%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV006-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 Jun 21 05:08:52 AM UTC 2025
% Result : Unsatisfiable 0.69s 0.91s
% Output : Proof 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : HWV006-1 : TPTP v9.0.0. Released v2.1.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 17:22:34 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.69/0.91 % SZS status Unsatisfiable
% 0.69/0.91 % SZS output start Proof
% 0.69/0.91 tff(value_type, type, (
% 0.69/0.91 value: ( $i * $i ) > $o)).
% 0.69/0.91 tff(n0_type, type, (
% 0.69/0.91 n0: $i)).
% 0.69/0.91 tff(out_type, type, (
% 0.69/0.91 out: ( $i * $i ) > $i)).
% 0.69/0.91 tff(h1_type, type, (
% 0.69/0.91 h1: $i > $i)).
% 0.69/0.91 tff(f_type, type, (
% 0.69/0.91 f: $i)).
% 0.69/0.91 tff(s_type, type, (
% 0.69/0.91 s: $i)).
% 0.69/0.91 tff(in_type, type, (
% 0.69/0.91 in: ( $i * $i ) > $i)).
% 0.69/0.91 tff(h2_type, type, (
% 0.69/0.91 h2: $i > $i)).
% 0.69/0.91 tff(n2_type, type, (
% 0.69/0.91 n2: $i)).
% 0.69/0.91 tff(and2_type, type, (
% 0.69/0.91 and2: $i > $i)).
% 0.69/0.91 tff(n1_type, type, (
% 0.69/0.91 n1: $i)).
% 0.69/0.91 tff(and1_type, type, (
% 0.69/0.91 and1: $i > $i)).
% 0.69/0.91 tff(mode_type, type, (
% 0.69/0.91 mode: ( $i * $i ) > $o)).
% 0.69/0.91 tff(ok_type, type, (
% 0.69/0.91 ok: $i)).
% 0.69/0.91 tff(abnormal_type, type, (
% 0.69/0.91 abnormal: $i)).
% 0.69/0.91 tff(or1_type, type, (
% 0.69/0.91 or1: $i > $i)).
% 0.69/0.91 tff(c_type, type, (
% 0.69/0.91 c: $i)).
% 0.69/0.91 tff(connection_type, type, (
% 0.69/0.91 connection: ( $i * $i ) > $o)).
% 0.69/0.91 tff(type_type, type, (
% 0.69/0.91 type: ( $i * $i ) > $o)).
% 0.69/0.91 tff(halfadder_type, type, (
% 0.69/0.91 halfadder: $i)).
% 0.69/0.91 tff(fulladder_type, type, (
% 0.69/0.91 fulladder: $i)).
% 0.69/0.91 tff(or_type, type, (
% 0.69/0.91 or: $i)).
% 0.69/0.91 tff(and_type, type, (
% 0.69/0.91 and: $i)).
% 0.69/0.91 tff(not1_type, type, (
% 0.69/0.91 not1: $i > $i)).
% 0.69/0.91 tff(not_type, type, (
% 0.69/0.91 not: $i)).
% 0.69/0.91 tff(equal_value_type, type, (
% 0.69/0.91 equal_value: ( $i * $i ) > $o)).
% 0.69/0.91 tff(1,assumption,(~value(out(n1, and2(h2(f))), n0)), introduced(assumption)).
% 0.69/0.91 tff(2,assumption,(value(out(c, h2(f)), n0)), introduced(assumption)).
% 0.69/0.91 tff(3,plain,
% 0.69/0.91 (type(f, fulladder) <=> type(f, fulladder)),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(4,axiom,(type(f, fulladder)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','f_isa_fulladder')).
% 0.69/0.91 tff(5,plain,
% 0.69/0.91 (type(f, fulladder)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.69/0.91 tff(6,plain,
% 0.69/0.91 (^[X: $i] : refl(((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ((~type(X, fulladder)) | type(h2(X), halfadder)))),
% 0.69/0.91 inference(bind,[status(th)],[])).
% 0.69/0.91 tff(7,plain,
% 0.69/0.91 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 0.69/0.91 inference(quant_intro,[status(thm)],[6])).
% 0.69/0.91 tff(8,plain,
% 0.69/0.91 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(9,axiom,(![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_halfadder2')).
% 0.69/0.91 tff(10,plain,
% 0.69/0.91 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.69/0.91 tff(11,plain,(
% 0.69/0.91 ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 0.69/0.91 inference(skolemize,[status(sab)],[10])).
% 0.69/0.91 tff(12,plain,
% 0.69/0.91 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.69/0.91 tff(13,plain,
% 0.69/0.91 (((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | ((~type(f, fulladder)) | type(h2(f), halfadder))) <=> ((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | (~type(f, fulladder)) | type(h2(f), halfadder))),
% 0.69/0.91 inference(rewrite,[status(thm)],[])).
% 0.69/0.91 tff(14,plain,
% 0.69/0.91 ((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | ((~type(f, fulladder)) | type(h2(f), halfadder))),
% 0.69/0.91 inference(quant_inst,[status(thm)],[])).
% 0.69/0.91 tff(15,plain,
% 0.69/0.91 ((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | (~type(f, fulladder)) | type(h2(f), halfadder)),
% 0.69/0.91 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.69/0.91 tff(16,plain,
% 0.69/0.91 (type(h2(f), halfadder)),
% 0.69/0.91 inference(unit_resolution,[status(thm)],[15, 12, 5])).
% 0.69/0.91 tff(17,plain,
% 0.69/0.91 (^[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)))))),
% 0.69/0.91 inference(bind,[status(th)],[])).
% 0.69/0.91 tff(18,plain,
% 0.69/0.91 (![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))))),
% 0.69/0.91 inference(quant_intro,[status(thm)],[17])).
% 0.69/0.91 tff(19,plain,
% 0.69/0.91 (![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))))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(20,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')).
% 0.69/0.92 tff(21,plain,
% 0.69/0.92 (![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.69/0.92 tff(22,plain,(
% 0.69/0.92 ![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 0.69/0.92 inference(skolemize,[status(sab)],[21])).
% 0.69/0.92 tff(23,plain,
% 0.69/0.92 (![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.69/0.92 tff(24,plain,
% 0.69/0.92 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h2(f), halfadder)) | connection(out(c, h2(f)), out(n1, and2(h2(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h2(f), halfadder)) | connection(out(c, h2(f)), out(n1, and2(h2(f)))))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(25,plain,
% 0.69/0.92 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h2(f), halfadder)) | connection(out(c, h2(f)), out(n1, and2(h2(f)))))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(26,plain,
% 0.69/0.92 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h2(f), halfadder)) | connection(out(c, h2(f)), out(n1, and2(h2(f))))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.69/0.92 tff(27,plain,
% 0.69/0.92 (connection(out(c, h2(f)), out(n1, and2(h2(f))))),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[26, 23, 16])).
% 0.69/0.92 tff(28,plain,
% 0.69/0.92 (^[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))))),
% 0.69/0.92 inference(bind,[status(th)],[])).
% 0.69/0.92 tff(29,plain,
% 0.69/0.92 (![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)))),
% 0.69/0.92 inference(quant_intro,[status(thm)],[28])).
% 0.69/0.92 tff(30,plain,
% 0.69/0.92 (![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)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(31,plain,
% 0.69/0.92 (^[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))))),
% 0.69/0.92 inference(bind,[status(th)],[])).
% 0.69/0.92 tff(32,plain,
% 0.69/0.92 (![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)))),
% 0.69/0.92 inference(quant_intro,[status(thm)],[31])).
% 0.69/0.92 tff(33,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')).
% 0.69/0.92 tff(34,plain,
% 0.69/0.92 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.69/0.92 tff(35,plain,
% 0.69/0.92 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.69/0.92 tff(36,plain,(
% 0.69/0.92 ![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 0.69/0.92 inference(skolemize,[status(sab)],[35])).
% 0.69/0.92 tff(37,plain,
% 0.69/0.92 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.69/0.92 tff(38,plain,
% 0.69/0.92 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and2(h2(f))), n0) | (~value(out(c, h2(f)), n0)) | (~connection(out(c, h2(f)), out(n1, and2(h2(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, and2(h2(f))), n0) | (~value(out(c, h2(f)), n0)) | (~connection(out(c, h2(f)), out(n1, and2(h2(f))))))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(39,plain,
% 0.69/0.92 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and2(h2(f))), n0) | (~value(out(c, h2(f)), n0)) | (~connection(out(c, h2(f)), out(n1, and2(h2(f))))))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(40,plain,
% 0.69/0.92 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, and2(h2(f))), n0) | (~value(out(c, h2(f)), n0)) | (~connection(out(c, h2(f)), out(n1, and2(h2(f)))))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.69/0.92 tff(41,plain,
% 0.69/0.92 ($false),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[40, 37, 27, 1, 2])).
% 0.69/0.92 tff(42,plain,(value(out(n1, and2(h2(f))), n0) | (~value(out(c, h2(f)), n0))), inference(lemma,lemma(discharge,[]))).
% 0.69/0.92 tff(43,plain,
% 0.69/0.92 (~value(out(c, h2(f)), n0)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[42, 1])).
% 0.69/0.92 tff(44,plain,
% 0.69/0.92 (^[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)))))),
% 0.69/0.92 inference(bind,[status(th)],[])).
% 0.69/0.92 tff(45,plain,
% 0.69/0.92 (![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))))),
% 0.69/0.92 inference(quant_intro,[status(thm)],[44])).
% 0.69/0.92 tff(46,plain,
% 0.69/0.92 (![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))))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(47,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')).
% 0.69/0.92 tff(48,plain,
% 0.69/0.92 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.69/0.92 tff(49,plain,(
% 0.69/0.92 ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 0.69/0.92 inference(skolemize,[status(sab)],[48])).
% 0.69/0.92 tff(50,plain,
% 0.69/0.92 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.69/0.92 tff(51,plain,
% 0.69/0.92 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | ((~type(f, fulladder)) | connection(out(c, h2(f)), in(n1, or1(f))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | (~type(f, fulladder)) | connection(out(c, h2(f)), in(n1, or1(f))))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(52,plain,
% 0.69/0.92 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | ((~type(f, fulladder)) | connection(out(c, h2(f)), in(n1, or1(f))))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(53,plain,
% 0.69/0.92 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | (~type(f, fulladder)) | connection(out(c, h2(f)), in(n1, or1(f)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.69/0.92 tff(54,plain,
% 0.69/0.92 (connection(out(c, h2(f)), in(n1, or1(f)))),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[53, 50, 5])).
% 0.69/0.92 tff(55,plain,
% 0.69/0.92 (^[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))))),
% 0.69/0.92 inference(bind,[status(th)],[])).
% 0.69/0.92 tff(56,plain,
% 0.69/0.92 (![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)))),
% 0.69/0.92 inference(quant_intro,[status(thm)],[55])).
% 0.69/0.92 tff(57,plain,
% 0.69/0.92 (![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)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(58,plain,
% 0.69/0.92 (^[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))))),
% 0.69/0.92 inference(bind,[status(th)],[])).
% 0.69/0.92 tff(59,plain,
% 0.69/0.92 (![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)))),
% 0.69/0.92 inference(quant_intro,[status(thm)],[58])).
% 0.69/0.92 tff(60,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')).
% 0.69/0.92 tff(61,plain,
% 0.69/0.92 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.69/0.92 tff(62,plain,
% 0.69/0.92 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.69/0.92 tff(63,plain,(
% 0.69/0.92 ![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 0.69/0.92 inference(skolemize,[status(sab)],[62])).
% 0.69/0.92 tff(64,plain,
% 0.69/0.92 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.69/0.92 tff(65,plain,
% 0.69/0.92 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n1, or1(f)), n0)) | value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, or1(f)), n0)) | value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f)))))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(66,plain,
% 0.69/0.92 ((value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f)))) | (~value(in(n1, or1(f)), n0))) <=> ((~value(in(n1, or1(f)), n0)) | value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f)))))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(67,plain,
% 0.69/0.92 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f)))) | (~value(in(n1, or1(f)), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n1, or1(f)), n0)) | value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f))))))),
% 0.69/0.92 inference(monotonicity,[status(thm)],[66])).
% 0.69/0.92 tff(68,plain,
% 0.69/0.92 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f)))) | (~value(in(n1, or1(f)), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, or1(f)), n0)) | value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f)))))),
% 0.69/0.92 inference(transitivity,[status(thm)],[67, 65])).
% 0.69/0.92 tff(69,plain,
% 0.69/0.92 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f)))) | (~value(in(n1, or1(f)), n0)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(70,plain,
% 0.69/0.92 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, or1(f)), n0)) | value(out(c, h2(f)), n0) | (~connection(out(c, h2(f)), in(n1, or1(f))))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.69/0.92 tff(71,plain,
% 0.69/0.92 ((~value(in(n1, or1(f)), n0)) | value(out(c, h2(f)), n0)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[70, 64, 54])).
% 0.69/0.92 tff(72,plain,
% 0.69/0.92 (~value(in(n1, or1(f)), n0)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[71, 43])).
% 0.69/0.92 tff(73,assumption,(~value(out(n1, or1(f)), n0)), introduced(assumption)).
% 0.69/0.92 tff(74,plain,
% 0.69/0.92 (^[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)))))),
% 0.69/0.92 inference(bind,[status(th)],[])).
% 0.69/0.92 tff(75,plain,
% 0.69/0.92 (![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))))),
% 0.69/0.92 inference(quant_intro,[status(thm)],[74])).
% 0.69/0.92 tff(76,plain,
% 0.69/0.92 (![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))))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(77,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')).
% 0.69/0.92 tff(78,plain,
% 0.69/0.92 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.69/0.92 tff(79,plain,(
% 0.69/0.92 ![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 0.69/0.92 inference(skolemize,[status(sab)],[78])).
% 0.69/0.92 tff(80,plain,
% 0.69/0.92 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.69/0.92 tff(81,plain,
% 0.69/0.92 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | ((~type(f, fulladder)) | connection(out(c, f), out(n1, or1(f))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | (~type(f, fulladder)) | connection(out(c, f), out(n1, or1(f))))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(82,plain,
% 0.69/0.92 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | ((~type(f, fulladder)) | connection(out(c, f), out(n1, or1(f))))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(83,plain,
% 0.69/0.92 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | (~type(f, fulladder)) | connection(out(c, f), out(n1, or1(f)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.69/0.92 tff(84,plain,
% 0.69/0.92 (connection(out(c, f), out(n1, or1(f)))),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[83, 80, 5])).
% 0.69/0.92 tff(85,plain,
% 0.69/0.92 (value(out(c, f), n0) <=> value(out(c, f), n0)),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(86,axiom,(value(out(c, f), n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','outc_0')).
% 0.69/0.92 tff(87,plain,
% 0.69/0.92 (value(out(c, f), n0)),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.69/0.92 tff(88,plain,
% 0.69/0.92 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))) | value(out(n1, or1(f)), n0))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))) | value(out(n1, or1(f)), n0))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(89,plain,
% 0.69/0.92 ((value(out(n1, or1(f)), n0) | (~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f))))) <=> ((~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))) | value(out(n1, or1(f)), n0))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(90,plain,
% 0.69/0.92 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, or1(f)), n0) | (~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))) | value(out(n1, or1(f)), n0)))),
% 0.69/0.92 inference(monotonicity,[status(thm)],[89])).
