).
% 18.15/11.92 tff(376,plain,
% 18.15/11.92 ((~mode(or1(f(n2, a)), ok)) | value(out(n1, or1(f(n2, a))), n0) | (~value(in(n1, or1(f(n2, a))), n0)) | (~value(in(n2, or1(f(n2, a))), n0))),
% 18.15/11.92 inference(unit_resolution,[status(thm)],[375, 369, 352])).
% 18.15/11.92 tff(377,plain,
% 18.15/11.92 ((~value(in(n1, or1(f(n2, a))), n0)) | (~value(in(n2, or1(f(n2, a))), n0))),
% 18.15/11.92 inference(unit_resolution,[status(thm)],[376, 359, 341])).
% 18.15/11.92 tff(378,plain,
% 18.15/11.92 (~value(in(n1, or1(f(n2, a))), n0)),
% 18.15/11.92 inference(unit_resolution,[status(thm)],[377, 288])).
% 18.15/11.92 tff(379,plain,
% 18.15/11.92 (^[X: $i] : refl(((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X)))) <=> ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X)))))),
% 18.15/11.92 inference(bind,[status(th)],[])).
% 18.15/11.92 tff(380,plain,
% 18.15/11.92 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 18.15/11.92 inference(quant_intro,[status(thm)],[379])).
% 18.15/11.92 tff(381,plain,
% 18.15/11.92 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 18.15/11.92 inference(rewrite,[status(thm)],[])).
% 18.15/11.92 tff(382,axiom,(![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_connection_outch2_in1or1')).
% 18.15/11.92 tff(383,plain,
% 18.15/11.92 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 18.15/11.92 inference(modus_ponens,[status(thm)],[382, 381])).
% 18.15/11.92 tff(384,plain,(
% 18.15/11.92 ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 18.15/11.92 inference(skolemize,[status(sab)],[383])).
% 18.15/11.92 tff(385,plain,
% 18.15/11.92 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 18.15/11.92 inference(modus_ponens,[status(thm)],[384, 380])).
% 18.15/11.92 tff(386,plain,
% 18.15/11.92 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | ((~type(f(n2, a), fulladder)) | connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a)))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | (~type(f(n2, a), fulladder)) | connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a)))))),
% 18.15/11.92 inference(rewrite,[status(thm)],[])).
% 18.15/11.92 tff(387,plain,
% 18.15/11.92 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | ((~type(f(n2, a), fulladder)) | connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a)))))),
% 18.15/11.92 inference(quant_inst,[status(thm)],[])).
% 18.15/11.92 tff(388,plain,
% 18.15/11.92 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | (~type(f(n2, a), fulladder)) | connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a))))),
% 18.15/11.92 inference(modus_ponens,[status(thm)],[387, 386])).
% 18.15/11.92 tff(389,plain,
% 18.15/11.92 (connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a))))),
% 18.15/11.92 inference(unit_resolution,[status(thm)],[388, 385, 48])).
% 18.15/11.92 tff(390,plain,
% 18.15/11.92 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, or1(f(n2, a))), n0) | (~value(out(c, h2(f(n2, a))), n0)) | (~connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(in(n1, or1(f(n2, a))), n0) | (~value(out(c, h2(f(n2, a))), n0)) | (~connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a))))))),
% 18.15/11.92 inference(rewrite,[status(thm)],[])).
% 18.15/11.92 tff(391,plain,
% 18.15/11.92 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, or1(f(n2, a))), n0) | (~value(out(c, h2(f(n2, a))), n0)) | (~connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a))))))),
% 18.15/11.92 inference(quant_inst,[status(thm)],[])).
% 18.15/11.92 tff(392,plain,
% 18.15/11.92 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(in(n1, or1(f(n2, a))), n0) | (~value(out(c, h2(f(n2, a))), n0)) | (~connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a)))))),
% 18.15/11.92 inference(modus_ponens,[status(thm)],[391, 390])).
% 18.15/11.92 tff(393,plain,
% 18.15/11.92 ($false),
% 18.15/11.92 inference(unit_resolution,[status(thm)],[392, 29, 389, 378, 174])).
% 18.15/11.92 % SZS output end Proof
%------------------------------------------------------------------------------