%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV008-1.001 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:08:53 AM UTC 2025
% Result : Unsatisfiable 0.64s 0.84s
% Output : Proof 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : HWV008-1.001 : TPTP v9.0.0. Released v2.1.0.
% 0.06/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 17:19:17 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.64/0.84 % SZS status Unsatisfiable
% 0.64/0.84 % SZS output start Proof
% 0.64/0.84 tff(value_type, type, (
% 0.64/0.84 value: ( $i * $i ) > $o)).
% 0.64/0.84 tff(n0_type, type, (
% 0.64/0.84 n0: $i)).
% 0.64/0.84 tff(out_type, type, (
% 0.64/0.84 out: ( $i * $i ) > $i)).
% 0.64/0.84 tff(h1_type, type, (
% 0.64/0.84 h1: $i > $i)).
% 0.64/0.84 tff(v_type, type, (
% 0.64/0.84 v: ( $i * $i ) > $i)).
% 0.64/0.84 tff(a_type, type, (
% 0.64/0.84 a: $i)).
% 0.64/0.84 tff(n1_type, type, (
% 0.64/0.84 n1: $i)).
% 0.64/0.84 tff(c_type, type, (
% 0.64/0.84 c: $i)).
% 0.64/0.84 tff(and2_type, type, (
% 0.64/0.84 and2: $i > $i)).
% 0.64/0.84 tff(in_type, type, (
% 0.64/0.84 in: ( $i * $i ) > $i)).
% 0.64/0.84 tff(n2_type, type, (
% 0.64/0.84 n2: $i)).
% 0.64/0.84 tff(connection_type, type, (
% 0.64/0.84 connection: ( $i * $i ) > $o)).
% 0.64/0.84 tff(type_type, type, (
% 0.64/0.84 type: ( $i * $i ) > $o)).
% 0.64/0.84 tff(nbit_adder_type, type, (
% 0.64/0.84 nbit_adder: $i > $i)).
% 0.64/0.84 tff(fulladder_type, type, (
% 0.64/0.84 fulladder: $i)).
% 0.64/0.84 tff(halfadder_type, type, (
% 0.64/0.84 halfadder: $i)).
% 0.64/0.84 tff(mode_type, type, (
% 0.64/0.84 mode: ( $i * $i ) > $o)).
% 0.64/0.84 tff(ok_type, type, (
% 0.64/0.84 ok: $i)).
% 0.64/0.84 tff(and_type, type, (
% 0.64/0.84 and: $i)).
% 0.64/0.84 tff(abnormal_type, type, (
% 0.64/0.84 abnormal: $i)).
% 0.64/0.84 tff(or1_type, type, (
% 0.64/0.84 or1: $i > $i)).
% 0.64/0.84 tff(h2_type, type, (
% 0.64/0.84 h2: $i > $i)).
% 0.64/0.84 tff(a1_type, type, (
% 0.64/0.84 a1: $i)).
% 0.64/0.84 tff(equal_value_type, type, (
% 0.64/0.84 equal_value: ( $i * $i ) > $o)).
% 0.64/0.84 tff(or_type, type, (
% 0.64/0.84 or: $i)).
% 0.64/0.84 tff(1,assumption,(~value(in(n2, and2(h1(v(n1, a)))), n0)), introduced(assumption)).
% 0.64/0.84 tff(2,assumption,(~value(in(n2, h1(v(n1, a))), n0)), introduced(assumption)).
% 0.64/0.84 tff(3,plain,
% 0.64/0.84 (type(a, nbit_adder(n1)) <=> type(a, nbit_adder(n1))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(4,axiom,(type(a, nbit_adder(n1))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_isa_1bit_adder')).
% 0.64/0.84 tff(5,plain,
% 0.64/0.84 (type(a, nbit_adder(n1))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.64/0.84 tff(6,plain,
% 0.64/0.84 (^[X: $i] : refl(((~type(X, nbit_adder(n1))) | connection(in(c, X), in(c, v(n1, X)))) <=> ((~type(X, nbit_adder(n1))) | connection(in(c, X), in(c, v(n1, X)))))),
% 0.64/0.84 inference(bind,[status(th)],[])).
% 0.64/0.84 tff(7,plain,
% 0.64/0.84 (![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(c, X), in(c, v(n1, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(c, X), in(c, v(n1, X))))),
% 0.64/0.84 inference(quant_intro,[status(thm)],[6])).
% 0.64/0.84 tff(8,plain,
% 0.64/0.84 (![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(c, X), in(c, v(n1, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(c, X), in(c, v(n1, X))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(9,axiom,(![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(c, X), in(c, v(n1, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nbit_adder_connection_inc_incv1')).
% 0.64/0.84 tff(10,plain,
% 0.64/0.84 (![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(c, X), in(c, v(n1, X))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.64/0.84 tff(11,plain,(
% 0.64/0.84 ![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(c, X), in(c, v(n1, X))))),
% 0.64/0.84 inference(skolemize,[status(sab)],[10])).
% 0.64/0.84 tff(12,plain,
% 0.64/0.84 (![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(c, X), in(c, v(n1, X))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.64/0.84 tff(13,plain,
% 0.64/0.84 (((~![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(c, X), in(c, v(n1, X))))) | ((~type(a, nbit_adder(n1))) | connection(in(c, a), in(c, v(n1, a))))) <=> ((~![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(c, X), in(c, v(n1, X))))) | (~type(a, nbit_adder(n1))) | connection(in(c, a), in(c, v(n1, a))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(14,plain,
% 0.64/0.84 ((~![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(c, X), in(c, v(n1, X))))) | ((~type(a, nbit_adder(n1))) | connection(in(c, a), in(c, v(n1, a))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(15,plain,
% 0.64/0.84 ((~![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(c, X), in(c, v(n1, X))))) | (~type(a, nbit_adder(n1))) | connection(in(c, a), in(c, v(n1, a)))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.64/0.84 tff(16,plain,
% 0.64/0.84 (connection(in(c, a), in(c, v(n1, a)))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[15, 12, 5])).
% 0.64/0.84 tff(17,plain,
% 0.64/0.84 (value(in(c, a), n0) <=> value(in(c, a), n0)),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(18,axiom,(value(in(c, a), n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','inc_0')).
% 0.64/0.85 tff(19,plain,
% 0.64/0.85 (value(in(c, a), n0)),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.64/0.85 tff(20,plain,
% 0.64/0.85 (^[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))))),
% 0.64/0.85 inference(bind,[status(th)],[])).
% 0.64/0.85 tff(21,plain,
% 0.64/0.85 (![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)))),
% 0.64/0.85 inference(quant_intro,[status(thm)],[20])).
% 0.64/0.85 tff(22,plain,
% 0.64/0.85 (![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)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(23,plain,
% 0.64/0.85 (^[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))))),
% 0.64/0.85 inference(bind,[status(th)],[])).
% 0.64/0.85 tff(24,plain,
% 0.64/0.85 (![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)))),
% 0.64/0.85 inference(quant_intro,[status(thm)],[23])).
% 0.64/0.85 tff(25,axiom,(![V: $i, P2: $i, P1: $i] : (((~connection(P1, P2)) | (~value(P1, V))) | value(P2, V))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','value_propagation1')).
% 0.64/0.85 tff(26,plain,
% 0.64/0.85 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.64/0.85 tff(27,plain,
% 0.64/0.85 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.64/0.85 tff(28,plain,(
% 0.64/0.85 ![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 0.64/0.85 inference(skolemize,[status(sab)],[27])).
% 0.64/0.85 tff(29,plain,
% 0.64/0.85 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.64/0.85 tff(30,plain,
% 0.64/0.85 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(c, a), n0)) | (~connection(in(c, a), in(c, v(n1, a)))) | value(in(c, v(n1, a)), n0))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(c, a), n0)) | (~connection(in(c, a), in(c, v(n1, a)))) | value(in(c, v(n1, a)), n0))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(31,plain,
% 0.64/0.85 ((value(in(c, v(n1, a)), n0) | (~value(in(c, a), n0)) | (~connection(in(c, a), in(c, v(n1, a))))) <=> ((~value(in(c, a), n0)) | (~connection(in(c, a), in(c, v(n1, a)))) | value(in(c, v(n1, a)), n0))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(32,plain,
% 0.64/0.85 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(c, v(n1, a)), n0) | (~value(in(c, a), n0)) | (~connection(in(c, a), in(c, v(n1, a)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(c, a), n0)) | (~connection(in(c, a), in(c, v(n1, a)))) | value(in(c, v(n1, a)), n0)))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[31])).
% 0.64/0.85 tff(33,plain,
% 0.64/0.85 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(c, v(n1, a)), n0) | (~value(in(c, a), n0)) | (~connection(in(c, a), in(c, v(n1, a)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(c, a), n0)) | (~connection(in(c, a), in(c, v(n1, a)))) | value(in(c, v(n1, a)), n0))),
% 0.64/0.85 inference(transitivity,[status(thm)],[32, 30])).
% 0.64/0.85 tff(34,plain,
% 0.64/0.85 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(c, v(n1, a)), n0) | (~value(in(c, a), n0)) | (~connection(in(c, a), in(c, v(n1, a)))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(35,plain,
% 0.64/0.85 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(c, a), n0)) | (~connection(in(c, a), in(c, v(n1, a)))) | value(in(c, v(n1, a)), n0)),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.64/0.85 tff(36,plain,
% 0.64/0.85 (value(in(c, v(n1, a)), n0)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[35, 29, 19, 16])).
% 0.64/0.85 tff(37,plain,
% 0.64/0.85 (^[X: $i] : refl(((~type(X, nbit_adder(n1))) | type(v(n1, X), fulladder)) <=> ((~type(X, nbit_adder(n1))) | type(v(n1, X), fulladder)))),
% 0.64/0.85 inference(bind,[status(th)],[])).
% 0.64/0.85 tff(38,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, nbit_adder(n1))) | type(v(n1, X), fulladder)) <=> ![X: $i] : ((~type(X, nbit_adder(n1))) | type(v(n1, X), fulladder))),
% 0.64/0.85 inference(quant_intro,[status(thm)],[37])).
% 0.64/0.85 tff(39,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, nbit_adder(n1))) | type(v(n1, X), fulladder)) <=> ![X: $i] : ((~type(X, nbit_adder(n1))) | type(v(n1, X), fulladder))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(40,axiom,(![X: $i] : ((~type(X, nbit_adder(n1))) | type(v(n1, X), fulladder))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nbit_adder_fulladder1')).
% 0.64/0.85 tff(41,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, nbit_adder(n1))) | type(v(n1, X), fulladder))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.64/0.85 tff(42,plain,(
% 0.64/0.85 ![X: $i] : ((~type(X, nbit_adder(n1))) | type(v(n1, X), fulladder))),
% 0.64/0.85 inference(skolemize,[status(sab)],[41])).
% 0.64/0.85 tff(43,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, nbit_adder(n1))) | type(v(n1, X), fulladder))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.64/0.85 tff(44,plain,
% 0.64/0.85 (((~![X: $i] : ((~type(X, nbit_adder(n1))) | type(v(n1, X), fulladder))) | ((~type(a, nbit_adder(n1))) | type(v(n1, a), fulladder))) <=> ((~![X: $i] : ((~type(X, nbit_adder(n1))) | type(v(n1, X), fulladder))) | (~type(a, nbit_adder(n1))) | type(v(n1, a), fulladder))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(45,plain,
% 0.64/0.85 ((~![X: $i] : ((~type(X, nbit_adder(n1))) | type(v(n1, X), fulladder))) | ((~type(a, nbit_adder(n1))) | type(v(n1, a), fulladder))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(46,plain,
% 0.64/0.85 ((~![X: $i] : ((~type(X, nbit_adder(n1))) | type(v(n1, X), fulladder))) | (~type(a, nbit_adder(n1))) | type(v(n1, a), fulladder)),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.64/0.85 tff(47,plain,
% 0.64/0.85 (type(v(n1, a), fulladder)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[46, 43, 5])).