% 0.69/0.92 tff(91,plain,
% 0.69/0.92 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, or1(f)), n0) | (~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))) | value(out(n1, or1(f)), n0))),
% 0.69/0.92 inference(transitivity,[status(thm)],[90, 88])).
% 0.69/0.92 tff(92,plain,
% 0.69/0.92 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, or1(f)), n0) | (~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(93,plain,
% 0.69/0.92 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(c, f), n0)) | (~connection(out(c, f), out(n1, or1(f)))) | value(out(n1, or1(f)), n0)),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.69/0.92 tff(94,plain,
% 0.69/0.92 ($false),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[93, 37, 87, 84, 73])).
% 0.69/0.92 tff(95,plain,(value(out(n1, or1(f)), n0)), inference(lemma,lemma(discharge,[]))).
% 0.69/0.92 tff(96,plain,
% 0.69/0.92 (^[X: $i] : refl(((~type(X, fulladder)) | type(or1(X), or)) <=> ((~type(X, fulladder)) | type(or1(X), or)))),
% 0.69/0.92 inference(bind,[status(th)],[])).
% 0.69/0.92 tff(97,plain,
% 0.69/0.92 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 0.69/0.92 inference(quant_intro,[status(thm)],[96])).
% 0.69/0.92 tff(98,plain,
% 0.69/0.92 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(99,axiom,(![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_or1')).
% 0.69/0.92 tff(100,plain,
% 0.69/0.92 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.69/0.92 tff(101,plain,(
% 0.69/0.92 ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 0.69/0.92 inference(skolemize,[status(sab)],[100])).
% 0.69/0.92 tff(102,plain,
% 0.69/0.92 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.69/0.92 tff(103,plain,
% 0.69/0.92 (((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | ((~type(f, fulladder)) | type(or1(f), or))) <=> ((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | (~type(f, fulladder)) | type(or1(f), or))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(104,plain,
% 0.69/0.92 ((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | ((~type(f, fulladder)) | type(or1(f), or))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(105,plain,
% 0.69/0.92 ((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | (~type(f, fulladder)) | type(or1(f), or)),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.69/0.92 tff(106,plain,
% 0.69/0.92 (type(or1(f), or)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[105, 102, 5])).
% 0.69/0.92 tff(107,plain,
% 0.69/0.92 (^[K: $i] : refl(((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or))) <=> ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or))))),
% 0.69/0.92 inference(bind,[status(th)],[])).
% 0.69/0.92 tff(108,plain,
% 0.69/0.92 (![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or))) <=> ![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 0.69/0.92 inference(quant_intro,[status(thm)],[107])).
% 0.69/0.92 tff(109,plain,
% 0.69/0.92 (![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or))) <=> ![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(110,plain,
% 0.69/0.92 (^[K: $i] : trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n0)) | (~type(K, or)))), (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n0)) | (~type(K, or))) | value(in(n1, K), n0)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n0)) | (~type(K, or))) | value(in(n1, K), n0)) <=> ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))), (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) <=> ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))))),
% 0.69/0.92 inference(bind,[status(th)],[])).
% 0.69/0.92 tff(111,plain,
% 0.69/0.92 (![K: $i] : ((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) <=> ![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 0.69/0.92 inference(quant_intro,[status(thm)],[110])).
% 0.69/0.92 tff(112,axiom,(![K: $i] : ((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','or_0_0x')).
% 0.69/0.92 tff(113,plain,
% 0.69/0.92 (![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.69/0.92 tff(114,plain,
% 0.69/0.92 (![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.69/0.92 tff(115,plain,(
% 0.69/0.92 ![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 0.69/0.92 inference(skolemize,[status(sab)],[114])).
% 0.69/0.92 tff(116,plain,
% 0.69/0.92 (![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.69/0.92 tff(117,plain,
% 0.69/0.92 (((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n1, or1(f)), n0) | (~type(or1(f), or)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | (~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n1, or1(f)), n0) | (~type(or1(f), or)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(118,plain,
% 0.69/0.92 (((~mode(or1(f), ok)) | value(in(n1, or1(f)), n0) | (~value(out(n1, or1(f)), n0)) | (~type(or1(f), or))) <=> ((~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n1, or1(f)), n0) | (~type(or1(f), or)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(119,plain,
% 0.69/0.92 (((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(f), ok)) | value(in(n1, or1(f)), n0) | (~value(out(n1, or1(f)), n0)) | (~type(or1(f), or)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n1, or1(f)), n0) | (~type(or1(f), or))))),
% 0.69/0.92 inference(monotonicity,[status(thm)],[118])).
% 0.69/0.92 tff(120,plain,
% 0.69/0.92 (((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(f), ok)) | value(in(n1, or1(f)), n0) | (~value(out(n1, or1(f)), n0)) | (~type(or1(f), or)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | (~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n1, or1(f)), n0) | (~type(or1(f), or)))),
% 0.69/0.92 inference(transitivity,[status(thm)],[119, 117])).
% 0.69/0.92 tff(121,plain,
% 0.69/0.92 ((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(f), ok)) | value(in(n1, or1(f)), n0) | (~value(out(n1, or1(f)), n0)) | (~type(or1(f), or)))),
% 0.69/0.92 inference(quant_inst,[status(thm)],[])).
% 0.69/0.92 tff(122,plain,
% 0.69/0.92 ((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | (~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n1, or1(f)), n0) | (~type(or1(f), or))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.69/0.92 tff(123,plain,
% 0.69/0.92 ((~mode(or1(f), ok)) | (~value(out(n1, or1(f)), n0)) | value(in(n1, or1(f)), n0)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[122, 116, 106])).
% 0.69/0.92 tff(124,plain,
% 0.69/0.92 ((~mode(or1(f), ok)) | value(in(n1, or1(f)), n0)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[123, 95])).
% 0.69/0.92 tff(125,plain,
% 0.69/0.92 (~mode(or1(f), ok)),
% 0.69/0.92 inference(unit_resolution,[status(thm)],[124, 72])).
% 0.69/0.92 tff(126,plain,
% 0.69/0.92 (^[Any: $i, K: $i] : refl((mode(K, abnormal) | mode(K, ok) | (~type(K, Any))) <=> (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))))),
% 0.69/0.92 inference(bind,[status(th)],[])).
% 0.69/0.92 tff(127,plain,
% 0.69/0.92 (![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)))),
% 0.69/0.92 inference(quant_intro,[status(thm)],[126])).
% 0.69/0.92 tff(128,plain,
% 0.69/0.92 (![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)))),
% 0.69/0.92 inference(rewrite,[status(thm)],[])).
% 0.69/0.92 tff(129,plain,
% 0.69/0.92 (^[Any: $i, K: $i] : rewrite((((~type(K, Any)) | mode(K, ok)) | mode(K, abnormal)) <=> (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))))),
% 0.69/0.92 inference(bind,[status(th)],[])).
% 0.69/0.92 tff(130,plain,
% 0.69/0.92 (![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)))),
% 0.69/0.92 inference(quant_intro,[status(thm)],[129])).
% 0.69/0.92 tff(131,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')).
% 0.69/0.92 tff(132,plain,
% 0.69/0.92 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.69/0.92 tff(133,plain,
% 0.69/0.92 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.69/0.92 tff(134,plain,(
% 0.69/0.92 ![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 0.69/0.92 inference(skolemize,[status(sab)],[133])).
% 0.69/0.92 tff(135,plain,
% 0.69/0.92 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 0.69/0.92 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.69/0.92 tff(136,plain,
% 0.69/0.92 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(or1(f), abnormal) | mode(or1(f), ok) | (~type(or1(f), or)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(or1(f), abnormal) | mode(or1(f), ok) | (~type(or1(f), or)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(137,plain,
% 0.69/0.93 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(or1(f), abnormal) | mode(or1(f), ok) | (~type(or1(f), or)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(138,plain,
% 0.69/0.93 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(or1(f), abnormal) | mode(or1(f), ok) | (~type(or1(f), or))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.69/0.93 tff(139,plain,
% 0.69/0.93 (mode(or1(f), abnormal) | mode(or1(f), ok)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[138, 135, 106])).
% 0.69/0.93 tff(140,plain,
% 0.69/0.93 (mode(or1(f), abnormal)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[139, 125])).
% 0.69/0.93 tff(141,plain,
% 0.69/0.93 (((~mode(or1(f), abnormal)) | (~mode(and1(h2(f)), abnormal))) <=> ((~mode(or1(f), abnormal)) | (~mode(and1(h2(f)), abnormal)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(142,axiom,((~mode(or1(f), abnormal)) | (~mode(and1(h2(f)), abnormal))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_or1_and1h2')).
% 0.69/0.93 tff(143,plain,
% 0.69/0.93 ((~mode(or1(f), abnormal)) | (~mode(and1(h2(f)), abnormal))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.69/0.93 tff(144,plain,
% 0.69/0.93 (~mode(and1(h2(f)), abnormal)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[143, 140])).
% 0.69/0.93 tff(145,plain,
% 0.69/0.93 (^[X: $i] : refl(((~type(X, halfadder)) | type(and1(X), and)) <=> ((~type(X, halfadder)) | type(and1(X), and)))),
% 0.69/0.93 inference(bind,[status(th)],[])).
% 0.69/0.93 tff(146,plain,
% 0.69/0.93 (![X: $i] : ((~type(X, halfadder)) | type(and1(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))),
% 0.69/0.93 inference(quant_intro,[status(thm)],[145])).
% 0.69/0.93 tff(147,plain,
% 0.69/0.93 (![X: $i] : ((~type(X, halfadder)) | type(and1(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(148,axiom,(![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_and1')).
% 0.69/0.93 tff(149,plain,
% 0.69/0.93 (![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.69/0.93 tff(150,plain,(
% 0.69/0.93 ![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))),
% 0.69/0.93 inference(skolemize,[status(sab)],[149])).
% 0.69/0.93 tff(151,plain,
% 0.69/0.93 (![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.69/0.93 tff(152,plain,
% 0.69/0.93 (((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | ((~type(h2(f), halfadder)) | type(and1(h2(f)), and))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | (~type(h2(f), halfadder)) | type(and1(h2(f)), and))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(153,plain,
% 0.69/0.93 ((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | ((~type(h2(f), halfadder)) | type(and1(h2(f)), and))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(154,plain,
% 0.69/0.93 ((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | (~type(h2(f), halfadder)) | type(and1(h2(f)), and)),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.69/0.93 tff(155,plain,
% 0.69/0.93 (type(and1(h2(f)), and)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[154, 151, 16])).
% 0.69/0.93 tff(156,plain,
% 0.69/0.93 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and1(h2(f)), abnormal) | mode(and1(h2(f)), ok) | (~type(and1(h2(f)), and)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and1(h2(f)), abnormal) | mode(and1(h2(f)), ok) | (~type(and1(h2(f)), and)))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(157,plain,
% 0.69/0.93 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and1(h2(f)), abnormal) | mode(and1(h2(f)), ok) | (~type(and1(h2(f)), and)))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(158,plain,
% 0.69/0.93 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and1(h2(f)), abnormal) | mode(and1(h2(f)), ok) | (~type(and1(h2(f)), and))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.69/0.93 tff(159,plain,
% 0.69/0.93 (mode(and1(h2(f)), abnormal) | mode(and1(h2(f)), ok)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[158, 135, 155])).
% 0.69/0.93 tff(160,plain,
% 0.69/0.93 (mode(and1(h2(f)), ok)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[159, 144])).
% 0.69/0.93 tff(161,plain,
% 0.69/0.93 (^[X: $i] : refl(((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X)))) <=> ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X)))))),
% 0.69/0.93 inference(bind,[status(th)],[])).
% 0.69/0.93 tff(162,plain,
% 0.69/0.93 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))),
% 0.69/0.93 inference(quant_intro,[status(thm)],[161])).
% 0.69/0.93 tff(163,plain,
% 0.69/0.93 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(164,axiom,(![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_connection_outs_outsh2')).
% 0.69/0.93 tff(165,plain,
% 0.69/0.93 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.69/0.93 tff(166,plain,(
% 0.69/0.93 ![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))),
% 0.69/0.93 inference(skolemize,[status(sab)],[165])).
% 0.69/0.93 tff(167,plain,
% 0.69/0.93 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.69/0.93 tff(168,plain,
% 0.69/0.93 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))) | ((~type(f, fulladder)) | connection(out(s, f), out(s, h2(f))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))) | (~type(f, fulladder)) | connection(out(s, f), out(s, h2(f))))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(169,plain,
% 0.69/0.93 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))) | ((~type(f, fulladder)) | connection(out(s, f), out(s, h2(f))))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(170,plain,
% 0.69/0.93 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, X), out(s, h2(X))))) | (~type(f, fulladder)) | connection(out(s, f), out(s, h2(f)))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.69/0.93 tff(171,plain,
% 0.69/0.93 (connection(out(s, f), out(s, h2(f)))),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[170, 167, 5])).
% 0.69/0.93 tff(172,plain,
% 0.69/0.93 (value(out(s, f), n1) <=> value(out(s, f), n1)),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(173,axiom,(value(out(s, f), n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','outs_1')).
% 0.69/0.93 tff(174,plain,
% 0.69/0.93 (value(out(s, f), n1)),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.69/0.93 tff(175,plain,
% 0.69/0.93 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))) | value(out(s, h2(f)), n1))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))) | value(out(s, h2(f)), n1))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(176,plain,
% 0.69/0.93 ((value(out(s, h2(f)), n1) | (~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f))))) <=> ((~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))) | value(out(s, h2(f)), n1))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(177,plain,
% 0.69/0.93 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(s, h2(f)), n1) | (~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))) | value(out(s, h2(f)), n1)))),
% 0.69/0.93 inference(monotonicity,[status(thm)],[176])).
% 0.69/0.93 tff(178,plain,
% 0.69/0.93 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(s, h2(f)), n1) | (~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))) | value(out(s, h2(f)), n1))),
% 0.69/0.93 inference(transitivity,[status(thm)],[177, 175])).
% 0.69/0.93 tff(179,plain,
% 0.69/0.93 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(s, h2(f)), n1) | (~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(180,plain,
% 0.69/0.93 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(s, f), n1)) | (~connection(out(s, f), out(s, h2(f)))) | value(out(s, h2(f)), n1)),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.69/0.93 tff(181,plain,
% 0.69/0.93 (value(out(s, h2(f)), n1)),
% 0.69/0.93 inference(unit_resolution,[status(thm)],[180, 37, 174, 171])).
% 0.69/0.93 tff(182,assumption,(~value(out(n1, and1(h2(f))), n1)), introduced(assumption)).
% 0.69/0.93 tff(183,plain,
% 0.69/0.93 (^[X: $i] : refl(((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X)))) <=> ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X)))))),
% 0.69/0.93 inference(bind,[status(th)],[])).
% 0.69/0.93 tff(184,plain,
% 0.69/0.93 (![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))),
% 0.69/0.93 inference(quant_intro,[status(thm)],[183])).
% 0.69/0.93 tff(185,plain,
% 0.69/0.93 (![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(186,axiom,(![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_connection_outs_out1and1')).
% 0.69/0.93 tff(187,plain,
% 0.69/0.93 (![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.69/0.93 tff(188,plain,(
% 0.69/0.93 ![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))),
% 0.69/0.93 inference(skolemize,[status(sab)],[187])).
% 0.69/0.93 tff(189,plain,
% 0.69/0.93 (![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))),
% 0.69/0.93 inference(modus_ponens,[status(thm)],[188, 184])).
% 0.69/0.93 tff(190,plain,
% 0.69/0.93 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))) | ((~type(h2(f), halfadder)) | connection(out(s, h2(f)), out(n1, and1(h2(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))) | (~type(h2(f), halfadder)) | connection(out(s, h2(f)), out(n1, and1(h2(f)))))),
% 0.69/0.93 inference(rewrite,[status(thm)],[])).
% 0.69/0.93 tff(191,plain,
% 0.69/0.93 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))) | ((~type(h2(f), halfadder)) | connection(out(s, h2(f)), out(n1, and1(h2(f)))))),
% 0.69/0.93 inference(quant_inst,[status(thm)],[])).
% 0.69/0.93 tff(192,plain,
% 0.69/0.93 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))) | (~type(h2(f), halfadder)) | connection(out(s, h2(f)), out(n1, and1(h2(f))))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.77/0.93 tff(193,plain,
% 0.77/0.93 (connection(out(s, h2(f)), out(n1, and1(h2(f))))),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[192, 189, 16])).
% 0.77/0.93 tff(194,plain,
% 0.77/0.93 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~connection(out(s, h2(f)), out(n1, and1(h2(f))))) | value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~connection(out(s, h2(f)), out(n1, and1(h2(f))))) | value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(195,plain,
% 0.77/0.93 ((value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1)) | (~connection(out(s, h2(f)), out(n1, and1(h2(f)))))) <=> ((~connection(out(s, h2(f)), out(n1, and1(h2(f))))) | value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(196,plain,
% 0.77/0.93 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1)) | (~connection(out(s, h2(f)), out(n1, and1(h2(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~connection(out(s, h2(f)), out(n1, and1(h2(f))))) | value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[195])).
% 0.77/0.93 tff(197,plain,
% 0.77/0.93 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1)) | (~connection(out(s, h2(f)), out(n1, and1(h2(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~connection(out(s, h2(f)), out(n1, and1(h2(f))))) | value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[196, 194])).
% 0.77/0.93 tff(198,plain,
% 0.77/0.93 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1)) | (~connection(out(s, h2(f)), out(n1, and1(h2(f))))))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(199,plain,
% 0.77/0.93 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~connection(out(s, h2(f)), out(n1, and1(h2(f))))) | value(out(n1, and1(h2(f))), n1) | (~value(out(s, h2(f)), n1))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.77/0.93 tff(200,plain,
% 0.77/0.93 ($false),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[199, 37, 193, 182, 181])).
% 0.77/0.93 tff(201,plain,(value(out(n1, and1(h2(f))), n1)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.93 tff(202,plain,
% 0.77/0.93 (^[K: $i] : refl(((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1)))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(203,plain,
% 0.77/0.93 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[202])).
% 0.77/0.93 tff(204,plain,
% 0.77/0.93 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(205,plain,
% 0.77/0.93 (^[K: $i] : trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n2, K), n1)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and))) | value(in(n2, K), n1)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and))) | value(in(n2, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n2, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(206,plain,
% 0.77/0.93 (![K: $i] : ((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n2, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[205])).
% 0.77/0.93 tff(207,axiom,(![K: $i] : ((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n2, K), n1))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','and_1_x1')).
% 0.77/0.93 tff(208,plain,
% 0.77/0.93 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.77/0.93 tff(209,plain,
% 0.77/0.93 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.77/0.93 tff(210,plain,(
% 0.77/0.93 ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))),
% 0.77/0.93 inference(skolemize,[status(sab)],[209])).
% 0.77/0.93 tff(211,plain,
% 0.77/0.93 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[210, 203])).
% 0.77/0.93 tff(212,plain,
% 0.77/0.93 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))) | ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n2, and1(h2(f))), n1) | (~type(and1(h2(f)), and)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))) | (~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n2, and1(h2(f))), n1) | (~type(and1(h2(f)), and)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(213,plain,
% 0.77/0.93 (((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | (~type(and1(h2(f)), and)) | value(in(n2, and1(h2(f))), n1)) <=> ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n2, and1(h2(f))), n1) | (~type(and1(h2(f)), and)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(214,plain,
% 0.77/0.93 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))) | ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | (~type(and1(h2(f)), and)) | value(in(n2, and1(h2(f))), n1))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))) | ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n2, and1(h2(f))), n1) | (~type(and1(h2(f)), and))))),
% 0.77/0.93 inference(monotonicity,[status(thm)],[213])).
% 0.77/0.93 tff(215,plain,
% 0.77/0.93 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))) | ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | (~type(and1(h2(f)), and)) | value(in(n2, and1(h2(f))), n1))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))) | (~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n2, and1(h2(f))), n1) | (~type(and1(h2(f)), and)))),
% 0.77/0.93 inference(transitivity,[status(thm)],[214, 212])).
% 0.77/0.93 tff(216,plain,
% 0.77/0.93 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))) | ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | (~type(and1(h2(f)), and)) | value(in(n2, and1(h2(f))), n1))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(217,plain,
% 0.77/0.93 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n2, K), n1))) | (~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n2, and1(h2(f))), n1) | (~type(and1(h2(f)), and))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.77/0.93 tff(218,plain,
% 0.77/0.93 ((~mode(and1(h2(f)), ok)) | (~value(out(n1, and1(h2(f))), n1)) | value(in(n2, and1(h2(f))), n1)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[217, 211, 155])).
% 0.77/0.93 tff(219,plain,
% 0.77/0.93 ((~mode(and1(h2(f)), ok)) | value(in(n2, and1(h2(f))), n1)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[218, 201])).
% 0.77/0.93 tff(220,plain,
% 0.77/0.93 (value(in(n2, and1(h2(f))), n1)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[219, 160])).
% 0.77/0.93 tff(221,plain,
% 0.77/0.93 (^[X: $i] : refl(((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X)))) <=> ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X)))))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(222,plain,
% 0.77/0.93 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[221])).
% 0.77/0.93 tff(223,plain,
% 0.77/0.93 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(224,axiom,(![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_connection_out1not1_in2and1')).
% 0.77/0.93 tff(225,plain,
% 0.77/0.93 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.77/0.93 tff(226,plain,(
% 0.77/0.93 ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))),
% 0.77/0.93 inference(skolemize,[status(sab)],[225])).
% 0.77/0.93 tff(227,plain,
% 0.77/0.93 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[226, 222])).
% 0.77/0.93 tff(228,plain,
% 0.77/0.93 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))) | ((~type(h2(f), halfadder)) | connection(out(n1, not1(h2(f))), in(n2, and1(h2(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))) | (~type(h2(f), halfadder)) | connection(out(n1, not1(h2(f))), in(n2, and1(h2(f)))))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(229,plain,
% 0.77/0.93 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))) | ((~type(h2(f), halfadder)) | connection(out(n1, not1(h2(f))), in(n2, and1(h2(f)))))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(230,plain,
% 0.77/0.93 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))) | (~type(h2(f), halfadder)) | connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.77/0.93 tff(231,plain,
% 0.77/0.93 (connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[230, 227, 16])).
% 0.77/0.93 tff(232,plain,
% 0.77/0.93 (((~mode(or1(f), abnormal)) | (~mode(not1(h2(f)), abnormal))) <=> ((~mode(or1(f), abnormal)) | (~mode(not1(h2(f)), abnormal)))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(233,axiom,((~mode(or1(f), abnormal)) | (~mode(not1(h2(f)), abnormal))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_or1_not1h2')).
% 0.77/0.93 tff(234,plain,
% 0.77/0.93 ((~mode(or1(f), abnormal)) | (~mode(not1(h2(f)), abnormal))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.77/0.93 tff(235,plain,
% 0.77/0.93 (~mode(not1(h2(f)), abnormal)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[234, 140])).
% 0.77/0.93 tff(236,plain,
% 0.77/0.93 (^[X: $i] : refl(((~type(X, halfadder)) | type(not1(X), not)) <=> ((~type(X, halfadder)) | type(not1(X), not)))),
% 0.77/0.93 inference(bind,[status(th)],[])).
% 0.77/0.93 tff(237,plain,
% 0.77/0.93 (![X: $i] : ((~type(X, halfadder)) | type(not1(X), not)) <=> ![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))),
% 0.77/0.93 inference(quant_intro,[status(thm)],[236])).
% 0.77/0.93 tff(238,plain,
% 0.77/0.93 (![X: $i] : ((~type(X, halfadder)) | type(not1(X), not)) <=> ![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(239,axiom,(![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_not1')).
% 0.77/0.93 tff(240,plain,
% 0.77/0.93 (![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.77/0.93 tff(241,plain,(
% 0.77/0.93 ![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))),
% 0.77/0.93 inference(skolemize,[status(sab)],[240])).
% 0.77/0.93 tff(242,plain,
% 0.77/0.93 (![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[241, 237])).
% 0.77/0.93 tff(243,plain,
% 0.77/0.93 (((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | ((~type(h2(f), halfadder)) | type(not1(h2(f)), not))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | (~type(h2(f), halfadder)) | type(not1(h2(f)), not))),
% 0.77/0.93 inference(rewrite,[status(thm)],[])).
% 0.77/0.93 tff(244,plain,
% 0.77/0.93 ((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | ((~type(h2(f), halfadder)) | type(not1(h2(f)), not))),
% 0.77/0.93 inference(quant_inst,[status(thm)],[])).
% 0.77/0.93 tff(245,plain,
% 0.77/0.93 ((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | (~type(h2(f), halfadder)) | type(not1(h2(f)), not)),
% 0.77/0.93 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.77/0.93 tff(246,plain,
% 0.77/0.93 (type(not1(h2(f)), not)),
% 0.77/0.93 inference(unit_resolution,[status(thm)],[245, 242, 16])).
% 0.77/0.93 tff(247,plain,
% 0.77/0.93 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(not1(h2(f)), abnormal) | mode(not1(h2(f)), ok) | (~type(not1(h2(f)), not)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(not1(h2(f)), abnormal) | mode(not1(h2(f)), ok) | (~type(not1(h2(f)), not)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(248,plain,
% 0.77/0.94 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(not1(h2(f)), abnormal) | mode(not1(h2(f)), ok) | (~type(not1(h2(f)), not)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(249,plain,
% 0.77/0.94 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(not1(h2(f)), abnormal) | mode(not1(h2(f)), ok) | (~type(not1(h2(f)), not))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.77/0.94 tff(250,plain,
% 0.77/0.94 (mode(not1(h2(f)), abnormal) | mode(not1(h2(f)), ok)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[249, 135, 246])).
% 0.77/0.94 tff(251,plain,
% 0.77/0.94 (mode(not1(h2(f)), ok)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[250, 235])).
% 0.77/0.94 tff(252,plain,
% 0.77/0.94 (^[X: $i] : refl(((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X)))) <=> ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X)))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(253,plain,
% 0.77/0.94 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[252])).
% 0.77/0.94 tff(254,plain,
% 0.77/0.94 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(255,axiom,(![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_connection_out1and2_in1not1')).
% 0.77/0.94 tff(256,plain,
% 0.77/0.94 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.77/0.94 tff(257,plain,(
% 0.77/0.94 ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))),
% 0.77/0.94 inference(skolemize,[status(sab)],[256])).
% 0.77/0.94 tff(258,plain,
% 0.77/0.94 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[257, 253])).
% 0.77/0.94 tff(259,plain,
% 0.77/0.94 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))) | ((~type(h2(f), halfadder)) | connection(out(n1, and2(h2(f))), in(n1, not1(h2(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))) | (~type(h2(f), halfadder)) | connection(out(n1, and2(h2(f))), in(n1, not1(h2(f)))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(260,plain,
% 0.77/0.94 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))) | ((~type(h2(f), halfadder)) | connection(out(n1, and2(h2(f))), in(n1, not1(h2(f)))))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(261,plain,
% 0.77/0.94 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))) | (~type(h2(f), halfadder)) | connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.77/0.94 tff(262,plain,
% 0.77/0.94 (connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[261, 258, 16])).
% 0.77/0.94 tff(263,plain,
% 0.77/0.94 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, and2(h2(f))), n0) | (~value(in(n1, not1(h2(f))), n0)) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, and2(h2(f))), n0) | (~value(in(n1, not1(h2(f))), n0)) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(264,plain,
% 0.77/0.94 ((value(out(n1, and2(h2(f))), n0) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))) | (~value(in(n1, not1(h2(f))), n0))) <=> (value(out(n1, and2(h2(f))), n0) | (~value(in(n1, not1(h2(f))), n0)) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(265,plain,
% 0.77/0.94 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, and2(h2(f))), n0) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))) | (~value(in(n1, not1(h2(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, and2(h2(f))), n0) | (~value(in(n1, not1(h2(f))), n0)) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f)))))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[264])).
% 0.77/0.94 tff(266,plain,
% 0.77/0.94 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, and2(h2(f))), n0) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))) | (~value(in(n1, not1(h2(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, and2(h2(f))), n0) | (~value(in(n1, not1(h2(f))), n0)) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))))),
% 0.77/0.94 inference(transitivity,[status(thm)],[265, 263])).
% 0.77/0.94 tff(267,plain,
% 0.77/0.94 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, and2(h2(f))), n0) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f))))) | (~value(in(n1, not1(h2(f))), n0)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(268,plain,
% 0.77/0.94 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, and2(h2(f))), n0) | (~value(in(n1, not1(h2(f))), n0)) | (~connection(out(n1, and2(h2(f))), in(n1, not1(h2(f)))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.77/0.94 tff(269,plain,
% 0.77/0.94 (~value(in(n1, not1(h2(f))), n0)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[268, 64, 262, 1])).
% 0.77/0.94 tff(270,plain,
% 0.77/0.94 (^[K: $i] : refl(((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(271,plain,
% 0.77/0.94 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not))) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[270])).
% 0.77/0.94 tff(272,plain,
% 0.77/0.94 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not))) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(273,plain,
% 0.77/0.94 (^[K: $i] : trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, not))) | (~value(out(n1, K), n1))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, not)))), (((((~mode(K, ok)) | (~type(K, not))) | (~value(out(n1, K), n1))) | value(in(n1, K), n0)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, not))) | value(in(n1, K), n0)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, not))) | value(in(n1, K), n0)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))), (((((~mode(K, ok)) | (~type(K, not))) | (~value(out(n1, K), n1))) | value(in(n1, K), n0)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(274,plain,
% 0.77/0.94 (![K: $i] : ((((~mode(K, ok)) | (~type(K, not))) | (~value(out(n1, K), n1))) | value(in(n1, K), n0)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[273])).