% 0.64/0.85 tff(48,plain,
% 0.64/0.85 (^[X: $i] : refl(((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X)))) <=> ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X)))))),
% 0.64/0.85 inference(bind,[status(th)],[])).
% 0.64/0.85 tff(49,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 0.64/0.85 inference(quant_intro,[status(thm)],[48])).
% 0.64/0.85 tff(50,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(51,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')).
% 0.64/0.85 tff(52,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.64/0.85 tff(53,plain,(
% 0.64/0.85 ![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 0.64/0.85 inference(skolemize,[status(sab)],[52])).
% 0.64/0.85 tff(54,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.64/0.85 tff(55,plain,
% 0.64/0.85 (((~![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))) | ((~type(v(n1, a), fulladder)) | connection(in(c, v(n1, a)), in(n2, h1(v(n1, a)))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))) | (~type(v(n1, a), fulladder)) | connection(in(c, v(n1, a)), in(n2, h1(v(n1, a)))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(56,plain,
% 0.64/0.85 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))) | ((~type(v(n1, a), fulladder)) | connection(in(c, v(n1, a)), in(n2, h1(v(n1, a)))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(57,plain,
% 0.64/0.85 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(c, X), in(n2, h1(X))))) | (~type(v(n1, a), fulladder)) | connection(in(c, v(n1, a)), in(n2, h1(v(n1, a))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.64/0.85 tff(58,plain,
% 0.64/0.85 (connection(in(c, v(n1, a)), in(n2, h1(v(n1, a))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[57, 54, 47])).
% 0.64/0.85 tff(59,plain,
% 0.64/0.85 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(c, v(n1, a)), n0)) | value(in(n2, h1(v(n1, a))), n0) | (~connection(in(c, v(n1, a)), in(n2, h1(v(n1, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(c, v(n1, a)), n0)) | value(in(n2, h1(v(n1, a))), n0) | (~connection(in(c, v(n1, a)), in(n2, h1(v(n1, a))))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(60,plain,
% 0.64/0.85 ((value(in(n2, h1(v(n1, a))), n0) | (~value(in(c, v(n1, a)), n0)) | (~connection(in(c, v(n1, a)), in(n2, h1(v(n1, a)))))) <=> ((~value(in(c, v(n1, a)), n0)) | value(in(n2, h1(v(n1, a))), n0) | (~connection(in(c, v(n1, a)), in(n2, h1(v(n1, a))))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(61,plain,
% 0.64/0.85 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, h1(v(n1, a))), n0) | (~value(in(c, v(n1, a)), n0)) | (~connection(in(c, v(n1, a)), in(n2, h1(v(n1, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(c, v(n1, a)), n0)) | value(in(n2, h1(v(n1, a))), n0) | (~connection(in(c, v(n1, a)), in(n2, h1(v(n1, a)))))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[60])).
% 0.64/0.85 tff(62,plain,
% 0.64/0.85 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, h1(v(n1, a))), n0) | (~value(in(c, v(n1, a)), n0)) | (~connection(in(c, v(n1, a)), in(n2, h1(v(n1, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(c, v(n1, a)), n0)) | value(in(n2, h1(v(n1, a))), n0) | (~connection(in(c, v(n1, a)), in(n2, h1(v(n1, a))))))),
% 0.64/0.85 inference(transitivity,[status(thm)],[61, 59])).
% 0.64/0.85 tff(63,plain,
% 0.64/0.85 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, h1(v(n1, a))), n0) | (~value(in(c, v(n1, a)), n0)) | (~connection(in(c, v(n1, a)), in(n2, h1(v(n1, a))))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(64,plain,
% 0.64/0.85 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(c, v(n1, a)), n0)) | value(in(n2, h1(v(n1, a))), n0) | (~connection(in(c, v(n1, a)), in(n2, h1(v(n1, a)))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.64/0.85 tff(65,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[64, 29, 58, 36, 2])).
% 0.64/0.85 tff(66,plain,(value(in(n2, h1(v(n1, a))), n0)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(67,plain,
% 0.64/0.85 (^[X: $i] : refl(((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ((~type(X, fulladder)) | type(h1(X), halfadder)))),
% 0.64/0.85 inference(bind,[status(th)],[])).
% 0.64/0.85 tff(68,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 0.64/0.85 inference(quant_intro,[status(thm)],[67])).
% 0.64/0.85 tff(69,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(70,axiom,(![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_halfadder1')).
% 0.64/0.85 tff(71,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.64/0.85 tff(72,plain,(
% 0.64/0.85 ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 0.64/0.85 inference(skolemize,[status(sab)],[71])).
% 0.64/0.85 tff(73,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.64/0.85 tff(74,plain,
% 0.64/0.85 (((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | ((~type(v(n1, a), fulladder)) | type(h1(v(n1, a)), halfadder))) <=> ((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | (~type(v(n1, a), fulladder)) | type(h1(v(n1, a)), halfadder))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(75,plain,
% 0.64/0.85 ((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | ((~type(v(n1, a), fulladder)) | type(h1(v(n1, a)), halfadder))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(76,plain,
% 0.64/0.85 ((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | (~type(v(n1, a), fulladder)) | type(h1(v(n1, a)), halfadder)),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.64/0.85 tff(77,plain,
% 0.64/0.85 (type(h1(v(n1, a)), halfadder)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[76, 73, 47])).
% 0.64/0.85 tff(78,plain,
% 0.64/0.85 (^[X: $i] : refl(((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X)))) <=> ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X)))))),
% 0.64/0.85 inference(bind,[status(th)],[])).
% 0.64/0.85 tff(79,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 0.64/0.85 inference(quant_intro,[status(thm)],[78])).
% 0.64/0.85 tff(80,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(81,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')).
% 0.64/0.85 tff(82,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.64/0.85 tff(83,plain,(
% 0.64/0.85 ![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 0.64/0.85 inference(skolemize,[status(sab)],[82])).
% 0.64/0.85 tff(84,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.64/0.85 tff(85,plain,
% 0.64/0.85 (((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))) | ((~type(h1(v(n1, a)), halfadder)) | connection(in(n2, h1(v(n1, a))), in(n2, and2(h1(v(n1, a))))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))) | (~type(h1(v(n1, a)), halfadder)) | connection(in(n2, h1(v(n1, a))), in(n2, and2(h1(v(n1, a))))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(86,plain,
% 0.64/0.85 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))) | ((~type(h1(v(n1, a)), halfadder)) | connection(in(n2, h1(v(n1, a))), in(n2, and2(h1(v(n1, a))))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(87,plain,
% 0.64/0.85 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n2, X), in(n2, and2(X))))) | (~type(h1(v(n1, a)), halfadder)) | connection(in(n2, h1(v(n1, a))), in(n2, and2(h1(v(n1, a)))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.64/0.85 tff(88,plain,
% 0.64/0.85 ((~type(h1(v(n1, a)), halfadder)) | connection(in(n2, h1(v(n1, a))), in(n2, and2(h1(v(n1, a)))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[87, 84])).
% 0.64/0.85 tff(89,plain,
% 0.64/0.85 (connection(in(n2, h1(v(n1, a))), in(n2, and2(h1(v(n1, a)))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[88, 77])).
% 0.64/0.85 tff(90,plain,
% 0.64/0.85 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(n2, h1(v(n1, a))), n0)) | value(in(n2, and2(h1(v(n1, a)))), n0) | (~connection(in(n2, h1(v(n1, a))), in(n2, and2(h1(v(n1, a)))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n2, h1(v(n1, a))), n0)) | value(in(n2, and2(h1(v(n1, a)))), n0) | (~connection(in(n2, h1(v(n1, a))), in(n2, and2(h1(v(n1, a)))))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(91,plain,
% 0.64/0.85 ((value(in(n2, and2(h1(v(n1, a)))), n0) | (~value(in(n2, h1(v(n1, a))), n0)) | (~connection(in(n2, h1(v(n1, a))), in(n2, and2(h1(v(n1, a))))))) <=> ((~value(in(n2, h1(v(n1, a))), n0)) | value(in(n2, and2(h1(v(n1, a)))), n0) | (~connection(in(n2, h1(v(n1, a))), in(n2, and2(h1(v(n1, a)))))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(92,plain,
% 0.64/0.85 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, and2(h1(v(n1, a)))), n0) | (~value(in(n2, h1(v(n1, a))), n0)) | (~connection(in(n2, h1(v(n1, a))), in(n2, and2(h1(v(n1, a)))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(n2, h1(v(n1, a))), n0)) | value(in(n2, and2(h1(v(n1, a)))), n0) | (~connection(in(n2, h1(v(n1, a))), in(n2, and2(h1(v(n1, a))))))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[91])).
% 0.64/0.85 tff(93,plain,
% 0.64/0.85 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, and2(h1(v(n1, a)))), n0) | (~value(in(n2, h1(v(n1, a))), n0)) | (~connection(in(n2, h1(v(n1, a))), in(n2, and2(h1(v(n1, a)))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n2, h1(v(n1, a))), n0)) | value(in(n2, and2(h1(v(n1, a)))), n0) | (~connection(in(n2, h1(v(n1, a))), in(n2, and2(h1(v(n1, a)))))))),
% 0.64/0.85 inference(transitivity,[status(thm)],[92, 90])).
% 0.64/0.85 tff(94,plain,
% 0.64/0.85 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n2, and2(h1(v(n1, a)))), n0) | (~value(in(n2, h1(v(n1, a))), n0)) | (~connection(in(n2, h1(v(n1, a))), in(n2, and2(h1(v(n1, a)))))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(95,plain,
% 0.64/0.85 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n2, h1(v(n1, a))), n0)) | value(in(n2, and2(h1(v(n1, a)))), n0) | (~connection(in(n2, h1(v(n1, a))), in(n2, and2(h1(v(n1, a))))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.64/0.85 tff(96,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[95, 29, 89, 66, 1])).
% 0.64/0.85 tff(97,plain,(value(in(n2, and2(h1(v(n1, a)))), n0)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(98,plain,
% 0.64/0.85 (^[X: $i] : refl(((~type(X, halfadder)) | type(and2(X), and)) <=> ((~type(X, halfadder)) | type(and2(X), and)))),
% 0.64/0.85 inference(bind,[status(th)],[])).
% 0.64/0.85 tff(99,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 0.64/0.85 inference(quant_intro,[status(thm)],[98])).
% 0.64/0.85 tff(100,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(101,axiom,(![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_and2')).
% 0.64/0.85 tff(102,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.64/0.85 tff(103,plain,(
% 0.64/0.85 ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 0.64/0.85 inference(skolemize,[status(sab)],[102])).
% 0.64/0.85 tff(104,plain,
% 0.64/0.85 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.64/0.85 tff(105,plain,
% 0.64/0.85 (((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h1(v(n1, a)), halfadder)) | type(and2(h1(v(n1, a))), and))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h1(v(n1, a)), halfadder)) | type(and2(h1(v(n1, a))), and))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(106,plain,
% 0.64/0.85 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h1(v(n1, a)), halfadder)) | type(and2(h1(v(n1, a))), and))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(107,plain,
% 0.64/0.85 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h1(v(n1, a)), halfadder)) | type(and2(h1(v(n1, a))), and)),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.64/0.85 tff(108,plain,
% 0.64/0.85 ((~type(h1(v(n1, a)), halfadder)) | type(and2(h1(v(n1, a))), and)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[107, 104])).
% 0.64/0.85 tff(109,plain,
% 0.64/0.85 (type(and2(h1(v(n1, a))), and)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[108, 77])).
% 0.64/0.85 tff(110,plain,
% 0.64/0.85 ((~mode(and2(h1(v(n1, a))), abnormal)) <=> (~mode(and2(h1(v(n1, a))), abnormal))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(111,axiom,(~mode(and2(h1(v(n1, a))), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_and2h1v1')).
% 0.64/0.85 tff(112,plain,
% 0.64/0.85 (~mode(and2(h1(v(n1, a))), abnormal)),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.64/0.85 tff(113,plain,
% 0.64/0.85 (^[Any: $i, K: $i] : refl((mode(K, abnormal) | mode(K, ok) | (~type(K, Any))) <=> (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))))),
% 0.64/0.85 inference(bind,[status(th)],[])).
% 0.64/0.85 tff(114,plain,
% 0.64/0.85 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))) <=> ![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 0.64/0.85 inference(quant_intro,[status(thm)],[113])).
% 0.64/0.85 tff(115,plain,
% 0.64/0.85 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))) <=> ![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(116,plain,
% 0.64/0.85 (^[Any: $i, K: $i] : rewrite((((~type(K, Any)) | mode(K, ok)) | mode(K, abnormal)) <=> (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))))),
% 0.64/0.85 inference(bind,[status(th)],[])).
% 0.64/0.85 tff(117,plain,
% 0.64/0.85 (![Any: $i, K: $i] : (((~type(K, Any)) | mode(K, ok)) | mode(K, abnormal)) <=> ![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 0.64/0.85 inference(quant_intro,[status(thm)],[116])).
% 0.64/0.85 tff(118,axiom,(![Any: $i, K: $i] : (((~type(K, Any)) | mode(K, ok)) | mode(K, abnormal))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','ok_or_abnormal')).
% 0.64/0.85 tff(119,plain,
% 0.64/0.85 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.64/0.85 tff(120,plain,
% 0.64/0.85 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.64/0.85 tff(121,plain,(
% 0.64/0.85 ![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 0.64/0.85 inference(skolemize,[status(sab)],[120])).
% 0.64/0.85 tff(122,plain,
% 0.64/0.85 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.64/0.85 tff(123,plain,
% 0.64/0.85 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h1(v(n1, a))), abnormal) | mode(and2(h1(v(n1, a))), ok) | (~type(and2(h1(v(n1, a))), and)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h1(v(n1, a))), abnormal) | mode(and2(h1(v(n1, a))), ok) | (~type(and2(h1(v(n1, a))), and)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(124,plain,
% 0.64/0.85 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h1(v(n1, a))), abnormal) | mode(and2(h1(v(n1, a))), ok) | (~type(and2(h1(v(n1, a))), and)))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(125,plain,
% 0.64/0.85 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h1(v(n1, a))), abnormal) | mode(and2(h1(v(n1, a))), ok) | (~type(and2(h1(v(n1, a))), and))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.64/0.85 tff(126,plain,
% 0.64/0.85 (mode(and2(h1(v(n1, a))), ok)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[125, 122, 112, 109])).
% 0.64/0.85 tff(127,plain,
% 0.64/0.85 (^[Any: $i, K: $i] : refl(((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and))) <=> ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and))))),
% 0.64/0.85 inference(bind,[status(th)],[])).
% 0.64/0.85 tff(128,plain,
% 0.64/0.85 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and))) <=> ![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 0.64/0.85 inference(quant_intro,[status(thm)],[127])).
% 0.64/0.85 tff(129,plain,
% 0.64/0.85 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and))) <=> ![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(130,plain,
% 0.64/0.85 (^[Any: $i, K: $i] : trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, and))) | (~value(in(Any, K), n0))) <=> ((~mode(K, ok)) | (~value(in(Any, K), n0)) | (~type(K, and)))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(in(Any, K), n0))) | value(out(n1, K), n0)) <=> (((~mode(K, ok)) | (~value(in(Any, K), n0)) | (~type(K, and))) | value(out(n1, K), n0)))), rewrite((((~mode(K, ok)) | (~value(in(Any, K), n0)) | (~type(K, and))) | value(out(n1, K), n0)) <=> ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(in(Any, K), n0))) | value(out(n1, K), n0)) <=> ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))))),
% 0.64/0.85 inference(bind,[status(th)],[])).
% 0.64/0.85 tff(131,plain,
% 0.64/0.85 (![Any: $i, K: $i] : ((((~mode(K, ok)) | (~type(K, and))) | (~value(in(Any, K), n0))) | value(out(n1, K), n0)) <=> ![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 0.64/0.85 inference(quant_intro,[status(thm)],[130])).
% 0.64/0.85 tff(132,axiom,(![Any: $i, K: $i] : ((((~mode(K, ok)) | (~type(K, and))) | (~value(in(Any, K), n0))) | value(out(n1, K), n0))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','and_0x_0')).
% 0.64/0.85 tff(133,plain,
% 0.64/0.85 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.64/0.85 tff(134,plain,
% 0.64/0.85 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.64/0.85 tff(135,plain,(
% 0.64/0.85 ![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 0.64/0.85 inference(skolemize,[status(sab)],[134])).
% 0.64/0.85 tff(136,plain,
% 0.64/0.85 (![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.64/0.85 tff(137,plain,
% 0.64/0.85 (((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h1(v(n1, a))), ok)) | value(out(n1, and2(h1(v(n1, a)))), n0) | (~value(in(n2, and2(h1(v(n1, a)))), n0)) | (~type(and2(h1(v(n1, a))), and)))) <=> ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | (~mode(and2(h1(v(n1, a))), ok)) | value(out(n1, and2(h1(v(n1, a)))), n0) | (~value(in(n2, and2(h1(v(n1, a)))), n0)) | (~type(and2(h1(v(n1, a))), and)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(138,plain,
% 0.64/0.85 ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h1(v(n1, a))), ok)) | value(out(n1, and2(h1(v(n1, a)))), n0) | (~value(in(n2, and2(h1(v(n1, a)))), n0)) | (~type(and2(h1(v(n1, a))), and)))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(139,plain,
% 0.64/0.85 ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | (~mode(and2(h1(v(n1, a))), ok)) | value(out(n1, and2(h1(v(n1, a)))), n0) | (~value(in(n2, and2(h1(v(n1, a)))), n0)) | (~type(and2(h1(v(n1, a))), and))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.64/0.85 tff(140,plain,
% 0.64/0.85 ((~mode(and2(h1(v(n1, a))), ok)) | value(out(n1, and2(h1(v(n1, a)))), n0) | (~value(in(n2, and2(h1(v(n1, a)))), n0))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[139, 136, 109])).
% 0.64/0.85 tff(141,plain,
% 0.64/0.85 (value(out(n1, and2(h1(v(n1, a)))), n0) | (~value(in(n2, and2(h1(v(n1, a)))), n0))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[140, 126])).
% 0.64/0.85 tff(142,plain,
% 0.64/0.85 (value(out(n1, and2(h1(v(n1, a)))), n0)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[141, 97])).
% 0.64/0.85 tff(143,plain,
% 0.64/0.85 (^[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)))))),
% 0.64/0.85 inference(bind,[status(th)],[])).
% 0.64/0.85 tff(144,plain,
% 0.64/0.85 (![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))))),
% 0.64/0.85 inference(quant_intro,[status(thm)],[143])).
% 0.64/0.85 tff(145,plain,
% 0.64/0.86 (![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(146,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')).
% 0.64/0.86 tff(147,plain,
% 0.64/0.86 (![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.64/0.86 tff(148,plain,(
% 0.64/0.86 ![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 0.64/0.86 inference(skolemize,[status(sab)],[147])).
% 0.64/0.86 tff(149,plain,
% 0.64/0.86 (![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.64/0.86 tff(150,plain,
% 0.64/0.86 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h1(v(n1, a)), halfadder)) | connection(out(c, h1(v(n1, a))), out(n1, and2(h1(v(n1, a))))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h1(v(n1, a)), halfadder)) | connection(out(c, h1(v(n1, a))), out(n1, and2(h1(v(n1, a))))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(151,plain,
% 0.64/0.86 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h1(v(n1, a)), halfadder)) | connection(out(c, h1(v(n1, a))), out(n1, and2(h1(v(n1, a))))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(152,plain,
% 0.64/0.86 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h1(v(n1, a)), halfadder)) | connection(out(c, h1(v(n1, a))), out(n1, and2(h1(v(n1, a)))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.64/0.86 tff(153,plain,
% 0.64/0.86 ((~type(h1(v(n1, a)), halfadder)) | connection(out(c, h1(v(n1, a))), out(n1, and2(h1(v(n1, a)))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[152, 149])).
% 0.64/0.86 tff(154,plain,
% 0.64/0.86 (connection(out(c, h1(v(n1, a))), out(n1, and2(h1(v(n1, a)))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[153, 77])).
% 0.64/0.86 tff(155,plain,
% 0.64/0.86 (^[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))))),
% 0.64/0.86 inference(bind,[status(th)],[])).
% 0.64/0.86 tff(156,plain,
% 0.64/0.86 (![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)))),
% 0.64/0.86 inference(quant_intro,[status(thm)],[155])).
% 0.64/0.86 tff(157,plain,
% 0.64/0.86 (![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)))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(158,plain,
% 0.64/0.86 (^[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))))),
% 0.64/0.86 inference(bind,[status(th)],[])).
% 0.64/0.86 tff(159,plain,
% 0.64/0.86 (![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)))),
% 0.64/0.86 inference(quant_intro,[status(thm)],[158])).
% 0.64/0.86 tff(160,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')).
% 0.64/0.86 tff(161,plain,
% 0.64/0.86 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.64/0.86 tff(162,plain,
% 0.64/0.86 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.64/0.86 tff(163,plain,(
% 0.64/0.86 ![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 0.64/0.86 inference(skolemize,[status(sab)],[162])).
% 0.64/0.86 tff(164,plain,
% 0.64/0.86 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.64/0.86 tff(165,plain,
% 0.64/0.86 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(out(n1, and2(h1(v(n1, a)))), n0)) | (~connection(out(c, h1(v(n1, a))), out(n1, and2(h1(v(n1, a)))))) | value(out(c, h1(v(n1, a))), n0))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and2(h1(v(n1, a)))), n0)) | (~connection(out(c, h1(v(n1, a))), out(n1, and2(h1(v(n1, a)))))) | value(out(c, h1(v(n1, a))), n0))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(166,plain,
% 0.64/0.86 ((value(out(c, h1(v(n1, a))), n0) | (~connection(out(c, h1(v(n1, a))), out(n1, and2(h1(v(n1, a)))))) | (~value(out(n1, and2(h1(v(n1, a)))), n0))) <=> ((~value(out(n1, and2(h1(v(n1, a)))), n0)) | (~connection(out(c, h1(v(n1, a))), out(n1, and2(h1(v(n1, a)))))) | value(out(c, h1(v(n1, a))), n0))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(167,plain,
% 0.64/0.86 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h1(v(n1, a))), n0) | (~connection(out(c, h1(v(n1, a))), out(n1, and2(h1(v(n1, a)))))) | (~value(out(n1, and2(h1(v(n1, a)))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(out(n1, and2(h1(v(n1, a)))), n0)) | (~connection(out(c, h1(v(n1, a))), out(n1, and2(h1(v(n1, a)))))) | value(out(c, h1(v(n1, a))), n0)))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[166])).