% 0.77/0.94 tff(275,axiom,(![K: $i] : ((((~mode(K, ok)) | (~type(K, not))) | (~value(out(n1, K), n1))) | value(in(n1, K), n0))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','not_1_0_bw')).
% 0.77/0.94 tff(276,plain,
% 0.77/0.94 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.77/0.94 tff(277,plain,
% 0.77/0.94 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[276, 272])).
% 0.77/0.94 tff(278,plain,(
% 0.77/0.94 ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))),
% 0.77/0.94 inference(skolemize,[status(sab)],[277])).
% 0.77/0.94 tff(279,plain,
% 0.77/0.94 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[278, 271])).
% 0.77/0.94 tff(280,plain,
% 0.77/0.94 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))) | ((~mode(not1(h2(f)), ok)) | (~value(out(n1, not1(h2(f))), n1)) | value(in(n1, not1(h2(f))), n0) | (~type(not1(h2(f)), not)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))) | (~mode(not1(h2(f)), ok)) | (~value(out(n1, not1(h2(f))), n1)) | value(in(n1, not1(h2(f))), n0) | (~type(not1(h2(f)), not)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(281,plain,
% 0.77/0.94 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))) | ((~mode(not1(h2(f)), ok)) | (~value(out(n1, not1(h2(f))), n1)) | value(in(n1, not1(h2(f))), n0) | (~type(not1(h2(f)), not)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(282,plain,
% 0.77/0.94 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n0) | (~type(K, not)))) | (~mode(not1(h2(f)), ok)) | (~value(out(n1, not1(h2(f))), n1)) | value(in(n1, not1(h2(f))), n0) | (~type(not1(h2(f)), not))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.77/0.94 tff(283,plain,
% 0.77/0.94 ((~mode(not1(h2(f)), ok)) | (~value(out(n1, not1(h2(f))), n1)) | value(in(n1, not1(h2(f))), n0) | (~type(not1(h2(f)), not))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[282, 279])).
% 0.77/0.94 tff(284,plain,
% 0.77/0.94 ((~mode(not1(h2(f)), ok)) | (~value(out(n1, not1(h2(f))), n1)) | value(in(n1, not1(h2(f))), n0)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[283, 246])).
% 0.77/0.94 tff(285,plain,
% 0.77/0.94 (~value(out(n1, not1(h2(f))), n1)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[284, 269, 251])).
% 0.77/0.94 tff(286,plain,
% 0.77/0.94 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, not1(h2(f))), n1) | (~value(in(n2, and1(h2(f))), n1)) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, not1(h2(f))), n1) | (~value(in(n2, and1(h2(f))), n1)) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(287,plain,
% 0.77/0.94 ((value(out(n1, not1(h2(f))), n1) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))) | (~value(in(n2, and1(h2(f))), n1))) <=> (value(out(n1, not1(h2(f))), n1) | (~value(in(n2, and1(h2(f))), n1)) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(288,plain,
% 0.77/0.94 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, not1(h2(f))), n1) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))) | (~value(in(n2, and1(h2(f))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, not1(h2(f))), n1) | (~value(in(n2, and1(h2(f))), n1)) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f)))))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[287])).
% 0.77/0.94 tff(289,plain,
% 0.77/0.94 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, not1(h2(f))), n1) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))) | (~value(in(n2, and1(h2(f))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, not1(h2(f))), n1) | (~value(in(n2, and1(h2(f))), n1)) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))))),
% 0.77/0.94 inference(transitivity,[status(thm)],[288, 286])).
% 0.77/0.94 tff(290,plain,
% 0.77/0.94 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, not1(h2(f))), n1) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f))))) | (~value(in(n2, and1(h2(f))), n1)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(291,plain,
% 0.77/0.94 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, not1(h2(f))), n1) | (~value(in(n2, and1(h2(f))), n1)) | (~connection(out(n1, not1(h2(f))), in(n2, and1(h2(f)))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.77/0.94 tff(292,plain,
% 0.77/0.94 ($false),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[291, 64, 285, 231, 220])).
% 0.77/0.94 tff(293,plain,(value(out(n1, and2(h2(f))), n0)), inference(lemma,lemma(discharge,[]))).
% 0.77/0.94 tff(294,plain,
% 0.77/0.94 (^[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)))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(295,plain,
% 0.77/0.94 (![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))))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[294])).
% 0.77/0.94 tff(296,plain,
% 0.77/0.94 (![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))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(297,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')).
% 0.77/0.94 tff(298,plain,
% 0.77/0.94 (![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.77/0.94 tff(299,plain,(
% 0.77/0.94 ![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 0.77/0.94 inference(skolemize,[status(sab)],[298])).
% 0.77/0.94 tff(300,plain,
% 0.77/0.94 (![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[299, 295])).
% 0.77/0.94 tff(301,plain,
% 0.77/0.94 (((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | ((~type(f, fulladder)) | connection(in(n1, f), in(n1, h2(f))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | (~type(f, fulladder)) | connection(in(n1, f), in(n1, h2(f))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(302,plain,
% 0.77/0.94 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | ((~type(f, fulladder)) | connection(in(n1, f), in(n1, h2(f))))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(303,plain,
% 0.77/0.94 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | (~type(f, fulladder)) | connection(in(n1, f), in(n1, h2(f)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.77/0.94 tff(304,plain,
% 0.77/0.94 (connection(in(n1, f), in(n1, h2(f)))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[303, 300, 5])).
% 0.77/0.94 tff(305,plain,
% 0.77/0.94 (value(in(n1, f), n1) <=> value(in(n1, f), n1)),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(306,axiom,(value(in(n1, f), n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','in1_1')).
% 0.77/0.94 tff(307,plain,
% 0.77/0.94 (value(in(n1, f), n1)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.77/0.94 tff(308,plain,
% 0.77/0.94 ((~equal_value(n0, n1)) <=> (~equal_value(n0, n1))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(309,axiom,(~equal_value(n0, n1)), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','equal_value1')).
% 0.77/0.94 tff(310,plain,
% 0.77/0.94 (~equal_value(n0, n1)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.77/0.94 tff(311,plain,
% 0.77/0.94 (^[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))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(312,plain,
% 0.77/0.94 (![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)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[311])).
% 0.77/0.94 tff(313,plain,
% 0.77/0.94 (![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)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(314,plain,
% 0.77/0.94 (^[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)))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(315,plain,
% 0.77/0.94 (![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)))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[314])).
% 0.77/0.94 tff(316,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')).
% 0.77/0.94 tff(317,plain,
% 0.77/0.94 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.77/0.94 tff(318,plain,
% 0.77/0.94 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[317, 313])).
% 0.77/0.94 tff(319,plain,(
% 0.77/0.94 ![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 0.77/0.94 inference(skolemize,[status(sab)],[318])).
% 0.77/0.94 tff(320,plain,
% 0.77/0.94 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[319, 312])).
% 0.77/0.94 tff(321,plain,
% 0.77/0.94 (((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(in(n1, f), n1)) | (~value(in(n1, f), n0)))) <=> ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n0, n1) | (~value(in(n1, f), n1)) | (~value(in(n1, f), n0)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(322,plain,
% 0.77/0.94 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(in(n1, f), n1)) | (~value(in(n1, f), n0)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(323,plain,
% 0.77/0.94 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n0, n1) | (~value(in(n1, f), n1)) | (~value(in(n1, f), n0))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.77/0.94 tff(324,plain,
% 0.77/0.94 (~value(in(n1, f), n0)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[323, 320, 310, 307])).
% 0.77/0.94 tff(325,plain,
% 0.77/0.94 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, f), n0) | (~connection(in(n1, f), in(n1, h2(f)))) | (~value(in(n1, h2(f)), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, f), n0) | (~connection(in(n1, f), in(n1, h2(f)))) | (~value(in(n1, h2(f)), n0)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(326,plain,
% 0.77/0.94 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, f), n0) | (~connection(in(n1, f), in(n1, h2(f)))) | (~value(in(n1, h2(f)), n0)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(327,plain,
% 0.77/0.94 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, f), n0) | (~connection(in(n1, f), in(n1, h2(f)))) | (~value(in(n1, h2(f)), n0))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.77/0.94 tff(328,plain,
% 0.77/0.94 (~value(in(n1, h2(f)), n0)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[327, 64, 324, 304])).
% 0.77/0.94 tff(329,plain,
% 0.77/0.94 (^[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)))))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(330,plain,
% 0.77/0.94 (![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))))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[329])).
% 0.77/0.94 tff(331,plain,
% 0.77/0.94 (![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))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(332,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')).
% 0.77/0.94 tff(333,plain,
% 0.77/0.94 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.77/0.94 tff(334,plain,(
% 0.77/0.94 ![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 0.77/0.94 inference(skolemize,[status(sab)],[333])).
% 0.77/0.94 tff(335,plain,
% 0.77/0.94 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[334, 330])).
% 0.77/0.94 tff(336,plain,
% 0.77/0.94 (((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h2(f), halfadder)) | connection(in(n1, h2(f)), in(n1, and2(h2(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h2(f), halfadder)) | connection(in(n1, h2(f)), in(n1, and2(h2(f)))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(337,plain,
% 0.77/0.94 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h2(f), halfadder)) | connection(in(n1, h2(f)), in(n1, and2(h2(f)))))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(338,plain,
% 0.77/0.94 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h2(f), halfadder)) | connection(in(n1, h2(f)), in(n1, and2(h2(f))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.77/0.94 tff(339,plain,
% 0.77/0.94 (connection(in(n1, h2(f)), in(n1, and2(h2(f))))),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[338, 335, 16])).
% 0.77/0.94 tff(340,plain,
% 0.77/0.94 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h2(f)), n0) | (~value(in(n1, and2(h2(f))), n0)) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h2(f)), n0) | (~value(in(n1, and2(h2(f))), n0)) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f))))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(341,plain,
% 0.77/0.94 ((value(in(n1, h2(f)), n0) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f))))) | (~value(in(n1, and2(h2(f))), n0))) <=> (value(in(n1, h2(f)), n0) | (~value(in(n1, and2(h2(f))), n0)) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f))))))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(342,plain,
% 0.77/0.94 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h2(f)), n0) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f))))) | (~value(in(n1, and2(h2(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h2(f)), n0) | (~value(in(n1, and2(h2(f))), n0)) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f)))))))),
% 0.77/0.94 inference(monotonicity,[status(thm)],[341])).
% 0.77/0.94 tff(343,plain,
% 0.77/0.94 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h2(f)), n0) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f))))) | (~value(in(n1, and2(h2(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h2(f)), n0) | (~value(in(n1, and2(h2(f))), n0)) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f))))))),
% 0.77/0.94 inference(transitivity,[status(thm)],[342, 340])).
% 0.77/0.94 tff(344,plain,
% 0.77/0.94 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h2(f)), n0) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f))))) | (~value(in(n1, and2(h2(f))), n0)))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(345,plain,
% 0.77/0.94 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h2(f)), n0) | (~value(in(n1, and2(h2(f))), n0)) | (~connection(in(n1, h2(f)), in(n1, and2(h2(f)))))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.77/0.94 tff(346,plain,
% 0.77/0.94 (~value(in(n1, and2(h2(f))), n0)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[345, 64, 339, 328])).
% 0.77/0.94 tff(347,plain,
% 0.77/0.94 (^[X: $i] : refl(((~type(X, halfadder)) | type(and2(X), and)) <=> ((~type(X, halfadder)) | type(and2(X), and)))),
% 0.77/0.94 inference(bind,[status(th)],[])).
% 0.77/0.94 tff(348,plain,
% 0.77/0.94 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 0.77/0.94 inference(quant_intro,[status(thm)],[347])).
% 0.77/0.94 tff(349,plain,
% 0.77/0.94 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(350,axiom,(![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_and2')).
% 0.77/0.94 tff(351,plain,
% 0.77/0.94 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.77/0.94 tff(352,plain,(
% 0.77/0.94 ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 0.77/0.94 inference(skolemize,[status(sab)],[351])).
% 0.77/0.94 tff(353,plain,
% 0.77/0.94 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[352, 348])).
% 0.77/0.94 tff(354,plain,
% 0.77/0.94 (((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h2(f), halfadder)) | type(and2(h2(f)), and))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h2(f), halfadder)) | type(and2(h2(f)), and))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(355,plain,
% 0.77/0.94 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h2(f), halfadder)) | type(and2(h2(f)), and))),
% 0.77/0.94 inference(quant_inst,[status(thm)],[])).
% 0.77/0.94 tff(356,plain,
% 0.77/0.94 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h2(f), halfadder)) | type(and2(h2(f)), and)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.77/0.94 tff(357,plain,
% 0.77/0.94 (type(and2(h2(f)), and)),
% 0.77/0.94 inference(unit_resolution,[status(thm)],[356, 353, 16])).
% 0.77/0.94 tff(358,plain,
% 0.77/0.94 ((~mode(and2(h2(f)), abnormal)) <=> (~mode(and2(h2(f)), abnormal))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(359,axiom,(~mode(and2(h2(f)), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_and2')).
% 0.77/0.94 tff(360,plain,
% 0.77/0.94 (~mode(and2(h2(f)), abnormal)),
% 0.77/0.94 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.77/0.94 tff(361,plain,
% 0.77/0.94 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h2(f)), abnormal) | mode(and2(h2(f)), ok) | (~type(and2(h2(f)), and)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h2(f)), abnormal) | mode(and2(h2(f)), ok) | (~type(and2(h2(f)), and)))),
% 0.77/0.94 inference(rewrite,[status(thm)],[])).
% 0.77/0.94 tff(362,plain,
% 0.77/0.94 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h2(f)), abnormal) | mode(and2(h2(f)), ok) | (~type(and2(h2(f)), and)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(363,plain,
% 0.77/0.95 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h2(f)), abnormal) | mode(and2(h2(f)), ok) | (~type(and2(h2(f)), and))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.77/0.95 tff(364,plain,
% 0.77/0.95 (mode(and2(h2(f)), ok)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[363, 135, 360, 357])).
% 0.77/0.95 tff(365,plain,
% 0.77/0.95 (^[K: $i] : refl(((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0))) <=> ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(366,plain,
% 0.77/0.95 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0))) <=> ![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[365])).
% 0.77/0.95 tff(367,plain,
% 0.77/0.95 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0))) <=> ![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(368,plain,
% 0.77/0.95 (^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n0))) <=> ((~mode(K, ok)) | (~type(K, and)) | (~value(out(n1, K), n0)))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) <=> (((~mode(K, ok)) | (~type(K, and)) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)))), rewrite((((~mode(K, ok)) | (~type(K, and)) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) <=> ((~mode(K, ok)) | (~type(K, and)) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) <=> ((~mode(K, ok)) | (~type(K, and)) | value(in(n1, K), n0) | (~value(out(n1, K), n0))))), ((((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) | value(in(n2, K), n0)) <=> (((~mode(K, ok)) | (~type(K, and)) | value(in(n1, K), n0) | (~value(out(n1, K), n0))) | value(in(n2, K), n0)))), rewrite((((~mode(K, ok)) | (~type(K, and)) | value(in(n1, K), n0) | (~value(out(n1, K), n0))) | value(in(n2, K), n0)) <=> ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))), ((((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) | value(in(n2, K), n0)) <=> ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(369,plain,
% 0.77/0.95 (![K: $i] : (((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) | value(in(n2, K), n0)) <=> ![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[368])).