% 0.64/0.86 tff(168,plain,
% 0.64/0.86 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h1(v(n1, a))), n0) | (~connection(out(c, h1(v(n1, a))), out(n1, and2(h1(v(n1, a)))))) | (~value(out(n1, and2(h1(v(n1, a)))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and2(h1(v(n1, a)))), n0)) | (~connection(out(c, h1(v(n1, a))), out(n1, and2(h1(v(n1, a)))))) | value(out(c, h1(v(n1, a))), n0))),
% 0.64/0.86 inference(transitivity,[status(thm)],[167, 165])).
% 0.64/0.86 tff(169,plain,
% 0.64/0.86 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h1(v(n1, a))), n0) | (~connection(out(c, h1(v(n1, a))), out(n1, and2(h1(v(n1, a)))))) | (~value(out(n1, and2(h1(v(n1, a)))), n0)))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(170,plain,
% 0.64/0.86 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and2(h1(v(n1, a)))), n0)) | (~connection(out(c, h1(v(n1, a))), out(n1, and2(h1(v(n1, a)))))) | value(out(c, h1(v(n1, a))), n0)),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.64/0.86 tff(171,plain,
% 0.64/0.86 (value(out(c, h1(v(n1, a))), n0)),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[170, 164, 154, 142])).
% 0.64/0.86 tff(172,plain,
% 0.64/0.86 (^[X: $i] : refl(((~type(X, nbit_adder(n1))) | connection(out(c, X), out(c, v(n1, X)))) <=> ((~type(X, nbit_adder(n1))) | connection(out(c, X), out(c, v(n1, X)))))),
% 0.64/0.86 inference(bind,[status(th)],[])).
% 0.64/0.86 tff(173,plain,
% 0.64/0.86 (![X: $i] : ((~type(X, nbit_adder(n1))) | connection(out(c, X), out(c, v(n1, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n1))) | connection(out(c, X), out(c, v(n1, X))))),
% 0.64/0.86 inference(quant_intro,[status(thm)],[172])).
% 0.64/0.86 tff(174,plain,
% 0.64/0.86 (![X: $i] : ((~type(X, nbit_adder(n1))) | connection(out(c, X), out(c, v(n1, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n1))) | connection(out(c, X), out(c, v(n1, X))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(175,axiom,(![X: $i] : ((~type(X, nbit_adder(n1))) | connection(out(c, X), out(c, v(n1, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nbit_adder_connection_outc_outcv1')).
% 0.64/0.86 tff(176,plain,
% 0.64/0.86 (![X: $i] : ((~type(X, nbit_adder(n1))) | connection(out(c, X), out(c, v(n1, X))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.64/0.86 tff(177,plain,(
% 0.64/0.86 ![X: $i] : ((~type(X, nbit_adder(n1))) | connection(out(c, X), out(c, v(n1, X))))),
% 0.64/0.86 inference(skolemize,[status(sab)],[176])).
% 0.64/0.86 tff(178,plain,
% 0.64/0.86 (![X: $i] : ((~type(X, nbit_adder(n1))) | connection(out(c, X), out(c, v(n1, X))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.64/0.86 tff(179,plain,
% 0.64/0.86 (((~![X: $i] : ((~type(X, nbit_adder(n1))) | connection(out(c, X), out(c, v(n1, X))))) | ((~type(a, nbit_adder(n1))) | connection(out(c, a), out(c, v(n1, a))))) <=> ((~![X: $i] : ((~type(X, nbit_adder(n1))) | connection(out(c, X), out(c, v(n1, X))))) | (~type(a, nbit_adder(n1))) | connection(out(c, a), out(c, v(n1, a))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(180,plain,
% 0.64/0.86 ((~![X: $i] : ((~type(X, nbit_adder(n1))) | connection(out(c, X), out(c, v(n1, X))))) | ((~type(a, nbit_adder(n1))) | connection(out(c, a), out(c, v(n1, a))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(181,plain,
% 0.64/0.86 ((~![X: $i] : ((~type(X, nbit_adder(n1))) | connection(out(c, X), out(c, v(n1, X))))) | (~type(a, nbit_adder(n1))) | connection(out(c, a), out(c, v(n1, a)))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.64/0.86 tff(182,plain,
% 0.64/0.86 (connection(out(c, a), out(c, v(n1, a)))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[181, 178, 5])).
% 0.64/0.86 tff(183,plain,
% 0.64/0.86 (value(out(c, a), n1) <=> value(out(c, a), n1)),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(184,axiom,(value(out(c, a), n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','outc_0')).
% 0.64/0.86 tff(185,plain,
% 0.64/0.86 (value(out(c, a), n1)),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.64/0.86 tff(186,plain,
% 0.64/0.86 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(out(c, a), n1)) | (~connection(out(c, a), out(c, v(n1, a)))) | value(out(c, v(n1, a)), n1))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(c, a), n1)) | (~connection(out(c, a), out(c, v(n1, a)))) | value(out(c, v(n1, a)), n1))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(187,plain,
% 0.64/0.86 ((value(out(c, v(n1, a)), n1) | (~value(out(c, a), n1)) | (~connection(out(c, a), out(c, v(n1, a))))) <=> ((~value(out(c, a), n1)) | (~connection(out(c, a), out(c, v(n1, a)))) | value(out(c, v(n1, a)), n1))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(188,plain,
% 0.64/0.86 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(c, v(n1, a)), n1) | (~value(out(c, a), n1)) | (~connection(out(c, a), out(c, v(n1, a)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(out(c, a), n1)) | (~connection(out(c, a), out(c, v(n1, a)))) | value(out(c, v(n1, a)), n1)))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[187])).
% 0.71/0.86 tff(189,plain,
% 0.71/0.86 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(c, v(n1, a)), n1) | (~value(out(c, a), n1)) | (~connection(out(c, a), out(c, v(n1, a)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(c, a), n1)) | (~connection(out(c, a), out(c, v(n1, a)))) | value(out(c, v(n1, a)), n1))),
% 0.71/0.86 inference(transitivity,[status(thm)],[188, 186])).
% 0.71/0.86 tff(190,plain,
% 0.71/0.86 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(c, v(n1, a)), n1) | (~value(out(c, a), n1)) | (~connection(out(c, a), out(c, v(n1, a)))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(191,plain,
% 0.71/0.86 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(out(c, a), n1)) | (~connection(out(c, a), out(c, v(n1, a)))) | value(out(c, v(n1, a)), n1)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.71/0.86 tff(192,plain,
% 0.71/0.86 (value(out(c, v(n1, a)), n1)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[191, 29, 185, 182])).
% 0.71/0.86 tff(193,assumption,(~value(out(n1, or1(v(n1, a))), n1)), introduced(assumption)).
% 0.71/0.86 tff(194,plain,
% 0.71/0.86 (^[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)))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(195,plain,
% 0.71/0.86 (![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))))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[194])).
% 0.71/0.86 tff(196,plain,
% 0.71/0.86 (![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))))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(197,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')).
% 0.71/0.86 tff(198,plain,
% 0.71/0.86 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.71/0.86 tff(199,plain,(
% 0.71/0.86 ![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 0.71/0.86 inference(skolemize,[status(sab)],[198])).
% 0.71/0.86 tff(200,plain,
% 0.71/0.86 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[199, 195])).
% 0.71/0.86 tff(201,plain,
% 0.71/0.86 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | ((~type(v(n1, a), fulladder)) | connection(out(c, v(n1, a)), out(n1, or1(v(n1, a)))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | (~type(v(n1, a), fulladder)) | connection(out(c, v(n1, a)), out(n1, or1(v(n1, a)))))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(202,plain,
% 0.71/0.86 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | ((~type(v(n1, a), fulladder)) | connection(out(c, v(n1, a)), out(n1, or1(v(n1, a)))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(203,plain,
% 0.71/0.86 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | (~type(v(n1, a), fulladder)) | connection(out(c, v(n1, a)), out(n1, or1(v(n1, a))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.71/0.86 tff(204,plain,
% 0.71/0.86 (connection(out(c, v(n1, a)), out(n1, or1(v(n1, a))))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[203, 200, 47])).
% 0.71/0.86 tff(205,plain,
% 0.71/0.86 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, or1(v(n1, a))), n1) | (~connection(out(c, v(n1, a)), out(n1, or1(v(n1, a))))) | (~value(out(c, v(n1, a)), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, or1(v(n1, a))), n1) | (~connection(out(c, v(n1, a)), out(n1, or1(v(n1, a))))) | (~value(out(c, v(n1, a)), n1)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(206,plain,
% 0.71/0.86 ((value(out(n1, or1(v(n1, a))), n1) | (~value(out(c, v(n1, a)), n1)) | (~connection(out(c, v(n1, a)), out(n1, or1(v(n1, a)))))) <=> (value(out(n1, or1(v(n1, a))), n1) | (~connection(out(c, v(n1, a)), out(n1, or1(v(n1, a))))) | (~value(out(c, v(n1, a)), n1)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(207,plain,
% 0.71/0.86 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, or1(v(n1, a))), n1) | (~value(out(c, v(n1, a)), n1)) | (~connection(out(c, v(n1, a)), out(n1, or1(v(n1, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, or1(v(n1, a))), n1) | (~connection(out(c, v(n1, a)), out(n1, or1(v(n1, a))))) | (~value(out(c, v(n1, a)), n1))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[206])).
% 0.71/0.86 tff(208,plain,
% 0.71/0.86 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, or1(v(n1, a))), n1) | (~value(out(c, v(n1, a)), n1)) | (~connection(out(c, v(n1, a)), out(n1, or1(v(n1, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, or1(v(n1, a))), n1) | (~connection(out(c, v(n1, a)), out(n1, or1(v(n1, a))))) | (~value(out(c, v(n1, a)), n1)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[207, 205])).
% 0.71/0.86 tff(209,plain,
% 0.71/0.86 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, or1(v(n1, a))), n1) | (~value(out(c, v(n1, a)), n1)) | (~connection(out(c, v(n1, a)), out(n1, or1(v(n1, a))))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(210,plain,
% 0.71/0.86 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, or1(v(n1, a))), n1) | (~connection(out(c, v(n1, a)), out(n1, or1(v(n1, a))))) | (~value(out(c, v(n1, a)), n1))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.71/0.86 tff(211,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[210, 29, 204, 193, 192])).
% 0.71/0.86 tff(212,plain,(value(out(n1, or1(v(n1, a))), n1)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(213,assumption,(~value(in(n1, and2(h2(v(n1, a)))), n0)), introduced(assumption)).
% 0.71/0.86 tff(214,assumption,(~value(in(n1, v(n1, a)), n0)), introduced(assumption)).
% 0.71/0.86 tff(215,plain,
% 0.71/0.86 (^[X: $i] : refl(((~type(X, nbit_adder(n1))) | connection(in(a1, X), in(n1, v(n1, X)))) <=> ((~type(X, nbit_adder(n1))) | connection(in(a1, X), in(n1, v(n1, X)))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(216,plain,
% 0.71/0.86 (![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(a1, X), in(n1, v(n1, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(a1, X), in(n1, v(n1, X))))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[215])).
% 0.71/0.86 tff(217,plain,
% 0.71/0.86 (![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(a1, X), in(n1, v(n1, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(a1, X), in(n1, v(n1, X))))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(218,axiom,(![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(a1, X), in(n1, v(n1, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nbit_adder_connection_ina1_in1v1')).