% 0.77/0.95 tff(370,axiom,(![K: $i] : (((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n0))) | value(in(n1, K), n0)) | value(in(n2, K), n0))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','and_0_00')).
% 0.77/0.95 tff(371,plain,
% 0.77/0.95 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.77/0.95 tff(372,plain,
% 0.77/0.95 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[371, 367])).
% 0.77/0.95 tff(373,plain,(
% 0.77/0.95 ![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 0.77/0.95 inference(skolemize,[status(sab)],[372])).
% 0.77/0.95 tff(374,plain,
% 0.77/0.95 (![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[373, 366])).
% 0.77/0.95 tff(375,plain,
% 0.77/0.95 (((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | ((~mode(and2(h2(f)), ok)) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)) | value(in(n2, and2(h2(f))), n0) | (~type(and2(h2(f)), and)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | (~mode(and2(h2(f)), ok)) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)) | value(in(n2, and2(h2(f))), n0) | (~type(and2(h2(f)), and)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(376,plain,
% 0.77/0.95 (((~mode(and2(h2(f)), ok)) | (~type(and2(h2(f)), and)) | value(in(n2, and2(h2(f))), n0) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0))) <=> ((~mode(and2(h2(f)), ok)) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)) | value(in(n2, and2(h2(f))), n0) | (~type(and2(h2(f)), and)))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(377,plain,
% 0.77/0.95 (((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | ((~mode(and2(h2(f)), ok)) | (~type(and2(h2(f)), and)) | value(in(n2, and2(h2(f))), n0) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | ((~mode(and2(h2(f)), ok)) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)) | value(in(n2, and2(h2(f))), n0) | (~type(and2(h2(f)), and))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[376])).
% 0.77/0.95 tff(378,plain,
% 0.77/0.95 (((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | ((~mode(and2(h2(f)), ok)) | (~type(and2(h2(f)), and)) | value(in(n2, and2(h2(f))), n0) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | (~mode(and2(h2(f)), ok)) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)) | value(in(n2, and2(h2(f))), n0) | (~type(and2(h2(f)), and)))),
% 0.77/0.95 inference(transitivity,[status(thm)],[377, 375])).
% 0.77/0.95 tff(379,plain,
% 0.77/0.95 ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | ((~mode(and2(h2(f)), ok)) | (~type(and2(h2(f)), and)) | value(in(n2, and2(h2(f))), n0) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(380,plain,
% 0.77/0.95 ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | (~mode(and2(h2(f)), ok)) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)) | value(in(n2, and2(h2(f))), n0) | (~type(and2(h2(f)), and))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.77/0.95 tff(381,plain,
% 0.77/0.95 ((~mode(and2(h2(f)), ok)) | value(in(n1, and2(h2(f))), n0) | (~value(out(n1, and2(h2(f))), n0)) | value(in(n2, and2(h2(f))), n0)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[380, 374, 357])).
% 0.77/0.95 tff(382,plain,
% 0.77/0.95 ((~value(out(n1, and2(h2(f))), n0)) | value(in(n2, and2(h2(f))), n0)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[381, 364, 346])).
% 0.77/0.95 tff(383,plain,
% 0.77/0.95 (value(in(n2, and2(h2(f))), n0)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[382, 293])).
% 0.77/0.95 tff(384,assumption,(~value(in(n2, h2(f)), n0)), introduced(assumption)).
% 0.77/0.95 tff(385,assumption,(value(in(n2, and2(h2(f))), n0)), introduced(assumption)).
% 0.77/0.95 tff(386,plain,
% 0.77/0.95 (^[X: $i] : refl(((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X)))) <=> ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X)))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(387,plain,
% 0.77/0.95 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[386])).
% 0.77/0.95 tff(388,plain,
% 0.77/0.95 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(389,axiom,(![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_connection_in2_in2and2')).
% 0.77/0.95 tff(390,plain,
% 0.77/0.95 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.77/0.95 tff(391,plain,(
% 0.77/0.95 ![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 0.77/0.95 inference(skolemize,[status(sab)],[390])).
% 0.77/0.95 tff(392,plain,
% 0.77/0.95 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[391, 387])).
% 0.77/0.95 tff(393,plain,
% 0.77/0.95 (((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))) | ((~type(h2(f), halfadder)) | connection(in(n2, h2(f)), in(n2, and2(h2(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))) | (~type(h2(f), halfadder)) | connection(in(n2, h2(f)), in(n2, and2(h2(f)))))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(394,plain,
% 0.77/0.95 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))) | ((~type(h2(f), halfadder)) | connection(in(n2, h2(f)), in(n2, and2(h2(f)))))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(395,plain,
% 0.77/0.95 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))) | (~type(h2(f), halfadder)) | connection(in(n2, h2(f)), in(n2, and2(h2(f))))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.77/0.95 tff(396,plain,
% 0.77/0.95 (connection(in(n2, h2(f)), in(n2, and2(h2(f))))),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[395, 392, 16])).
% 0.77/0.95 tff(397,plain,
% 0.77/0.95 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n2, and2(h2(f))), n0)) | value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, and2(h2(f))), n0)) | value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f))))))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(398,plain,
% 0.77/0.95 ((value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f))))) | (~value(in(n2, and2(h2(f))), n0))) <=> ((~value(in(n2, and2(h2(f))), n0)) | value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f))))))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(399,plain,
% 0.77/0.95 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f))))) | (~value(in(n2, and2(h2(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n2, and2(h2(f))), n0)) | value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f)))))))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[398])).
% 0.77/0.95 tff(400,plain,
% 0.77/0.95 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f))))) | (~value(in(n2, and2(h2(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, and2(h2(f))), n0)) | value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f))))))),
% 0.77/0.95 inference(transitivity,[status(thm)],[399, 397])).
% 0.77/0.95 tff(401,plain,
% 0.77/0.95 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f))))) | (~value(in(n2, and2(h2(f))), n0)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(402,plain,
% 0.77/0.95 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, and2(h2(f))), n0)) | value(in(n2, h2(f)), n0) | (~connection(in(n2, h2(f)), in(n2, and2(h2(f)))))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.77/0.95 tff(403,plain,
% 0.77/0.95 ($false),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[402, 64, 396, 385, 384])).
% 0.77/0.95 tff(404,plain,(value(in(n2, h2(f)), n0) | (~value(in(n2, and2(h2(f))), n0))), inference(lemma,lemma(discharge,[]))).
% 0.77/0.95 tff(405,plain,
% 0.77/0.95 (value(in(n2, h2(f)), n0)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[404, 383])).
% 0.77/0.95 tff(406,plain,
% 0.77/0.95 (^[X: $i] : refl(((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X)))) <=> ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X)))))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(407,plain,
% 0.77/0.95 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[406])).
% 0.77/0.95 tff(408,plain,
% 0.77/0.95 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(409,axiom,(![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_connection_outsh1_in2h2')).
% 0.77/0.95 tff(410,plain,
% 0.77/0.95 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.77/0.95 tff(411,plain,(
% 0.77/0.95 ![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))),
% 0.77/0.95 inference(skolemize,[status(sab)],[410])).
% 0.77/0.95 tff(412,plain,
% 0.77/0.95 (![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[411, 407])).
% 0.77/0.95 tff(413,plain,
% 0.77/0.95 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))) | ((~type(f, fulladder)) | connection(out(s, h1(f)), in(n2, h2(f))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))) | (~type(f, fulladder)) | connection(out(s, h1(f)), in(n2, h2(f))))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(414,plain,
% 0.77/0.95 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))) | ((~type(f, fulladder)) | connection(out(s, h1(f)), in(n2, h2(f))))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(415,plain,
% 0.77/0.95 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(s, h1(X)), in(n2, h2(X))))) | (~type(f, fulladder)) | connection(out(s, h1(f)), in(n2, h2(f)))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.77/0.95 tff(416,plain,
% 0.77/0.95 (connection(out(s, h1(f)), in(n2, h2(f)))),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[415, 412, 5])).
% 0.77/0.95 tff(417,plain,
% 0.77/0.95 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n2, h2(f)), n0)) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | value(out(s, h1(f)), n0))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, h2(f)), n0)) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | value(out(s, h1(f)), n0))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(418,plain,
% 0.77/0.95 ((value(out(s, h1(f)), n0) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | (~value(in(n2, h2(f)), n0))) <=> ((~value(in(n2, h2(f)), n0)) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | value(out(s, h1(f)), n0))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(419,plain,
% 0.77/0.95 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(s, h1(f)), n0) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | (~value(in(n2, h2(f)), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n2, h2(f)), n0)) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | value(out(s, h1(f)), n0)))),
% 0.77/0.95 inference(monotonicity,[status(thm)],[418])).
% 0.77/0.95 tff(420,plain,
% 0.77/0.95 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(s, h1(f)), n0) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | (~value(in(n2, h2(f)), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, h2(f)), n0)) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | value(out(s, h1(f)), n0))),
% 0.77/0.95 inference(transitivity,[status(thm)],[419, 417])).
% 0.77/0.95 tff(421,plain,
% 0.77/0.95 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(s, h1(f)), n0) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | (~value(in(n2, h2(f)), n0)))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(422,plain,
% 0.77/0.95 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, h2(f)), n0)) | (~connection(out(s, h1(f)), in(n2, h2(f)))) | value(out(s, h1(f)), n0)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.77/0.95 tff(423,plain,
% 0.77/0.95 (value(out(s, h1(f)), n0)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[422, 64, 416, 405])).
% 0.77/0.95 tff(424,plain,
% 0.77/0.95 (^[X: $i] : refl(((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ((~type(X, fulladder)) | type(h1(X), halfadder)))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(425,plain,
% 0.77/0.95 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[424])).
% 0.77/0.95 tff(426,plain,
% 0.77/0.95 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(427,axiom,(![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_halfadder1')).
% 0.77/0.95 tff(428,plain,
% 0.77/0.95 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.77/0.95 tff(429,plain,(
% 0.77/0.95 ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 0.77/0.95 inference(skolemize,[status(sab)],[428])).
% 0.77/0.95 tff(430,plain,
% 0.77/0.95 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[429, 425])).
% 0.77/0.95 tff(431,plain,
% 0.77/0.95 (((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | ((~type(f, fulladder)) | type(h1(f), halfadder))) <=> ((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | (~type(f, fulladder)) | type(h1(f), halfadder))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(432,plain,
% 0.77/0.95 ((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | ((~type(f, fulladder)) | type(h1(f), halfadder))),
% 0.77/0.95 inference(quant_inst,[status(thm)],[])).
% 0.77/0.95 tff(433,plain,
% 0.77/0.95 ((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | (~type(f, fulladder)) | type(h1(f), halfadder)),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[432, 431])).
% 0.77/0.95 tff(434,plain,
% 0.77/0.95 (type(h1(f), halfadder)),
% 0.77/0.95 inference(unit_resolution,[status(thm)],[433, 430, 5])).
% 0.77/0.95 tff(435,plain,
% 0.77/0.95 (^[X: $i] : refl(((~type(X, halfadder)) | type(or1(X), or)) <=> ((~type(X, halfadder)) | type(or1(X), or)))),
% 0.77/0.95 inference(bind,[status(th)],[])).
% 0.77/0.95 tff(436,plain,
% 0.77/0.95 (![X: $i] : ((~type(X, halfadder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))),
% 0.77/0.95 inference(quant_intro,[status(thm)],[435])).
% 0.77/0.95 tff(437,plain,
% 0.77/0.95 (![X: $i] : ((~type(X, halfadder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.95 tff(438,axiom,(![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_or1')).
% 0.77/0.95 tff(439,plain,
% 0.77/0.95 (![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.77/0.95 tff(440,plain,(
% 0.77/0.95 ![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))),
% 0.77/0.95 inference(skolemize,[status(sab)],[439])).
% 0.77/0.95 tff(441,plain,
% 0.77/0.95 (![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))),
% 0.77/0.95 inference(modus_ponens,[status(thm)],[440, 436])).
% 0.77/0.95 tff(442,plain,
% 0.77/0.95 (((~![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))) | ((~type(h1(f), halfadder)) | type(or1(h1(f)), or))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))) | (~type(h1(f), halfadder)) | type(or1(h1(f)), or))),
% 0.77/0.95 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(443,plain,
% 0.77/0.96 ((~![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))) | ((~type(h1(f), halfadder)) | type(or1(h1(f)), or))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(444,plain,
% 0.77/0.96 ((~![X: $i] : ((~type(X, halfadder)) | type(or1(X), or))) | (~type(h1(f), halfadder)) | type(or1(h1(f)), or)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[443, 442])).
% 0.77/0.96 tff(445,plain,
% 0.77/0.96 (type(or1(h1(f)), or)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[444, 441, 434])).
% 0.77/0.96 tff(446,plain,
% 0.77/0.96 ((~mode(or1(h1(f)), abnormal)) <=> (~mode(or1(h1(f)), abnormal))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(447,axiom,(~mode(or1(h1(f)), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_or1h1')).
% 0.77/0.96 tff(448,plain,
% 0.77/0.96 (~mode(or1(h1(f)), abnormal)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.77/0.96 tff(449,plain,
% 0.77/0.96 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(or1(h1(f)), abnormal) | mode(or1(h1(f)), ok) | (~type(or1(h1(f)), or)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(or1(h1(f)), abnormal) | mode(or1(h1(f)), ok) | (~type(or1(h1(f)), or)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(450,plain,
% 0.77/0.96 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(or1(h1(f)), abnormal) | mode(or1(h1(f)), ok) | (~type(or1(h1(f)), or)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(451,plain,
% 0.77/0.96 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(or1(h1(f)), abnormal) | mode(or1(h1(f)), ok) | (~type(or1(h1(f)), or))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[450, 449])).
% 0.77/0.96 tff(452,plain,
% 0.77/0.96 (mode(or1(h1(f)), ok)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[451, 135, 448, 445])).
% 0.77/0.96 tff(453,plain,
% 0.77/0.96 (^[X: $i] : refl(((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X)))) <=> ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X)))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(454,plain,
% 0.77/0.96 (![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[453])).
% 0.77/0.96 tff(455,plain,
% 0.77/0.96 (![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(456,axiom,(![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_connection_inc_in2h1')).
% 0.77/0.96 tff(457,plain,
% 0.77/0.96 (![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.77/0.96 tff(458,plain,(
% 0.77/0.96 ![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 0.77/0.96 inference(skolemize,[status(sab)],[457])).
% 0.77/0.96 tff(459,plain,
% 0.77/0.96 (![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[458, 454])).