% 0.71/0.86 tff(219,plain,
% 0.71/0.86 (![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(a1, X), in(n1, v(n1, X))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.71/0.86 tff(220,plain,(
% 0.71/0.86 ![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(a1, X), in(n1, v(n1, X))))),
% 0.71/0.86 inference(skolemize,[status(sab)],[219])).
% 0.71/0.86 tff(221,plain,
% 0.71/0.86 (![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(a1, X), in(n1, v(n1, X))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[220, 216])).
% 0.71/0.86 tff(222,plain,
% 0.71/0.86 (((~![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(a1, X), in(n1, v(n1, X))))) | ((~type(a, nbit_adder(n1))) | connection(in(a1, a), in(n1, v(n1, a))))) <=> ((~![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(a1, X), in(n1, v(n1, X))))) | (~type(a, nbit_adder(n1))) | connection(in(a1, a), in(n1, v(n1, a))))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(223,plain,
% 0.71/0.86 ((~![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(a1, X), in(n1, v(n1, X))))) | ((~type(a, nbit_adder(n1))) | connection(in(a1, a), in(n1, v(n1, a))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(224,plain,
% 0.71/0.86 ((~![X: $i] : ((~type(X, nbit_adder(n1))) | connection(in(a1, X), in(n1, v(n1, X))))) | (~type(a, nbit_adder(n1))) | connection(in(a1, a), in(n1, v(n1, a)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.71/0.86 tff(225,plain,
% 0.71/0.86 (connection(in(a1, a), in(n1, v(n1, a)))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[224, 221, 5])).
% 0.71/0.86 tff(226,plain,
% 0.71/0.86 (value(in(a1, a), n0) <=> value(in(a1, a), n0)),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(227,axiom,(value(in(a1, a), n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ina1_0')).
% 0.71/0.86 tff(228,plain,
% 0.71/0.86 (value(in(a1, a), n0)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.71/0.86 tff(229,plain,
% 0.71/0.86 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(a1, a), n0)) | (~connection(in(a1, a), in(n1, v(n1, a)))) | value(in(n1, v(n1, a)), n0))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(a1, a), n0)) | (~connection(in(a1, a), in(n1, v(n1, a)))) | value(in(n1, v(n1, a)), n0))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(230,plain,
% 0.71/0.86 ((value(in(n1, v(n1, a)), n0) | (~value(in(a1, a), n0)) | (~connection(in(a1, a), in(n1, v(n1, a))))) <=> ((~value(in(a1, a), n0)) | (~connection(in(a1, a), in(n1, v(n1, a)))) | value(in(n1, v(n1, a)), n0))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(231,plain,
% 0.71/0.86 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, v(n1, a)), n0) | (~value(in(a1, a), n0)) | (~connection(in(a1, a), in(n1, v(n1, a)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(a1, a), n0)) | (~connection(in(a1, a), in(n1, v(n1, a)))) | value(in(n1, v(n1, a)), n0)))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[230])).
% 0.71/0.86 tff(232,plain,
% 0.71/0.86 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, v(n1, a)), n0) | (~value(in(a1, a), n0)) | (~connection(in(a1, a), in(n1, v(n1, a)))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(a1, a), n0)) | (~connection(in(a1, a), in(n1, v(n1, a)))) | value(in(n1, v(n1, a)), n0))),
% 0.71/0.86 inference(transitivity,[status(thm)],[231, 229])).
% 0.71/0.86 tff(233,plain,
% 0.71/0.86 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, v(n1, a)), n0) | (~value(in(a1, a), n0)) | (~connection(in(a1, a), in(n1, v(n1, a)))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(234,plain,
% 0.71/0.86 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(a1, a), n0)) | (~connection(in(a1, a), in(n1, v(n1, a)))) | value(in(n1, v(n1, a)), n0)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.71/0.86 tff(235,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[234, 29, 228, 225, 214])).
% 0.71/0.86 tff(236,plain,(value(in(n1, v(n1, a)), n0)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.86 tff(237,plain,
% 0.71/0.86 (^[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)))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(238,plain,
% 0.71/0.86 (![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))))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[237])).
% 0.71/0.86 tff(239,plain,
% 0.71/0.86 (![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))))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(240,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')).
% 0.71/0.86 tff(241,plain,
% 0.71/0.86 (![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.71/0.86 tff(242,plain,(
% 0.71/0.86 ![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 0.71/0.86 inference(skolemize,[status(sab)],[241])).
% 0.71/0.86 tff(243,plain,
% 0.71/0.86 (![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[242, 238])).
% 0.71/0.86 tff(244,plain,
% 0.71/0.86 (((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | ((~type(v(n1, a), fulladder)) | connection(in(n1, v(n1, a)), in(n1, h2(v(n1, a)))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | (~type(v(n1, a), fulladder)) | connection(in(n1, v(n1, a)), in(n1, h2(v(n1, a)))))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(245,plain,
% 0.71/0.86 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | ((~type(v(n1, a), fulladder)) | connection(in(n1, v(n1, a)), in(n1, h2(v(n1, a)))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(246,plain,
% 0.71/0.86 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | (~type(v(n1, a), fulladder)) | connection(in(n1, v(n1, a)), in(n1, h2(v(n1, a))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.71/0.86 tff(247,plain,
% 0.71/0.86 (connection(in(n1, v(n1, a)), in(n1, h2(v(n1, a))))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[246, 243, 47])).
% 0.71/0.86 tff(248,plain,
% 0.71/0.86 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(n1, v(n1, a)), n0)) | value(in(n1, h2(v(n1, a))), n0) | (~connection(in(n1, v(n1, a)), in(n1, h2(v(n1, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n1, v(n1, a)), n0)) | value(in(n1, h2(v(n1, a))), n0) | (~connection(in(n1, v(n1, a)), in(n1, h2(v(n1, a))))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(249,plain,
% 0.71/0.87 ((value(in(n1, h2(v(n1, a))), n0) | (~value(in(n1, v(n1, a)), n0)) | (~connection(in(n1, v(n1, a)), in(n1, h2(v(n1, a)))))) <=> ((~value(in(n1, v(n1, a)), n0)) | value(in(n1, h2(v(n1, a))), n0) | (~connection(in(n1, v(n1, a)), in(n1, h2(v(n1, a))))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(250,plain,
% 0.71/0.87 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, h2(v(n1, a))), n0) | (~value(in(n1, v(n1, a)), n0)) | (~connection(in(n1, v(n1, a)), in(n1, h2(v(n1, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(n1, v(n1, a)), n0)) | value(in(n1, h2(v(n1, a))), n0) | (~connection(in(n1, v(n1, a)), in(n1, h2(v(n1, a)))))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[249])).
% 0.71/0.87 tff(251,plain,
% 0.71/0.87 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, h2(v(n1, a))), n0) | (~value(in(n1, v(n1, a)), n0)) | (~connection(in(n1, v(n1, a)), in(n1, h2(v(n1, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n1, v(n1, a)), n0)) | value(in(n1, h2(v(n1, a))), n0) | (~connection(in(n1, v(n1, a)), in(n1, h2(v(n1, a))))))),
% 0.71/0.87 inference(transitivity,[status(thm)],[250, 248])).
% 0.71/0.87 tff(252,plain,
% 0.71/0.87 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, h2(v(n1, a))), n0) | (~value(in(n1, v(n1, a)), n0)) | (~connection(in(n1, v(n1, a)), in(n1, h2(v(n1, a))))))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(253,plain,
% 0.71/0.87 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n1, v(n1, a)), n0)) | value(in(n1, h2(v(n1, a))), n0) | (~connection(in(n1, v(n1, a)), in(n1, h2(v(n1, a)))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.71/0.87 tff(254,plain,
% 0.71/0.87 (value(in(n1, h2(v(n1, a))), n0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[253, 29, 247, 236])).
% 0.71/0.87 tff(255,plain,
% 0.71/0.87 (^[X: $i] : refl(((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ((~type(X, fulladder)) | type(h2(X), halfadder)))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(256,plain,
% 0.71/0.87 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[255])).
% 0.71/0.87 tff(257,plain,
% 0.71/0.87 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(258,axiom,(![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_halfadder2')).
% 0.71/0.87 tff(259,plain,
% 0.71/0.87 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.71/0.87 tff(260,plain,(
% 0.71/0.87 ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 0.71/0.87 inference(skolemize,[status(sab)],[259])).
% 0.71/0.87 tff(261,plain,
% 0.71/0.87 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[260, 256])).
% 0.71/0.87 tff(262,plain,
% 0.71/0.87 (((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | ((~type(v(n1, a), fulladder)) | type(h2(v(n1, a)), halfadder))) <=> ((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | (~type(v(n1, a), fulladder)) | type(h2(v(n1, a)), halfadder))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(263,plain,
% 0.71/0.87 ((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | ((~type(v(n1, a), fulladder)) | type(h2(v(n1, a)), halfadder))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(264,plain,
% 0.71/0.87 ((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | (~type(v(n1, a), fulladder)) | type(h2(v(n1, a)), halfadder)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.71/0.87 tff(265,plain,
% 0.71/0.87 (type(h2(v(n1, a)), halfadder)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[264, 261, 47])).
% 0.71/0.87 tff(266,plain,
% 0.71/0.87 (^[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)))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(267,plain,
% 0.71/0.87 (![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))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[266])).
% 0.71/0.87 tff(268,plain,
% 0.71/0.87 (![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))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(269,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')).
% 0.71/0.87 tff(270,plain,
% 0.71/0.87 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.71/0.87 tff(271,plain,(
% 0.71/0.87 ![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 0.71/0.87 inference(skolemize,[status(sab)],[270])).
% 0.71/0.87 tff(272,plain,
% 0.71/0.87 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[271, 267])).
% 0.71/0.87 tff(273,plain,
% 0.71/0.87 (((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h2(v(n1, a)), halfadder)) | connection(in(n1, h2(v(n1, a))), in(n1, and2(h2(v(n1, a))))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h2(v(n1, a)), halfadder)) | connection(in(n1, h2(v(n1, a))), in(n1, and2(h2(v(n1, a))))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(274,plain,
% 0.71/0.87 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h2(v(n1, a)), halfadder)) | connection(in(n1, h2(v(n1, a))), in(n1, and2(h2(v(n1, a))))))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(275,plain,
% 0.71/0.87 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h2(v(n1, a)), halfadder)) | connection(in(n1, h2(v(n1, a))), in(n1, and2(h2(v(n1, a)))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.71/0.87 tff(276,plain,
% 0.71/0.87 ((~type(h2(v(n1, a)), halfadder)) | connection(in(n1, h2(v(n1, a))), in(n1, and2(h2(v(n1, a)))))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[275, 272])).
% 0.71/0.87 tff(277,plain,
% 0.71/0.87 (connection(in(n1, h2(v(n1, a))), in(n1, and2(h2(v(n1, a)))))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[276, 265])).