% 0.77/0.96 tff(460,plain,
% 0.77/0.96 (((~![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))) | ((~type(f, fulladder)) | connection(in(c, f), in(n2, h1(f))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))) | (~type(f, fulladder)) | connection(in(c, f), in(n2, h1(f))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(461,plain,
% 0.77/0.96 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))) | ((~type(f, fulladder)) | connection(in(c, f), in(n2, h1(f))))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(462,plain,
% 0.77/0.96 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))) | (~type(f, fulladder)) | connection(in(c, f), in(n2, h1(f)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[461, 460])).
% 0.77/0.96 tff(463,plain,
% 0.77/0.96 (connection(in(c, f), in(n2, h1(f)))),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[462, 459, 5])).
% 0.77/0.96 tff(464,plain,
% 0.77/0.96 (value(in(c, f), n1) <=> value(in(c, f), n1)),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(465,axiom,(value(in(c, f), n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','inc_1')).
% 0.77/0.96 tff(466,plain,
% 0.77/0.96 (value(in(c, f), n1)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.77/0.96 tff(467,plain,
% 0.77/0.96 (((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(in(c, f), n1)) | (~value(in(c, f), n0)))) <=> ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n0, n1) | (~value(in(c, f), n1)) | (~value(in(c, f), n0)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(468,plain,
% 0.77/0.96 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(in(c, f), n1)) | (~value(in(c, f), n0)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(469,plain,
% 0.77/0.96 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n0, n1) | (~value(in(c, f), n1)) | (~value(in(c, f), n0))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.77/0.96 tff(470,plain,
% 0.77/0.96 (~value(in(c, f), n0)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[469, 320, 310, 466])).
% 0.77/0.96 tff(471,plain,
% 0.77/0.96 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(c, f), n0) | (~connection(in(c, f), in(n2, h1(f)))) | (~value(in(n2, h1(f)), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(c, f), n0) | (~connection(in(c, f), in(n2, h1(f)))) | (~value(in(n2, h1(f)), n0)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(472,plain,
% 0.77/0.96 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(c, f), n0) | (~connection(in(c, f), in(n2, h1(f)))) | (~value(in(n2, h1(f)), n0)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(473,plain,
% 0.77/0.96 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(c, f), n0) | (~connection(in(c, f), in(n2, h1(f)))) | (~value(in(n2, h1(f)), n0))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[472, 471])).
% 0.77/0.96 tff(474,plain,
% 0.77/0.96 (~value(in(n2, h1(f)), n0)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[473, 64, 470, 463])).
% 0.77/0.96 tff(475,plain,
% 0.77/0.96 (^[X: $i] : refl(((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X)))) <=> ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X)))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(476,plain,
% 0.77/0.96 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[475])).
% 0.77/0.96 tff(477,plain,
% 0.77/0.96 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(478,axiom,(![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_connection_in2_in2or1')).
% 0.77/0.96 tff(479,plain,
% 0.77/0.96 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[478, 477])).
% 0.77/0.96 tff(480,plain,(
% 0.77/0.96 ![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))),
% 0.77/0.96 inference(skolemize,[status(sab)],[479])).
% 0.77/0.96 tff(481,plain,
% 0.77/0.96 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[480, 476])).
% 0.77/0.96 tff(482,plain,
% 0.77/0.96 (((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))) | ((~type(h1(f), halfadder)) | connection(in(n2, h1(f)), in(n2, or1(h1(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))) | (~type(h1(f), halfadder)) | connection(in(n2, h1(f)), in(n2, or1(h1(f)))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(483,plain,
% 0.77/0.96 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))) | ((~type(h1(f), halfadder)) | connection(in(n2, h1(f)), in(n2, or1(h1(f)))))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(484,plain,
% 0.77/0.96 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, or1(X))))) | (~type(h1(f), halfadder)) | connection(in(n2, h1(f)), in(n2, or1(h1(f))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[483, 482])).
% 0.77/0.96 tff(485,plain,
% 0.77/0.96 (connection(in(n2, h1(f)), in(n2, or1(h1(f))))),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[484, 481, 434])).
% 0.77/0.96 tff(486,plain,
% 0.77/0.96 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h1(f)), n0) | (~value(in(n2, or1(h1(f))), n0)) | (~connection(in(n2, h1(f)), in(n2, or1(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n2, h1(f)), n0) | (~value(in(n2, or1(h1(f))), n0)) | (~connection(in(n2, h1(f)), in(n2, or1(h1(f))))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(487,plain,
% 0.77/0.96 ((value(in(n2, h1(f)), n0) | (~connection(in(n2, h1(f)), in(n2, or1(h1(f))))) | (~value(in(n2, or1(h1(f))), n0))) <=> (value(in(n2, h1(f)), n0) | (~value(in(n2, or1(h1(f))), n0)) | (~connection(in(n2, h1(f)), in(n2, or1(h1(f))))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(488,plain,
% 0.77/0.96 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h1(f)), n0) | (~connection(in(n2, h1(f)), in(n2, or1(h1(f))))) | (~value(in(n2, or1(h1(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h1(f)), n0) | (~value(in(n2, or1(h1(f))), n0)) | (~connection(in(n2, h1(f)), in(n2, or1(h1(f)))))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[487])).
% 0.77/0.96 tff(489,plain,
% 0.77/0.96 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h1(f)), n0) | (~connection(in(n2, h1(f)), in(n2, or1(h1(f))))) | (~value(in(n2, or1(h1(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n2, h1(f)), n0) | (~value(in(n2, or1(h1(f))), n0)) | (~connection(in(n2, h1(f)), in(n2, or1(h1(f))))))),
% 0.77/0.96 inference(transitivity,[status(thm)],[488, 486])).
% 0.77/0.96 tff(490,plain,
% 0.77/0.96 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, h1(f)), n0) | (~connection(in(n2, h1(f)), in(n2, or1(h1(f))))) | (~value(in(n2, or1(h1(f))), n0)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(491,plain,
% 0.77/0.96 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n2, h1(f)), n0) | (~value(in(n2, or1(h1(f))), n0)) | (~connection(in(n2, h1(f)), in(n2, or1(h1(f)))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.77/0.96 tff(492,plain,
% 0.77/0.96 (~value(in(n2, or1(h1(f))), n0)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[491, 64, 485, 474])).
% 0.77/0.96 tff(493,plain,
% 0.77/0.96 (^[K: $i] : refl(((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or))) <=> ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(494,plain,
% 0.77/0.96 (![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or))) <=> ![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[493])).
% 0.77/0.96 tff(495,plain,
% 0.77/0.96 (![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or))) <=> ![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(496,plain,
% 0.77/0.96 (^[K: $i] : trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n0)) | (~type(K, or)))), (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) | value(in(n2, K), n0)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n0)) | (~type(K, or))) | value(in(n2, K), n0)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n0)) | (~type(K, or))) | value(in(n2, K), n0)) <=> ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))), (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) | value(in(n2, K), n0)) <=> ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(497,plain,
% 0.77/0.96 (![K: $i] : ((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) | value(in(n2, K), n0)) <=> ![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[496])).
% 0.77/0.96 tff(498,axiom,(![K: $i] : ((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n0))) | value(in(n2, K), n0))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','or_0_01')).
% 0.77/0.96 tff(499,plain,
% 0.77/0.96 (![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.77/0.96 tff(500,plain,
% 0.77/0.96 (![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[499, 495])).
% 0.77/0.96 tff(501,plain,(
% 0.77/0.96 ![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 0.77/0.96 inference(skolemize,[status(sab)],[500])).
% 0.77/0.96 tff(502,plain,
% 0.77/0.96 (![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[501, 494])).
% 0.77/0.96 tff(503,plain,
% 0.77/0.96 (((~![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(h1(f)), ok)) | (~value(out(n1, or1(h1(f))), n0)) | value(in(n2, or1(h1(f))), n0) | (~type(or1(h1(f)), or)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | (~mode(or1(h1(f)), ok)) | (~value(out(n1, or1(h1(f))), n0)) | value(in(n2, or1(h1(f))), n0) | (~type(or1(h1(f)), or)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(504,plain,
% 0.77/0.96 (((~mode(or1(h1(f)), ok)) | value(in(n2, or1(h1(f))), n0) | (~value(out(n1, or1(h1(f))), n0)) | (~type(or1(h1(f)), or))) <=> ((~mode(or1(h1(f)), ok)) | (~value(out(n1, or1(h1(f))), n0)) | value(in(n2, or1(h1(f))), n0) | (~type(or1(h1(f)), or)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(505,plain,
% 0.77/0.96 (((~![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(h1(f)), ok)) | value(in(n2, or1(h1(f))), n0) | (~value(out(n1, or1(h1(f))), n0)) | (~type(or1(h1(f)), or)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(h1(f)), ok)) | (~value(out(n1, or1(h1(f))), n0)) | value(in(n2, or1(h1(f))), n0) | (~type(or1(h1(f)), or))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[504])).
% 0.77/0.96 tff(506,plain,
% 0.77/0.96 (((~![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(h1(f)), ok)) | value(in(n2, or1(h1(f))), n0) | (~value(out(n1, or1(h1(f))), n0)) | (~type(or1(h1(f)), or)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | (~mode(or1(h1(f)), ok)) | (~value(out(n1, or1(h1(f))), n0)) | value(in(n2, or1(h1(f))), n0) | (~type(or1(h1(f)), or)))),
% 0.77/0.96 inference(transitivity,[status(thm)],[505, 503])).
% 0.77/0.96 tff(507,plain,
% 0.77/0.96 ((~![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | ((~mode(or1(h1(f)), ok)) | value(in(n2, or1(h1(f))), n0) | (~value(out(n1, or1(h1(f))), n0)) | (~type(or1(h1(f)), or)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(508,plain,
% 0.77/0.96 ((~![K: $i] : ((~mode(K, ok)) | value(in(n2, K), n0) | (~value(out(n1, K), n0)) | (~type(K, or)))) | (~mode(or1(h1(f)), ok)) | (~value(out(n1, or1(h1(f))), n0)) | value(in(n2, or1(h1(f))), n0) | (~type(or1(h1(f)), or))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[507, 506])).
% 0.77/0.96 tff(509,plain,
% 0.77/0.96 ((~mode(or1(h1(f)), ok)) | (~value(out(n1, or1(h1(f))), n0)) | value(in(n2, or1(h1(f))), n0)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[508, 502, 445])).
% 0.77/0.96 tff(510,plain,
% 0.77/0.96 (~value(out(n1, or1(h1(f))), n0)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[509, 492, 452])).
% 0.77/0.96 tff(511,plain,
% 0.77/0.96 (^[X: $i] : refl(((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X)))) <=> ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X)))))),
% 0.77/0.96 inference(bind,[status(th)],[])).
% 0.77/0.96 tff(512,plain,
% 0.77/0.96 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))),
% 0.77/0.96 inference(quant_intro,[status(thm)],[511])).
% 0.77/0.96 tff(513,plain,
% 0.77/0.96 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(514,axiom,(![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_connection_out1or1_in1_and1')).
% 0.77/0.96 tff(515,plain,
% 0.77/0.96 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.77/0.96 tff(516,plain,(
% 0.77/0.96 ![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))),
% 0.77/0.96 inference(skolemize,[status(sab)],[515])).
% 0.77/0.96 tff(517,plain,
% 0.77/0.96 (![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[516, 512])).
% 0.77/0.96 tff(518,plain,
% 0.77/0.96 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))) | ((~type(h1(f), halfadder)) | connection(out(n1, or1(h1(f))), in(n1, and1(h1(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))) | (~type(h1(f), halfadder)) | connection(out(n1, or1(h1(f))), in(n1, and1(h1(f)))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(519,plain,
% 0.77/0.96 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))) | ((~type(h1(f), halfadder)) | connection(out(n1, or1(h1(f))), in(n1, and1(h1(f)))))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(520,plain,
% 0.77/0.96 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, or1(X)), in(n1, and1(X))))) | (~type(h1(f), halfadder)) | connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[519, 518])).
% 0.77/0.96 tff(521,plain,
% 0.77/0.96 (connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[520, 517, 434])).
% 0.77/0.96 tff(522,plain,
% 0.77/0.96 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, or1(h1(f))), n0) | (~value(in(n1, and1(h1(f))), n0)) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, or1(h1(f))), n0) | (~value(in(n1, and1(h1(f))), n0)) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(523,plain,
% 0.77/0.96 ((value(out(n1, or1(h1(f))), n0) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))) | (~value(in(n1, and1(h1(f))), n0))) <=> (value(out(n1, or1(h1(f))), n0) | (~value(in(n1, and1(h1(f))), n0)) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(524,plain,
% 0.77/0.96 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, or1(h1(f))), n0) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))) | (~value(in(n1, and1(h1(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, or1(h1(f))), n0) | (~value(in(n1, and1(h1(f))), n0)) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f)))))))),
% 0.77/0.96 inference(monotonicity,[status(thm)],[523])).
% 0.77/0.96 tff(525,plain,
% 0.77/0.96 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, or1(h1(f))), n0) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))) | (~value(in(n1, and1(h1(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, or1(h1(f))), n0) | (~value(in(n1, and1(h1(f))), n0)) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))))),
% 0.77/0.96 inference(transitivity,[status(thm)],[524, 522])).
% 0.77/0.96 tff(526,plain,
% 0.77/0.96 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, or1(h1(f))), n0) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f))))) | (~value(in(n1, and1(h1(f))), n0)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(527,plain,
% 0.77/0.96 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, or1(h1(f))), n0) | (~value(in(n1, and1(h1(f))), n0)) | (~connection(out(n1, or1(h1(f))), in(n1, and1(h1(f)))))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[526, 525])).
% 0.77/0.96 tff(528,plain,
% 0.77/0.96 (~value(in(n1, and1(h1(f))), n0)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[527, 64, 521, 510])).
% 0.77/0.96 tff(529,plain,
% 0.77/0.96 (((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | ((~type(h1(f), halfadder)) | type(and1(h1(f)), and))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | (~type(h1(f), halfadder)) | type(and1(h1(f)), and))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(530,plain,
% 0.77/0.96 ((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | ((~type(h1(f), halfadder)) | type(and1(h1(f)), and))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(531,plain,
% 0.77/0.96 ((~![X: $i] : ((~type(X, halfadder)) | type(and1(X), and))) | (~type(h1(f), halfadder)) | type(and1(h1(f)), and)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[530, 529])).
% 0.77/0.96 tff(532,plain,
% 0.77/0.96 (type(and1(h1(f)), and)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[531, 151, 434])).
% 0.77/0.96 tff(533,plain,
% 0.77/0.96 ((~mode(and1(h1(f)), abnormal)) <=> (~mode(and1(h1(f)), abnormal))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(534,axiom,(~mode(and1(h1(f)), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_and1h1')).
% 0.77/0.96 tff(535,plain,
% 0.77/0.96 (~mode(and1(h1(f)), abnormal)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[534, 533])).