% 0.71/0.87 tff(278,plain,
% 0.71/0.87 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(n1, h2(v(n1, a))), n0)) | value(in(n1, and2(h2(v(n1, a)))), n0) | (~connection(in(n1, h2(v(n1, a))), in(n1, and2(h2(v(n1, a)))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n1, h2(v(n1, a))), n0)) | value(in(n1, and2(h2(v(n1, a)))), n0) | (~connection(in(n1, h2(v(n1, a))), in(n1, and2(h2(v(n1, a)))))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(279,plain,
% 0.71/0.87 ((value(in(n1, and2(h2(v(n1, a)))), n0) | (~value(in(n1, h2(v(n1, a))), n0)) | (~connection(in(n1, h2(v(n1, a))), in(n1, and2(h2(v(n1, a))))))) <=> ((~value(in(n1, h2(v(n1, a))), n0)) | value(in(n1, and2(h2(v(n1, a)))), n0) | (~connection(in(n1, h2(v(n1, a))), in(n1, and2(h2(v(n1, a)))))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(280,plain,
% 0.71/0.87 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, and2(h2(v(n1, a)))), n0) | (~value(in(n1, h2(v(n1, a))), n0)) | (~connection(in(n1, h2(v(n1, a))), in(n1, and2(h2(v(n1, a)))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | ((~value(in(n1, h2(v(n1, a))), n0)) | value(in(n1, and2(h2(v(n1, a)))), n0) | (~connection(in(n1, h2(v(n1, a))), in(n1, and2(h2(v(n1, a))))))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[279])).
% 0.71/0.87 tff(281,plain,
% 0.71/0.87 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, and2(h2(v(n1, a)))), n0) | (~value(in(n1, h2(v(n1, a))), n0)) | (~connection(in(n1, h2(v(n1, a))), in(n1, and2(h2(v(n1, a)))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n1, h2(v(n1, a))), n0)) | value(in(n1, and2(h2(v(n1, a)))), n0) | (~connection(in(n1, h2(v(n1, a))), in(n1, and2(h2(v(n1, a)))))))),
% 0.72/0.87 inference(transitivity,[status(thm)],[280, 278])).
% 0.72/0.87 tff(282,plain,
% 0.72/0.87 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(in(n1, and2(h2(v(n1, a)))), n0) | (~value(in(n1, h2(v(n1, a))), n0)) | (~connection(in(n1, h2(v(n1, a))), in(n1, and2(h2(v(n1, a)))))))),
% 0.72/0.87 inference(quant_inst,[status(thm)],[])).
% 0.72/0.87 tff(283,plain,
% 0.72/0.87 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (~value(in(n1, h2(v(n1, a))), n0)) | value(in(n1, and2(h2(v(n1, a)))), n0) | (~connection(in(n1, h2(v(n1, a))), in(n1, and2(h2(v(n1, a))))))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.72/0.87 tff(284,plain,
% 0.72/0.87 ($false),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[283, 29, 277, 254, 213])).
% 0.72/0.87 tff(285,plain,(value(in(n1, and2(h2(v(n1, a)))), n0)), inference(lemma,lemma(discharge,[]))).
% 0.72/0.87 tff(286,plain,
% 0.72/0.87 (((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h2(v(n1, a)), halfadder)) | type(and2(h2(v(n1, a))), and))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h2(v(n1, a)), halfadder)) | type(and2(h2(v(n1, a))), and))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(287,plain,
% 0.72/0.87 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h2(v(n1, a)), halfadder)) | type(and2(h2(v(n1, a))), and))),
% 0.72/0.87 inference(quant_inst,[status(thm)],[])).
% 0.72/0.87 tff(288,plain,
% 0.72/0.87 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h2(v(n1, a)), halfadder)) | type(and2(h2(v(n1, a))), and)),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.72/0.87 tff(289,plain,
% 0.72/0.87 ((~type(h2(v(n1, a)), halfadder)) | type(and2(h2(v(n1, a))), and)),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[288, 104])).
% 0.72/0.87 tff(290,plain,
% 0.72/0.87 (type(and2(h2(v(n1, a))), and)),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[289, 265])).
% 0.72/0.87 tff(291,plain,
% 0.72/0.87 ((~mode(and2(h2(v(n1, a))), abnormal)) <=> (~mode(and2(h2(v(n1, a))), abnormal))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(292,axiom,(~mode(and2(h2(v(n1, a))), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_and2h2v1')).
% 0.72/0.87 tff(293,plain,
% 0.72/0.87 (~mode(and2(h2(v(n1, a))), abnormal)),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.72/0.87 tff(294,plain,
% 0.72/0.87 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h2(v(n1, a))), abnormal) | mode(and2(h2(v(n1, a))), ok) | (~type(and2(h2(v(n1, a))), and)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h2(v(n1, a))), abnormal) | mode(and2(h2(v(n1, a))), ok) | (~type(and2(h2(v(n1, a))), and)))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(295,plain,
% 0.72/0.87 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h2(v(n1, a))), abnormal) | mode(and2(h2(v(n1, a))), ok) | (~type(and2(h2(v(n1, a))), and)))),
% 0.72/0.87 inference(quant_inst,[status(thm)],[])).
% 0.72/0.87 tff(296,plain,
% 0.72/0.87 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h2(v(n1, a))), abnormal) | mode(and2(h2(v(n1, a))), ok) | (~type(and2(h2(v(n1, a))), and))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.72/0.87 tff(297,plain,
% 0.72/0.87 (mode(and2(h2(v(n1, a))), ok)),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[296, 122, 293, 290])).
% 0.72/0.87 tff(298,plain,
% 0.72/0.87 (((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h2(v(n1, a))), ok)) | value(out(n1, and2(h2(v(n1, a)))), n0) | (~type(and2(h2(v(n1, a))), and)) | (~value(in(n1, and2(h2(v(n1, a)))), n0)))) <=> ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | (~mode(and2(h2(v(n1, a))), ok)) | value(out(n1, and2(h2(v(n1, a)))), n0) | (~type(and2(h2(v(n1, a))), and)) | (~value(in(n1, and2(h2(v(n1, a)))), n0)))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(299,plain,
% 0.72/0.87 (((~mode(and2(h2(v(n1, a))), ok)) | value(out(n1, and2(h2(v(n1, a)))), n0) | (~value(in(n1, and2(h2(v(n1, a)))), n0)) | (~type(and2(h2(v(n1, a))), and))) <=> ((~mode(and2(h2(v(n1, a))), ok)) | value(out(n1, and2(h2(v(n1, a)))), n0) | (~type(and2(h2(v(n1, a))), and)) | (~value(in(n1, and2(h2(v(n1, a)))), n0)))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(300,plain,
% 0.72/0.87 (((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h2(v(n1, a))), ok)) | value(out(n1, and2(h2(v(n1, a)))), n0) | (~value(in(n1, and2(h2(v(n1, a)))), n0)) | (~type(and2(h2(v(n1, a))), and)))) <=> ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h2(v(n1, a))), ok)) | value(out(n1, and2(h2(v(n1, a)))), n0) | (~type(and2(h2(v(n1, a))), and)) | (~value(in(n1, and2(h2(v(n1, a)))), n0))))),
% 0.72/0.87 inference(monotonicity,[status(thm)],[299])).
% 0.72/0.87 tff(301,plain,
% 0.72/0.87 (((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h2(v(n1, a))), ok)) | value(out(n1, and2(h2(v(n1, a)))), n0) | (~value(in(n1, and2(h2(v(n1, a)))), n0)) | (~type(and2(h2(v(n1, a))), and)))) <=> ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | (~mode(and2(h2(v(n1, a))), ok)) | value(out(n1, and2(h2(v(n1, a)))), n0) | (~type(and2(h2(v(n1, a))), and)) | (~value(in(n1, and2(h2(v(n1, a)))), n0)))),
% 0.72/0.87 inference(transitivity,[status(thm)],[300, 298])).
% 0.72/0.87 tff(302,plain,
% 0.72/0.87 ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | ((~mode(and2(h2(v(n1, a))), ok)) | value(out(n1, and2(h2(v(n1, a)))), n0) | (~value(in(n1, and2(h2(v(n1, a)))), n0)) | (~type(and2(h2(v(n1, a))), and)))),
% 0.72/0.87 inference(quant_inst,[status(thm)],[])).
% 0.72/0.87 tff(303,plain,
% 0.72/0.87 ((~![Any: $i, K: $i] : ((~mode(K, ok)) | value(out(n1, K), n0) | (~value(in(Any, K), n0)) | (~type(K, and)))) | (~mode(and2(h2(v(n1, a))), ok)) | value(out(n1, and2(h2(v(n1, a)))), n0) | (~type(and2(h2(v(n1, a))), and)) | (~value(in(n1, and2(h2(v(n1, a)))), n0))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.72/0.87 tff(304,plain,
% 0.72/0.87 ((~mode(and2(h2(v(n1, a))), ok)) | value(out(n1, and2(h2(v(n1, a)))), n0) | (~value(in(n1, and2(h2(v(n1, a)))), n0))),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[303, 136, 290])).
% 0.72/0.87 tff(305,plain,
% 0.72/0.87 (value(out(n1, and2(h2(v(n1, a)))), n0) | (~value(in(n1, and2(h2(v(n1, a)))), n0))),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[304, 297])).
% 0.72/0.87 tff(306,plain,
% 0.72/0.87 (value(out(n1, and2(h2(v(n1, a)))), n0)),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[305, 285])).
% 0.72/0.87 tff(307,plain,
% 0.72/0.87 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h2(v(n1, a)), halfadder)) | connection(out(c, h2(v(n1, a))), out(n1, and2(h2(v(n1, a))))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h2(v(n1, a)), halfadder)) | connection(out(c, h2(v(n1, a))), out(n1, and2(h2(v(n1, a))))))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(308,plain,
% 0.72/0.87 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h2(v(n1, a)), halfadder)) | connection(out(c, h2(v(n1, a))), out(n1, and2(h2(v(n1, a))))))),
% 0.72/0.87 inference(quant_inst,[status(thm)],[])).
% 0.72/0.87 tff(309,plain,
% 0.72/0.87 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h2(v(n1, a)), halfadder)) | connection(out(c, h2(v(n1, a))), out(n1, and2(h2(v(n1, a)))))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.72/0.87 tff(310,plain,
% 0.72/0.87 ((~type(h2(v(n1, a)), halfadder)) | connection(out(c, h2(v(n1, a))), out(n1, and2(h2(v(n1, a)))))),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[309, 149])).
% 0.72/0.87 tff(311,plain,
% 0.72/0.87 (connection(out(c, h2(v(n1, a))), out(n1, and2(h2(v(n1, a)))))),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[310, 265])).
% 0.72/0.87 tff(312,plain,
% 0.72/0.87 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(out(n1, and2(h2(v(n1, a)))), n0)) | (~connection(out(c, h2(v(n1, a))), out(n1, and2(h2(v(n1, a)))))) | value(out(c, h2(v(n1, a))), n0))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and2(h2(v(n1, a)))), n0)) | (~connection(out(c, h2(v(n1, a))), out(n1, and2(h2(v(n1, a)))))) | value(out(c, h2(v(n1, a))), n0))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(313,plain,
% 0.72/0.87 ((value(out(c, h2(v(n1, a))), n0) | (~connection(out(c, h2(v(n1, a))), out(n1, and2(h2(v(n1, a)))))) | (~value(out(n1, and2(h2(v(n1, a)))), n0))) <=> ((~value(out(n1, and2(h2(v(n1, a)))), n0)) | (~connection(out(c, h2(v(n1, a))), out(n1, and2(h2(v(n1, a)))))) | value(out(c, h2(v(n1, a))), n0))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(314,plain,
% 0.72/0.87 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(v(n1, a))), n0) | (~connection(out(c, h2(v(n1, a))), out(n1, and2(h2(v(n1, a)))))) | (~value(out(n1, and2(h2(v(n1, a)))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(out(n1, and2(h2(v(n1, a)))), n0)) | (~connection(out(c, h2(v(n1, a))), out(n1, and2(h2(v(n1, a)))))) | value(out(c, h2(v(n1, a))), n0)))),
% 0.72/0.87 inference(monotonicity,[status(thm)],[313])).