% 0.77/0.96 tff(536,plain,
% 0.77/0.96 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and1(h1(f)), abnormal) | mode(and1(h1(f)), ok) | (~type(and1(h1(f)), and)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and1(h1(f)), abnormal) | mode(and1(h1(f)), ok) | (~type(and1(h1(f)), and)))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(537,plain,
% 0.77/0.96 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and1(h1(f)), abnormal) | mode(and1(h1(f)), ok) | (~type(and1(h1(f)), and)))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(538,plain,
% 0.77/0.96 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and1(h1(f)), abnormal) | mode(and1(h1(f)), ok) | (~type(and1(h1(f)), and))),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.77/0.96 tff(539,plain,
% 0.77/0.96 (mode(and1(h1(f)), ok)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[538, 135, 535, 532])).
% 0.77/0.96 tff(540,plain,
% 0.77/0.96 (((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | ((~type(h1(f), halfadder)) | type(not1(h1(f)), not))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | (~type(h1(f), halfadder)) | type(not1(h1(f)), not))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(541,plain,
% 0.77/0.96 ((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | ((~type(h1(f), halfadder)) | type(not1(h1(f)), not))),
% 0.77/0.96 inference(quant_inst,[status(thm)],[])).
% 0.77/0.96 tff(542,plain,
% 0.77/0.96 ((~![X: $i] : ((~type(X, halfadder)) | type(not1(X), not))) | (~type(h1(f), halfadder)) | type(not1(h1(f)), not)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[541, 540])).
% 0.77/0.96 tff(543,plain,
% 0.77/0.96 (type(not1(h1(f)), not)),
% 0.77/0.96 inference(unit_resolution,[status(thm)],[542, 242, 434])).
% 0.77/0.96 tff(544,plain,
% 0.77/0.96 ((~mode(not1(h1(f)), abnormal)) <=> (~mode(not1(h1(f)), abnormal))),
% 0.77/0.96 inference(rewrite,[status(thm)],[])).
% 0.77/0.96 tff(545,axiom,(~mode(not1(h1(f)), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_not1h1')).
% 0.77/0.96 tff(546,plain,
% 0.77/0.96 (~mode(not1(h1(f)), abnormal)),
% 0.77/0.96 inference(modus_ponens,[status(thm)],[545, 544])).
% 0.77/0.96 tff(547,plain,
% 0.77/0.96 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(not1(h1(f)), abnormal) | mode(not1(h1(f)), ok) | (~type(not1(h1(f)), not)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(not1(h1(f)), abnormal) | mode(not1(h1(f)), ok) | (~type(not1(h1(f)), not)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(548,plain,
% 0.77/0.97 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(not1(h1(f)), abnormal) | mode(not1(h1(f)), ok) | (~type(not1(h1(f)), not)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(549,plain,
% 0.77/0.97 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(not1(h1(f)), abnormal) | mode(not1(h1(f)), ok) | (~type(not1(h1(f)), not))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[548, 547])).
% 0.77/0.97 tff(550,plain,
% 0.77/0.97 (mode(not1(h1(f)), ok)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[549, 135, 546, 543])).
% 0.77/0.97 tff(551,plain,
% 0.77/0.97 (((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h1(f), halfadder)) | type(and2(h1(f)), and))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h1(f), halfadder)) | type(and2(h1(f)), and))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(552,plain,
% 0.77/0.97 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h1(f), halfadder)) | type(and2(h1(f)), and))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(553,plain,
% 0.77/0.97 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h1(f), halfadder)) | type(and2(h1(f)), and)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[552, 551])).
% 0.77/0.97 tff(554,plain,
% 0.77/0.97 (type(and2(h1(f)), and)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[553, 353, 434])).
% 0.77/0.97 tff(555,plain,
% 0.77/0.97 ((~mode(and2(h1(f)), abnormal)) <=> (~mode(and2(h1(f)), abnormal))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(556,axiom,(~mode(and2(h1(f)), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_and2h1')).
% 0.77/0.97 tff(557,plain,
% 0.77/0.97 (~mode(and2(h1(f)), abnormal)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.77/0.97 tff(558,plain,
% 0.77/0.97 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h1(f)), abnormal) | mode(and2(h1(f)), ok) | (~type(and2(h1(f)), and)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h1(f)), abnormal) | mode(and2(h1(f)), ok) | (~type(and2(h1(f)), and)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(559,plain,
% 0.77/0.97 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h1(f)), abnormal) | mode(and2(h1(f)), ok) | (~type(and2(h1(f)), and)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(560,plain,
% 0.77/0.97 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h1(f)), abnormal) | mode(and2(h1(f)), ok) | (~type(and2(h1(f)), and))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[559, 558])).
% 0.77/0.97 tff(561,plain,
% 0.77/0.97 (mode(and2(h1(f)), ok)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[560, 135, 557, 554])).
% 0.77/0.97 tff(562,plain,
% 0.77/0.97 (^[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)))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(563,plain,
% 0.77/0.97 (![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))))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[562])).
% 0.77/0.97 tff(564,plain,
% 0.77/0.97 (![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))))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(565,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')).
% 0.77/0.97 tff(566,plain,
% 0.77/0.97 (![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.77/0.97 tff(567,plain,(
% 0.77/0.97 ![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 0.77/0.97 inference(skolemize,[status(sab)],[566])).
% 0.77/0.97 tff(568,plain,
% 0.77/0.97 (![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[567, 563])).
% 0.77/0.97 tff(569,plain,
% 0.77/0.97 (((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | ((~type(f, fulladder)) | connection(in(n2, f), in(n1, h1(f))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | (~type(f, fulladder)) | connection(in(n2, f), in(n1, h1(f))))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(570,plain,
% 0.77/0.97 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | ((~type(f, fulladder)) | connection(in(n2, f), in(n1, h1(f))))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(571,plain,
% 0.77/0.97 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | (~type(f, fulladder)) | connection(in(n2, f), in(n1, h1(f)))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[570, 569])).
% 0.77/0.97 tff(572,plain,
% 0.77/0.97 (connection(in(n2, f), in(n1, h1(f)))),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[571, 568, 5])).
% 0.77/0.97 tff(573,plain,
% 0.77/0.97 (value(in(n2, f), n0) <=> value(in(n2, f), n0)),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(574,axiom,(value(in(n2, f), n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','in2_0')).
% 0.77/0.97 tff(575,plain,
% 0.77/0.97 (value(in(n2, f), n0)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[574, 573])).
% 0.77/0.97 tff(576,plain,
% 0.77/0.97 ((~equal_value(n1, n0)) <=> (~equal_value(n1, n0))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(577,axiom,(~equal_value(n1, n0)), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','equal_value2')).
% 0.77/0.97 tff(578,plain,
% 0.77/0.97 (~equal_value(n1, n0)),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[577, 576])).
% 0.77/0.97 tff(579,plain,
% 0.77/0.97 (((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n1, n0) | (~value(in(n2, f), n0)) | (~value(in(n2, f), n1)))) <=> ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n1, n0) | (~value(in(n2, f), n0)) | (~value(in(n2, f), n1)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(580,plain,
% 0.77/0.97 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n1, n0) | (~value(in(n2, f), n0)) | (~value(in(n2, f), n1)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(581,plain,
% 0.77/0.97 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n1, n0) | (~value(in(n2, f), n0)) | (~value(in(n2, f), n1))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[580, 579])).
% 0.77/0.97 tff(582,plain,
% 0.77/0.97 (~value(in(n2, f), n1)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[581, 320, 578, 575])).
% 0.77/0.97 tff(583,plain,
% 0.77/0.97 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, f), n1) | (~connection(in(n2, f), in(n1, h1(f)))) | (~value(in(n1, h1(f)), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n2, f), n1) | (~connection(in(n2, f), in(n1, h1(f)))) | (~value(in(n1, h1(f)), n1)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(584,plain,
% 0.77/0.97 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, f), n1) | (~connection(in(n2, f), in(n1, h1(f)))) | (~value(in(n1, h1(f)), n1)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(585,plain,
% 0.77/0.97 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n2, f), n1) | (~connection(in(n2, f), in(n1, h1(f)))) | (~value(in(n1, h1(f)), n1))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[584, 583])).
% 0.77/0.97 tff(586,plain,
% 0.77/0.97 (~value(in(n1, h1(f)), n1)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[585, 64, 582, 572])).
% 0.77/0.97 tff(587,plain,
% 0.77/0.97 (((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h1(f), halfadder)) | connection(in(n1, h1(f)), in(n1, and2(h1(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h1(f), halfadder)) | connection(in(n1, h1(f)), in(n1, and2(h1(f)))))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(588,plain,
% 0.77/0.97 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h1(f), halfadder)) | connection(in(n1, h1(f)), in(n1, and2(h1(f)))))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(589,plain,
% 0.77/0.97 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h1(f), halfadder)) | connection(in(n1, h1(f)), in(n1, and2(h1(f))))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[588, 587])).
% 0.77/0.97 tff(590,plain,
% 0.77/0.97 (connection(in(n1, h1(f)), in(n1, and2(h1(f))))),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[589, 335, 434])).
% 0.77/0.97 tff(591,plain,
% 0.77/0.97 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h1(f)), n1) | (~value(in(n1, and2(h1(f))), n1)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h1(f)), n1) | (~value(in(n1, and2(h1(f))), n1)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(592,plain,
% 0.77/0.97 ((value(in(n1, h1(f)), n1) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))) | (~value(in(n1, and2(h1(f))), n1))) <=> (value(in(n1, h1(f)), n1) | (~value(in(n1, and2(h1(f))), n1)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(593,plain,
% 0.77/0.97 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h1(f)), n1) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))) | (~value(in(n1, and2(h1(f))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h1(f)), n1) | (~value(in(n1, and2(h1(f))), n1)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f)))))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[592])).
% 0.77/0.97 tff(594,plain,
% 0.77/0.97 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h1(f)), n1) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))) | (~value(in(n1, and2(h1(f))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h1(f)), n1) | (~value(in(n1, and2(h1(f))), n1)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))))),
% 0.77/0.97 inference(transitivity,[status(thm)],[593, 591])).
% 0.77/0.97 tff(595,plain,
% 0.77/0.97 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h1(f)), n1) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f))))) | (~value(in(n1, and2(h1(f))), n1)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(596,plain,
% 0.77/0.97 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h1(f)), n1) | (~value(in(n1, and2(h1(f))), n1)) | (~connection(in(n1, h1(f)), in(n1, and2(h1(f)))))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[595, 594])).
% 0.77/0.97 tff(597,plain,
% 0.77/0.97 (~value(in(n1, and2(h1(f))), n1)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[596, 64, 590, 586])).
% 0.77/0.97 tff(598,plain,
% 0.77/0.97 (^[K: $i] : refl(((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1)))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(599,plain,
% 0.77/0.97 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[598])).
% 0.77/0.97 tff(600,plain,
% 0.77/0.97 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(601,plain,
% 0.77/0.97 (^[K: $i] : trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and))) | value(in(n1, K), n1)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and))) | value(in(n1, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(602,plain,
% 0.77/0.97 (![K: $i] : ((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[601])).
% 0.77/0.97 tff(603,axiom,(![K: $i] : ((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','and_1_1x')).
% 0.77/0.97 tff(604,plain,
% 0.77/0.97 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[603, 602])).
% 0.77/0.97 tff(605,plain,
% 0.77/0.97 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[604, 600])).
% 0.77/0.97 tff(606,plain,(
% 0.77/0.97 ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 0.77/0.97 inference(skolemize,[status(sab)],[605])).
% 0.77/0.97 tff(607,plain,
% 0.77/0.97 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[606, 599])).
% 0.77/0.97 tff(608,plain,
% 0.77/0.97 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and2(h1(f)), ok)) | (~value(out(n1, and2(h1(f))), n1)) | value(in(n1, and2(h1(f))), n1) | (~type(and2(h1(f)), and)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | (~mode(and2(h1(f)), ok)) | (~value(out(n1, and2(h1(f))), n1)) | value(in(n1, and2(h1(f))), n1) | (~type(and2(h1(f)), and)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(609,plain,
% 0.77/0.97 (((~mode(and2(h1(f)), ok)) | (~value(out(n1, and2(h1(f))), n1)) | (~type(and2(h1(f)), and)) | value(in(n1, and2(h1(f))), n1)) <=> ((~mode(and2(h1(f)), ok)) | (~value(out(n1, and2(h1(f))), n1)) | value(in(n1, and2(h1(f))), n1) | (~type(and2(h1(f)), and)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(610,plain,
% 0.77/0.97 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and2(h1(f)), ok)) | (~value(out(n1, and2(h1(f))), n1)) | (~type(and2(h1(f)), and)) | value(in(n1, and2(h1(f))), n1))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and2(h1(f)), ok)) | (~value(out(n1, and2(h1(f))), n1)) | value(in(n1, and2(h1(f))), n1) | (~type(and2(h1(f)), and))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[609])).
% 0.77/0.97 tff(611,plain,
% 0.77/0.97 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and2(h1(f)), ok)) | (~value(out(n1, and2(h1(f))), n1)) | (~type(and2(h1(f)), and)) | value(in(n1, and2(h1(f))), n1))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | (~mode(and2(h1(f)), ok)) | (~value(out(n1, and2(h1(f))), n1)) | value(in(n1, and2(h1(f))), n1) | (~type(and2(h1(f)), and)))),
% 0.77/0.97 inference(transitivity,[status(thm)],[610, 608])).
% 0.77/0.97 tff(612,plain,
% 0.77/0.97 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and2(h1(f)), ok)) | (~value(out(n1, and2(h1(f))), n1)) | (~type(and2(h1(f)), and)) | value(in(n1, and2(h1(f))), n1))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(613,plain,
% 0.77/0.97 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | (~mode(and2(h1(f)), ok)) | (~value(out(n1, and2(h1(f))), n1)) | value(in(n1, and2(h1(f))), n1) | (~type(and2(h1(f)), and))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[612, 611])).
% 0.77/0.97 tff(614,plain,
% 0.77/0.97 ((~mode(and2(h1(f)), ok)) | (~value(out(n1, and2(h1(f))), n1)) | value(in(n1, and2(h1(f))), n1)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[613, 607, 554])).
% 0.77/0.97 tff(615,plain,
% 0.77/0.97 (~value(out(n1, and2(h1(f))), n1)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[614, 597, 561])).
% 0.77/0.97 tff(616,plain,
% 0.77/0.97 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))) | ((~type(h1(f), halfadder)) | connection(out(n1, and2(h1(f))), in(n1, not1(h1(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))) | (~type(h1(f), halfadder)) | connection(out(n1, and2(h1(f))), in(n1, not1(h1(f)))))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(617,plain,
% 0.77/0.97 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))) | ((~type(h1(f), halfadder)) | connection(out(n1, and2(h1(f))), in(n1, not1(h1(f)))))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(618,plain,
% 0.77/0.97 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, and2(X)), in(n1, not1(X))))) | (~type(h1(f), halfadder)) | connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[617, 616])).
% 0.77/0.97 tff(619,plain,
% 0.77/0.97 (connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[618, 258, 434])).