% 0.72/0.87 tff(315,plain,
% 0.72/0.87 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(v(n1, a))), n0) | (~connection(out(c, h2(v(n1, a))), out(n1, and2(h2(v(n1, a)))))) | (~value(out(n1, and2(h2(v(n1, a)))), n0)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and2(h2(v(n1, a)))), n0)) | (~connection(out(c, h2(v(n1, a))), out(n1, and2(h2(v(n1, a)))))) | value(out(c, h2(v(n1, a))), n0))),
% 0.72/0.87 inference(transitivity,[status(thm)],[314, 312])).
% 0.72/0.87 tff(316,plain,
% 0.72/0.87 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(v(n1, a))), n0) | (~connection(out(c, h2(v(n1, a))), out(n1, and2(h2(v(n1, a)))))) | (~value(out(n1, and2(h2(v(n1, a)))), n0)))),
% 0.72/0.87 inference(quant_inst,[status(thm)],[])).
% 0.72/0.87 tff(317,plain,
% 0.72/0.87 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(out(n1, and2(h2(v(n1, a)))), n0)) | (~connection(out(c, h2(v(n1, a))), out(n1, and2(h2(v(n1, a)))))) | value(out(c, h2(v(n1, a))), n0)),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.72/0.87 tff(318,plain,
% 0.72/0.87 (value(out(c, h2(v(n1, a))), n0)),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[317, 164, 311, 306])).
% 0.72/0.87 tff(319,plain,
% 0.72/0.87 ((~equal_value(n1, n0)) <=> (~equal_value(n1, n0))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(320,axiom,(~equal_value(n1, n0)), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','equal_value2')).
% 0.72/0.87 tff(321,plain,
% 0.72/0.87 (~equal_value(n1, n0)),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.72/0.87 tff(322,plain,
% 0.72/0.87 (^[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))))),
% 0.72/0.87 inference(bind,[status(th)],[])).
% 0.72/0.87 tff(323,plain,
% 0.72/0.87 (![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)))),
% 0.72/0.87 inference(quant_intro,[status(thm)],[322])).
% 0.72/0.87 tff(324,plain,
% 0.72/0.87 (![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)))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(325,plain,
% 0.72/0.87 (^[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)))))),
% 0.72/0.87 inference(bind,[status(th)],[])).
% 0.72/0.87 tff(326,plain,
% 0.72/0.87 (![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)))),
% 0.72/0.87 inference(quant_intro,[status(thm)],[325])).
% 0.72/0.87 tff(327,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')).
% 0.72/0.87 tff(328,plain,
% 0.72/0.87 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.72/0.87 tff(329,plain,
% 0.72/0.87 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[328, 324])).
% 0.72/0.88 tff(330,plain,(
% 0.72/0.88 ![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 0.72/0.88 inference(skolemize,[status(sab)],[329])).
% 0.72/0.88 tff(331,plain,
% 0.72/0.88 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[330, 323])).
% 0.72/0.88 tff(332,plain,
% 0.72/0.88 (((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n1, n0) | (~value(out(c, h2(v(n1, a))), n0)) | (~value(out(c, h2(v(n1, a))), n1)))) <=> ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n1, n0) | (~value(out(c, h2(v(n1, a))), n0)) | (~value(out(c, h2(v(n1, a))), n1)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(333,plain,
% 0.72/0.88 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n1, n0) | (~value(out(c, h2(v(n1, a))), n0)) | (~value(out(c, h2(v(n1, a))), n1)))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(334,plain,
% 0.72/0.88 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n1, n0) | (~value(out(c, h2(v(n1, a))), n0)) | (~value(out(c, h2(v(n1, a))), n1))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.72/0.88 tff(335,plain,
% 0.72/0.88 (~value(out(c, h2(v(n1, a))), n1)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[334, 331, 321, 318])).
% 0.72/0.88 tff(336,plain,
% 0.72/0.88 (^[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)))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(337,plain,
% 0.72/0.88 (![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))))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[336])).
% 0.72/0.88 tff(338,plain,
% 0.72/0.88 (![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))))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(339,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')).
% 0.72/0.88 tff(340,plain,
% 0.72/0.88 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.72/0.88 tff(341,plain,(
% 0.72/0.88 ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 0.72/0.88 inference(skolemize,[status(sab)],[340])).
% 0.72/0.88 tff(342,plain,
% 0.72/0.88 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[341, 337])).
% 0.72/0.88 tff(343,plain,
% 0.72/0.88 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | ((~type(v(n1, a), fulladder)) | connection(out(c, h2(v(n1, a))), in(n1, or1(v(n1, a)))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | (~type(v(n1, a), fulladder)) | connection(out(c, h2(v(n1, a))), in(n1, or1(v(n1, a)))))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(344,plain,
% 0.72/0.88 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | ((~type(v(n1, a), fulladder)) | connection(out(c, h2(v(n1, a))), in(n1, or1(v(n1, a)))))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(345,plain,
% 0.72/0.88 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | (~type(v(n1, a), fulladder)) | connection(out(c, h2(v(n1, a))), in(n1, or1(v(n1, a))))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.72/0.88 tff(346,plain,
% 0.72/0.88 (connection(out(c, h2(v(n1, a))), in(n1, or1(v(n1, a))))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[345, 342, 47])).
% 0.72/0.88 tff(347,plain,
% 0.72/0.88 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n1, or1(v(n1, a))), n1)) | value(out(c, h2(v(n1, a))), n1) | (~connection(out(c, h2(v(n1, a))), in(n1, or1(v(n1, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, or1(v(n1, a))), n1)) | value(out(c, h2(v(n1, a))), n1) | (~connection(out(c, h2(v(n1, a))), in(n1, or1(v(n1, a))))))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(348,plain,
% 0.72/0.88 ((value(out(c, h2(v(n1, a))), n1) | (~connection(out(c, h2(v(n1, a))), in(n1, or1(v(n1, a))))) | (~value(in(n1, or1(v(n1, a))), n1))) <=> ((~value(in(n1, or1(v(n1, a))), n1)) | value(out(c, h2(v(n1, a))), n1) | (~connection(out(c, h2(v(n1, a))), in(n1, or1(v(n1, a))))))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(349,plain,
% 0.72/0.88 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(v(n1, a))), n1) | (~connection(out(c, h2(v(n1, a))), in(n1, or1(v(n1, a))))) | (~value(in(n1, or1(v(n1, a))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n1, or1(v(n1, a))), n1)) | value(out(c, h2(v(n1, a))), n1) | (~connection(out(c, h2(v(n1, a))), in(n1, or1(v(n1, a)))))))),
% 0.72/0.88 inference(monotonicity,[status(thm)],[348])).
% 0.72/0.88 tff(350,plain,
% 0.72/0.88 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(v(n1, a))), n1) | (~connection(out(c, h2(v(n1, a))), in(n1, or1(v(n1, a))))) | (~value(in(n1, or1(v(n1, a))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, or1(v(n1, a))), n1)) | value(out(c, h2(v(n1, a))), n1) | (~connection(out(c, h2(v(n1, a))), in(n1, or1(v(n1, a))))))),
% 0.72/0.88 inference(transitivity,[status(thm)],[349, 347])).
% 0.72/0.88 tff(351,plain,
% 0.72/0.88 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(v(n1, a))), n1) | (~connection(out(c, h2(v(n1, a))), in(n1, or1(v(n1, a))))) | (~value(in(n1, or1(v(n1, a))), n1)))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(352,plain,
% 0.72/0.88 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, or1(v(n1, a))), n1)) | value(out(c, h2(v(n1, a))), n1) | (~connection(out(c, h2(v(n1, a))), in(n1, or1(v(n1, a)))))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[351, 350])).
% 0.72/0.88 tff(353,plain,
% 0.72/0.88 (~value(in(n1, or1(v(n1, a))), n1)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[352, 164, 346, 335])).
% 0.72/0.88 tff(354,plain,
% 0.72/0.88 (^[X: $i] : refl(((~type(X, fulladder)) | type(or1(X), or)) <=> ((~type(X, fulladder)) | type(or1(X), or)))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(355,plain,
% 0.72/0.88 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[354])).
% 0.72/0.88 tff(356,plain,
% 0.72/0.88 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(357,axiom,(![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_or1')).
% 0.72/0.88 tff(358,plain,
% 0.72/0.88 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.72/0.88 tff(359,plain,(
% 0.72/0.88 ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 0.72/0.88 inference(skolemize,[status(sab)],[358])).
% 0.72/0.88 tff(360,plain,
% 0.72/0.88 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[359, 355])).
% 0.72/0.88 tff(361,plain,
% 0.72/0.88 (((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | ((~type(v(n1, a), fulladder)) | type(or1(v(n1, a)), or))) <=> ((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | (~type(v(n1, a), fulladder)) | type(or1(v(n1, a)), or))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(362,plain,
% 0.72/0.88 ((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | ((~type(v(n1, a), fulladder)) | type(or1(v(n1, a)), or))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(363,plain,
% 0.72/0.88 ((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | (~type(v(n1, a), fulladder)) | type(or1(v(n1, a)), or)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.72/0.88 tff(364,plain,
% 0.72/0.88 (type(or1(v(n1, a)), or)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[363, 360, 47])).
% 0.72/0.88 tff(365,plain,
% 0.72/0.88 ((~mode(or1(v(n1, a)), abnormal)) <=> (~mode(or1(v(n1, a)), abnormal))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(366,axiom,(~mode(or1(v(n1, a)), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_or1v1')).
% 0.72/0.88 tff(367,plain,
% 0.72/0.88 (~mode(or1(v(n1, a)), abnormal)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.72/0.88 tff(368,plain,
% 0.72/0.88 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(or1(v(n1, a)), abnormal) | mode(or1(v(n1, a)), ok) | (~type(or1(v(n1, a)), or)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(or1(v(n1, a)), abnormal) | mode(or1(v(n1, a)), ok) | (~type(or1(v(n1, a)), or)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(369,plain,
% 0.72/0.88 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(or1(v(n1, a)), abnormal) | mode(or1(v(n1, a)), ok) | (~type(or1(v(n1, a)), or)))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(370,plain,
% 0.72/0.88 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(or1(v(n1, a)), abnormal) | mode(or1(v(n1, a)), ok) | (~type(or1(v(n1, a)), or))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.72/0.88 tff(371,plain,
% 0.72/0.88 (mode(or1(v(n1, a)), ok)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[370, 122, 367, 364])).
% 0.72/0.88 tff(372,plain,
% 0.72/0.88 (^[K: $i] : refl(((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(373,plain,
% 0.72/0.88 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or))) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[372])).
% 0.72/0.88 tff(374,plain,
% 0.72/0.88 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or))) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(375,plain,
% 0.72/0.88 (^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, or)))), (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, or))) | value(in(n1, K), n1)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, or))) | value(in(n1, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n1) | (~type(K, or)))), (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n1) | (~type(K, or))))), ((((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) | value(in(n2, K), n1)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n1) | (~type(K, or))) | value(in(n2, K), n1)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n1) | (~type(K, or))) | value(in(n2, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))), ((((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) | value(in(n2, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(376,plain,
% 0.72/0.88 (![K: $i] : (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) | value(in(n2, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[375])).
% 0.72/0.88 tff(377,axiom,(![K: $i] : (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) | value(in(n2, K), n1))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','or_1_11')).
% 0.72/0.88 tff(378,plain,
% 0.72/0.88 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.72/0.88 tff(379,plain,
% 0.72/0.88 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[378, 374])).
% 0.72/0.88 tff(380,plain,(
% 0.72/0.88 ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 0.72/0.88 inference(skolemize,[status(sab)],[379])).