% 0.77/0.97 tff(620,plain,
% 0.77/0.97 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n1, not1(h1(f))), n1)) | value(out(n1, and2(h1(f))), n1) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, not1(h1(f))), n1)) | value(out(n1, and2(h1(f))), n1) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(621,plain,
% 0.77/0.97 ((value(out(n1, and2(h1(f))), n1) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))) | (~value(in(n1, not1(h1(f))), n1))) <=> ((~value(in(n1, not1(h1(f))), n1)) | value(out(n1, and2(h1(f))), n1) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(622,plain,
% 0.77/0.97 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, and2(h1(f))), n1) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))) | (~value(in(n1, not1(h1(f))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n1, not1(h1(f))), n1)) | value(out(n1, and2(h1(f))), n1) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f)))))))),
% 0.77/0.97 inference(monotonicity,[status(thm)],[621])).
% 0.77/0.97 tff(623,plain,
% 0.77/0.97 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, and2(h1(f))), n1) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))) | (~value(in(n1, not1(h1(f))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, not1(h1(f))), n1)) | value(out(n1, and2(h1(f))), n1) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))))),
% 0.77/0.97 inference(transitivity,[status(thm)],[622, 620])).
% 0.77/0.97 tff(624,plain,
% 0.77/0.97 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, and2(h1(f))), n1) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f))))) | (~value(in(n1, not1(h1(f))), n1)))),
% 0.77/0.97 inference(quant_inst,[status(thm)],[])).
% 0.77/0.97 tff(625,plain,
% 0.77/0.97 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, not1(h1(f))), n1)) | value(out(n1, and2(h1(f))), n1) | (~connection(out(n1, and2(h1(f))), in(n1, not1(h1(f)))))),
% 0.77/0.97 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.77/0.97 tff(626,plain,
% 0.77/0.97 (~value(in(n1, not1(h1(f))), n1)),
% 0.77/0.97 inference(unit_resolution,[status(thm)],[625, 64, 619, 615])).
% 0.77/0.97 tff(627,plain,
% 0.77/0.97 (^[K: $i] : refl(((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not))) <=> ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(628,plain,
% 0.77/0.97 (![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not))) <=> ![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not)))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[627])).
% 0.77/0.97 tff(629,plain,
% 0.77/0.97 (![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not))) <=> ![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not)))),
% 0.77/0.97 inference(rewrite,[status(thm)],[])).
% 0.77/0.97 tff(630,plain,
% 0.77/0.97 (^[K: $i] : trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, not))) | (~value(out(n1, K), n0))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n0)) | (~type(K, not)))), (((((~mode(K, ok)) | (~type(K, not))) | (~value(out(n1, K), n0))) | value(in(n1, K), n1)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n0)) | (~type(K, not))) | value(in(n1, K), n1)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n0)) | (~type(K, not))) | value(in(n1, K), n1)) <=> ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not)))), (((((~mode(K, ok)) | (~type(K, not))) | (~value(out(n1, K), n0))) | value(in(n1, K), n1)) <=> ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not)))))),
% 0.77/0.97 inference(bind,[status(th)],[])).
% 0.77/0.97 tff(631,plain,
% 0.77/0.97 (![K: $i] : ((((~mode(K, ok)) | (~type(K, not))) | (~value(out(n1, K), n0))) | value(in(n1, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not)))),
% 0.77/0.97 inference(quant_intro,[status(thm)],[630])).
% 0.77/0.97 tff(632,axiom,(![K: $i] : ((((~mode(K, ok)) | (~type(K, not))) | (~value(out(n1, K), n0))) | value(in(n1, K), n1))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','not_0_1_bw')).
% 0.77/0.97 tff(633,plain,
% 0.77/0.97 (![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not)))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[632, 631])).
% 0.77/0.98 tff(634,plain,
% 0.77/0.98 (![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not)))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[633, 629])).
% 0.77/0.98 tff(635,plain,(
% 0.77/0.98 ![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not)))),
% 0.77/0.98 inference(skolemize,[status(sab)],[634])).
% 0.77/0.98 tff(636,plain,
% 0.77/0.98 (![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not)))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[635, 628])).
% 0.77/0.98 tff(637,plain,
% 0.77/0.98 (((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not)))) | ((~mode(not1(h1(f)), ok)) | (~type(not1(h1(f)), not)) | value(in(n1, not1(h1(f))), n1) | (~value(out(n1, not1(h1(f))), n0)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not)))) | (~mode(not1(h1(f)), ok)) | (~type(not1(h1(f)), not)) | value(in(n1, not1(h1(f))), n1) | (~value(out(n1, not1(h1(f))), n0)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(638,plain,
% 0.77/0.98 (((~mode(not1(h1(f)), ok)) | value(in(n1, not1(h1(f))), n1) | (~value(out(n1, not1(h1(f))), n0)) | (~type(not1(h1(f)), not))) <=> ((~mode(not1(h1(f)), ok)) | (~type(not1(h1(f)), not)) | value(in(n1, not1(h1(f))), n1) | (~value(out(n1, not1(h1(f))), n0)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(639,plain,
% 0.77/0.98 (((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not)))) | ((~mode(not1(h1(f)), ok)) | value(in(n1, not1(h1(f))), n1) | (~value(out(n1, not1(h1(f))), n0)) | (~type(not1(h1(f)), not)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not)))) | ((~mode(not1(h1(f)), ok)) | (~type(not1(h1(f)), not)) | value(in(n1, not1(h1(f))), n1) | (~value(out(n1, not1(h1(f))), n0))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[638])).
% 0.77/0.98 tff(640,plain,
% 0.77/0.98 (((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not)))) | ((~mode(not1(h1(f)), ok)) | value(in(n1, not1(h1(f))), n1) | (~value(out(n1, not1(h1(f))), n0)) | (~type(not1(h1(f)), not)))) <=> ((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not)))) | (~mode(not1(h1(f)), ok)) | (~type(not1(h1(f)), not)) | value(in(n1, not1(h1(f))), n1) | (~value(out(n1, not1(h1(f))), n0)))),
% 0.77/0.98 inference(transitivity,[status(thm)],[639, 637])).
% 0.77/0.98 tff(641,plain,
% 0.77/0.98 ((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not)))) | ((~mode(not1(h1(f)), ok)) | value(in(n1, not1(h1(f))), n1) | (~value(out(n1, not1(h1(f))), n0)) | (~type(not1(h1(f)), not)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(642,plain,
% 0.77/0.98 ((~![K: $i] : ((~mode(K, ok)) | value(in(n1, K), n1) | (~value(out(n1, K), n0)) | (~type(K, not)))) | (~mode(not1(h1(f)), ok)) | (~type(not1(h1(f)), not)) | value(in(n1, not1(h1(f))), n1) | (~value(out(n1, not1(h1(f))), n0))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[641, 640])).
% 0.77/0.98 tff(643,plain,
% 0.77/0.98 ((~mode(not1(h1(f)), ok)) | value(in(n1, not1(h1(f))), n1) | (~value(out(n1, not1(h1(f))), n0))),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[642, 636, 543])).
% 0.77/0.98 tff(644,plain,
% 0.77/0.98 (~value(out(n1, not1(h1(f))), n0)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[643, 626, 550])).
% 0.77/0.98 tff(645,plain,
% 0.77/0.98 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))) | ((~type(h1(f), halfadder)) | connection(out(n1, not1(h1(f))), in(n2, and1(h1(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))) | (~type(h1(f), halfadder)) | connection(out(n1, not1(h1(f))), in(n2, and1(h1(f)))))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(646,plain,
% 0.77/0.98 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))) | ((~type(h1(f), halfadder)) | connection(out(n1, not1(h1(f))), in(n2, and1(h1(f)))))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(647,plain,
% 0.77/0.98 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(n1, not1(X)), in(n2, and1(X))))) | (~type(h1(f), halfadder)) | connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[646, 645])).
% 0.77/0.98 tff(648,plain,
% 0.77/0.98 (connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[647, 227, 434])).
% 0.77/0.98 tff(649,plain,
% 0.77/0.98 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, not1(h1(f))), n0) | (~value(in(n2, and1(h1(f))), n0)) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, not1(h1(f))), n0) | (~value(in(n2, and1(h1(f))), n0)) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(650,plain,
% 0.77/0.98 ((value(out(n1, not1(h1(f))), n0) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))) | (~value(in(n2, and1(h1(f))), n0))) <=> (value(out(n1, not1(h1(f))), n0) | (~value(in(n2, and1(h1(f))), n0)) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(651,plain,
% 0.77/0.98 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, not1(h1(f))), n0) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))) | (~value(in(n2, and1(h1(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, not1(h1(f))), n0) | (~value(in(n2, and1(h1(f))), n0)) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f)))))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[650])).
% 0.77/0.98 tff(652,plain,
% 0.77/0.98 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, not1(h1(f))), n0) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))) | (~value(in(n2, and1(h1(f))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, not1(h1(f))), n0) | (~value(in(n2, and1(h1(f))), n0)) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))))),
% 0.77/0.98 inference(transitivity,[status(thm)],[651, 649])).
% 0.77/0.98 tff(653,plain,
% 0.77/0.98 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(n1, not1(h1(f))), n0) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f))))) | (~value(in(n2, and1(h1(f))), n0)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(654,plain,
% 0.77/0.98 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(out(n1, not1(h1(f))), n0) | (~value(in(n2, and1(h1(f))), n0)) | (~connection(out(n1, not1(h1(f))), in(n2, and1(h1(f)))))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[653, 652])).
% 0.77/0.98 tff(655,plain,
% 0.77/0.98 (~value(in(n2, and1(h1(f))), n0)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[654, 64, 648, 644])).
% 0.77/0.98 tff(656,plain,
% 0.77/0.98 (((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | ((~mode(and1(h1(f)), ok)) | value(in(n1, and1(h1(f))), n0) | (~value(out(n1, and1(h1(f))), n0)) | value(in(n2, and1(h1(f))), n0) | (~type(and1(h1(f)), and)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | (~mode(and1(h1(f)), ok)) | value(in(n1, and1(h1(f))), n0) | (~value(out(n1, and1(h1(f))), n0)) | value(in(n2, and1(h1(f))), n0) | (~type(and1(h1(f)), and)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(657,plain,
% 0.77/0.98 (((~mode(and1(h1(f)), ok)) | (~type(and1(h1(f)), and)) | value(in(n2, and1(h1(f))), n0) | value(in(n1, and1(h1(f))), n0) | (~value(out(n1, and1(h1(f))), n0))) <=> ((~mode(and1(h1(f)), ok)) | value(in(n1, and1(h1(f))), n0) | (~value(out(n1, and1(h1(f))), n0)) | value(in(n2, and1(h1(f))), n0) | (~type(and1(h1(f)), and)))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(658,plain,
% 0.77/0.98 (((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | ((~mode(and1(h1(f)), ok)) | (~type(and1(h1(f)), and)) | value(in(n2, and1(h1(f))), n0) | value(in(n1, and1(h1(f))), n0) | (~value(out(n1, and1(h1(f))), n0)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | ((~mode(and1(h1(f)), ok)) | value(in(n1, and1(h1(f))), n0) | (~value(out(n1, and1(h1(f))), n0)) | value(in(n2, and1(h1(f))), n0) | (~type(and1(h1(f)), and))))),
% 0.77/0.98 inference(monotonicity,[status(thm)],[657])).
% 0.77/0.98 tff(659,plain,
% 0.77/0.98 (((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | ((~mode(and1(h1(f)), ok)) | (~type(and1(h1(f)), and)) | value(in(n2, and1(h1(f))), n0) | value(in(n1, and1(h1(f))), n0) | (~value(out(n1, and1(h1(f))), n0)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | (~mode(and1(h1(f)), ok)) | value(in(n1, and1(h1(f))), n0) | (~value(out(n1, and1(h1(f))), n0)) | value(in(n2, and1(h1(f))), n0) | (~type(and1(h1(f)), and)))),
% 0.77/0.98 inference(transitivity,[status(thm)],[658, 656])).
% 0.77/0.98 tff(660,plain,
% 0.77/0.98 ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | ((~mode(and1(h1(f)), ok)) | (~type(and1(h1(f)), and)) | value(in(n2, and1(h1(f))), n0) | value(in(n1, and1(h1(f))), n0) | (~value(out(n1, and1(h1(f))), n0)))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(661,plain,
% 0.77/0.98 ((~![K: $i] : ((~mode(K, ok)) | (~type(K, and)) | value(in(n2, K), n0) | value(in(n1, K), n0) | (~value(out(n1, K), n0)))) | (~mode(and1(h1(f)), ok)) | value(in(n1, and1(h1(f))), n0) | (~value(out(n1, and1(h1(f))), n0)) | value(in(n2, and1(h1(f))), n0) | (~type(and1(h1(f)), and))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[660, 659])).
% 0.77/0.98 tff(662,plain,
% 0.77/0.98 ((~mode(and1(h1(f)), ok)) | value(in(n1, and1(h1(f))), n0) | (~value(out(n1, and1(h1(f))), n0)) | value(in(n2, and1(h1(f))), n0)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[661, 374, 532])).
% 0.77/0.98 tff(663,plain,
% 0.77/0.98 (~value(out(n1, and1(h1(f))), n0)),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[662, 655, 539, 528])).
% 0.77/0.98 tff(664,plain,
% 0.77/0.98 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))) | ((~type(h1(f), halfadder)) | connection(out(s, h1(f)), out(n1, and1(h1(f)))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))) | (~type(h1(f), halfadder)) | connection(out(s, h1(f)), out(n1, and1(h1(f)))))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(665,plain,
% 0.77/0.98 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))) | ((~type(h1(f), halfadder)) | connection(out(s, h1(f)), out(n1, and1(h1(f)))))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(666,plain,
% 0.77/0.98 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(s, X), out(n1, and1(X))))) | (~type(h1(f), halfadder)) | connection(out(s, h1(f)), out(n1, and1(h1(f))))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[665, 664])).
% 0.77/0.98 tff(667,plain,
% 0.77/0.98 (connection(out(s, h1(f)), out(n1, and1(h1(f))))),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[666, 189, 434])).
% 0.77/0.98 tff(668,plain,
% 0.77/0.98 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and1(h1(f))), n0) | (~value(out(s, h1(f)), n0)) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, and1(h1(f))), n0) | (~value(out(s, h1(f)), n0)) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))))),
% 0.77/0.98 inference(rewrite,[status(thm)],[])).
% 0.77/0.98 tff(669,plain,
% 0.77/0.98 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and1(h1(f))), n0) | (~value(out(s, h1(f)), n0)) | (~connection(out(s, h1(f)), out(n1, and1(h1(f))))))),
% 0.77/0.98 inference(quant_inst,[status(thm)],[])).
% 0.77/0.98 tff(670,plain,
% 0.77/0.98 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, and1(h1(f))), n0) | (~value(out(s, h1(f)), n0)) | (~connection(out(s, h1(f)), out(n1, and1(h1(f)))))),
% 0.77/0.98 inference(modus_ponens,[status(thm)],[669, 668])).
% 0.77/0.98 tff(671,plain,
% 0.77/0.98 ($false),
% 0.77/0.98 inference(unit_resolution,[status(thm)],[670, 37, 667, 663, 423])).
% 0.77/0.98 % SZS output end Proof
% 0.77/0.98 % E exiting
%------------------------------------------------------------------------------