% 0.72/0.88 tff(381,plain,
% 0.72/0.88 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[380, 373])).
% 0.72/0.88 tff(382,plain,
% 0.72/0.88 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))) | ((~mode(or1(v(n1, a)), ok)) | value(in(n1, or1(v(n1, a))), n1) | (~type(or1(v(n1, a)), or)) | (~value(out(n1, or1(v(n1, a))), n1)) | value(in(n2, or1(v(n1, a))), n1))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))) | (~mode(or1(v(n1, a)), ok)) | value(in(n1, or1(v(n1, a))), n1) | (~type(or1(v(n1, a)), or)) | (~value(out(n1, or1(v(n1, a))), n1)) | value(in(n2, or1(v(n1, a))), n1))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(383,plain,
% 0.72/0.88 (((~mode(or1(v(n1, a)), ok)) | (~value(out(n1, or1(v(n1, a))), n1)) | value(in(n2, or1(v(n1, a))), n1) | value(in(n1, or1(v(n1, a))), n1) | (~type(or1(v(n1, a)), or))) <=> ((~mode(or1(v(n1, a)), ok)) | value(in(n1, or1(v(n1, a))), n1) | (~type(or1(v(n1, a)), or)) | (~value(out(n1, or1(v(n1, a))), n1)) | value(in(n2, or1(v(n1, a))), n1))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(384,plain,
% 0.72/0.88 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))) | ((~mode(or1(v(n1, a)), ok)) | (~value(out(n1, or1(v(n1, a))), n1)) | value(in(n2, or1(v(n1, a))), n1) | value(in(n1, or1(v(n1, a))), n1) | (~type(or1(v(n1, a)), or)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))) | ((~mode(or1(v(n1, a)), ok)) | value(in(n1, or1(v(n1, a))), n1) | (~type(or1(v(n1, a)), or)) | (~value(out(n1, or1(v(n1, a))), n1)) | value(in(n2, or1(v(n1, a))), n1)))),
% 0.72/0.88 inference(monotonicity,[status(thm)],[383])).
% 0.72/0.88 tff(385,plain,
% 0.72/0.88 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))) | ((~mode(or1(v(n1, a)), ok)) | (~value(out(n1, or1(v(n1, a))), n1)) | value(in(n2, or1(v(n1, a))), n1) | value(in(n1, or1(v(n1, a))), n1) | (~type(or1(v(n1, a)), or)))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))) | (~mode(or1(v(n1, a)), ok)) | value(in(n1, or1(v(n1, a))), n1) | (~type(or1(v(n1, a)), or)) | (~value(out(n1, or1(v(n1, a))), n1)) | value(in(n2, or1(v(n1, a))), n1))),
% 0.72/0.88 inference(transitivity,[status(thm)],[384, 382])).
% 0.72/0.88 tff(386,plain,
% 0.72/0.88 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))) | ((~mode(or1(v(n1, a)), ok)) | (~value(out(n1, or1(v(n1, a))), n1)) | value(in(n2, or1(v(n1, a))), n1) | value(in(n1, or1(v(n1, a))), n1) | (~type(or1(v(n1, a)), or)))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(387,plain,
% 0.72/0.88 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))) | (~mode(or1(v(n1, a)), ok)) | value(in(n1, or1(v(n1, a))), n1) | (~type(or1(v(n1, a)), or)) | (~value(out(n1, or1(v(n1, a))), n1)) | value(in(n2, or1(v(n1, a))), n1)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.72/0.88 tff(388,plain,
% 0.72/0.88 ((~mode(or1(v(n1, a)), ok)) | value(in(n1, or1(v(n1, a))), n1) | (~value(out(n1, or1(v(n1, a))), n1)) | value(in(n2, or1(v(n1, a))), n1)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[387, 381, 364])).
% 0.72/0.88 tff(389,plain,
% 0.72/0.88 (value(in(n1, or1(v(n1, a))), n1) | (~value(out(n1, or1(v(n1, a))), n1)) | value(in(n2, or1(v(n1, a))), n1)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[388, 371])).
% 0.72/0.88 tff(390,plain,
% 0.72/0.88 ((~value(out(n1, or1(v(n1, a))), n1)) | value(in(n2, or1(v(n1, a))), n1)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[389, 353])).
% 0.72/0.88 tff(391,plain,
% 0.72/0.88 (value(in(n2, or1(v(n1, a))), n1)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[390, 212])).
% 0.72/0.88 tff(392,plain,
% 0.72/0.88 (^[X: $i] : refl(((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X)))) <=> ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X)))))),
% 0.72/0.88 inference(bind,[status(th)],[])).
% 0.72/0.88 tff(393,plain,
% 0.72/0.88 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 0.72/0.88 inference(quant_intro,[status(thm)],[392])).
% 0.72/0.88 tff(394,plain,
% 0.72/0.88 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(395,axiom,(![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_connection_outch1_in2or1')).
% 0.72/0.88 tff(396,plain,
% 0.72/0.88 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.72/0.88 tff(397,plain,(
% 0.72/0.88 ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 0.72/0.88 inference(skolemize,[status(sab)],[396])).
% 0.72/0.88 tff(398,plain,
% 0.72/0.88 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[397, 393])).
% 0.72/0.88 tff(399,plain,
% 0.72/0.88 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))) | ((~type(v(n1, a), fulladder)) | connection(out(c, h1(v(n1, a))), in(n2, or1(v(n1, a)))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))) | (~type(v(n1, a), fulladder)) | connection(out(c, h1(v(n1, a))), in(n2, or1(v(n1, a)))))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(400,plain,
% 0.72/0.88 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))) | ((~type(v(n1, a), fulladder)) | connection(out(c, h1(v(n1, a))), in(n2, or1(v(n1, a)))))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(401,plain,
% 0.72/0.88 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))) | (~type(v(n1, a), fulladder)) | connection(out(c, h1(v(n1, a))), in(n2, or1(v(n1, a))))),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.72/0.88 tff(402,plain,
% 0.72/0.88 (connection(out(c, h1(v(n1, a))), in(n2, or1(v(n1, a))))),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[401, 398, 47])).
% 0.72/0.88 tff(403,plain,
% 0.72/0.88 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n2, or1(v(n1, a))), n1)) | (~connection(out(c, h1(v(n1, a))), in(n2, or1(v(n1, a))))) | value(out(c, h1(v(n1, a))), n1))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, or1(v(n1, a))), n1)) | (~connection(out(c, h1(v(n1, a))), in(n2, or1(v(n1, a))))) | value(out(c, h1(v(n1, a))), n1))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(404,plain,
% 0.72/0.88 ((value(out(c, h1(v(n1, a))), n1) | (~connection(out(c, h1(v(n1, a))), in(n2, or1(v(n1, a))))) | (~value(in(n2, or1(v(n1, a))), n1))) <=> ((~value(in(n2, or1(v(n1, a))), n1)) | (~connection(out(c, h1(v(n1, a))), in(n2, or1(v(n1, a))))) | value(out(c, h1(v(n1, a))), n1))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(405,plain,
% 0.72/0.88 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h1(v(n1, a))), n1) | (~connection(out(c, h1(v(n1, a))), in(n2, or1(v(n1, a))))) | (~value(in(n2, or1(v(n1, a))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n2, or1(v(n1, a))), n1)) | (~connection(out(c, h1(v(n1, a))), in(n2, or1(v(n1, a))))) | value(out(c, h1(v(n1, a))), n1)))),
% 0.72/0.88 inference(monotonicity,[status(thm)],[404])).
% 0.72/0.88 tff(406,plain,
% 0.72/0.88 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h1(v(n1, a))), n1) | (~connection(out(c, h1(v(n1, a))), in(n2, or1(v(n1, a))))) | (~value(in(n2, or1(v(n1, a))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, or1(v(n1, a))), n1)) | (~connection(out(c, h1(v(n1, a))), in(n2, or1(v(n1, a))))) | value(out(c, h1(v(n1, a))), n1))),
% 0.72/0.88 inference(transitivity,[status(thm)],[405, 403])).
% 0.72/0.88 tff(407,plain,
% 0.72/0.88 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h1(v(n1, a))), n1) | (~connection(out(c, h1(v(n1, a))), in(n2, or1(v(n1, a))))) | (~value(in(n2, or1(v(n1, a))), n1)))),
% 0.72/0.88 inference(quant_inst,[status(thm)],[])).
% 0.72/0.88 tff(408,plain,
% 0.72/0.88 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, or1(v(n1, a))), n1)) | (~connection(out(c, h1(v(n1, a))), in(n2, or1(v(n1, a))))) | value(out(c, h1(v(n1, a))), n1)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.72/0.88 tff(409,plain,
% 0.72/0.88 (value(out(c, h1(v(n1, a))), n1)),
% 0.72/0.88 inference(unit_resolution,[status(thm)],[408, 164, 402, 391])).
% 0.72/0.88 tff(410,plain,
% 0.72/0.88 ((~equal_value(n0, n1)) <=> (~equal_value(n0, n1))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(411,axiom,(~equal_value(n0, n1)), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','equal_value1')).
% 0.72/0.88 tff(412,plain,
% 0.72/0.88 (~equal_value(n0, n1)),
% 0.72/0.88 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.72/0.88 tff(413,plain,
% 0.72/0.88 (((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(out(c, h1(v(n1, a))), n0)) | (~value(out(c, h1(v(n1, a))), n1)))) <=> ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n0, n1) | (~value(out(c, h1(v(n1, a))), n0)) | (~value(out(c, h1(v(n1, a))), n1)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(414,plain,
% 0.72/0.88 ((equal_value(n0, n1) | (~value(out(c, h1(v(n1, a))), n1)) | (~value(out(c, h1(v(n1, a))), n0))) <=> (equal_value(n0, n1) | (~value(out(c, h1(v(n1, a))), n0)) | (~value(out(c, h1(v(n1, a))), n1)))),
% 0.72/0.88 inference(rewrite,[status(thm)],[])).
% 0.72/0.88 tff(415,plain,
% 0.72/0.88 (((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(out(c, h1(v(n1, a))), n1)) | (~value(out(c, h1(v(n1, a))), n0)))) <=> ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(out(c, h1(v(n1, a))), n0)) | (~value(out(c, h1(v(n1, a))), n1))))),
% 0.72/0.88 inference(monotonicity,[status(thm)],[414])).
% 0.72/0.88 tff(416,plain,
% 0.72/0.88 (((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(out(c, h1(v(n1, a))), n1)) | (~value(out(c, h1(v(n1, a))), n0)))) <=> ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n0, n1) | (~value(out(c, h1(v(n1, a))), n0)) | (~value(out(c, h1(v(n1, a))), n1)))),
% 0.72/0.89 inference(transitivity,[status(thm)],[415, 413])).
% 0.72/0.89 tff(417,plain,
% 0.72/0.89 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n0, n1) | (~value(out(c, h1(v(n1, a))), n1)) | (~value(out(c, h1(v(n1, a))), n0)))),
% 0.72/0.89 inference(quant_inst,[status(thm)],[])).
% 0.72/0.89 tff(418,plain,
% 0.72/0.89 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n0, n1) | (~value(out(c, h1(v(n1, a))), n0)) | (~value(out(c, h1(v(n1, a))), n1))),
% 0.72/0.89 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.72/0.89 tff(419,plain,
% 0.72/0.89 ($false),
% 0.72/0.89 inference(unit_resolution,[status(thm)],[418, 331, 412, 409, 171])).
% 0.72/0.89 % SZS output end Proof
% 0.72/0.89 % E exiting
%------------------------------------------------------------------------------