%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV008-1.002 : TPTP v9.0.0. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:08:53 AM UTC 2025
% Result : Unsatisfiable 2.14s 2.32s
% Output : Proof 2.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : HWV008-1.002 : TPTP v9.0.0. Bugfixed v2.2.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 17:23:04 EDT 2025
% 0.13/0.35 % CPUTime :
% 2.14/2.32 % SZS status Unsatisfiable
% 2.14/2.32 % SZS output start Proof
% 2.14/2.32 tff(value_type, type, (
% 2.14/2.32 value: ( $i * $i ) > $o)).
% 2.14/2.32 tff(n1_type, type, (
% 2.14/2.32 n1: $i)).
% 2.14/2.32 tff(out_type, type, (
% 2.14/2.32 out: ( $i * $i ) > $i)).
% 2.14/2.32 tff(h2_type, type, (
% 2.14/2.32 h2: $i > $i)).
% 2.14/2.32 tff(f_type, type, (
% 2.14/2.32 f: ( $i * $i ) > $i)).
% 2.14/2.32 tff(a_type, type, (
% 2.14/2.32 a: $i)).
% 2.14/2.32 tff(n2_type, type, (
% 2.14/2.32 n2: $i)).
% 2.14/2.32 tff(c_type, type, (
% 2.14/2.32 c: $i)).
% 2.14/2.32 tff(in_type, type, (
% 2.14/2.32 in: ( $i * $i ) > $i)).
% 2.14/2.32 tff(or1_type, type, (
% 2.14/2.32 or1: $i > $i)).
% 2.14/2.32 tff(h1_type, type, (
% 2.14/2.32 h1: $i > $i)).
% 2.14/2.32 tff(and2_type, type, (
% 2.14/2.32 and2: $i > $i)).
% 2.14/2.32 tff(mode_type, type, (
% 2.14/2.32 mode: ( $i * $i ) > $o)).
% 2.14/2.32 tff(ok_type, type, (
% 2.14/2.32 ok: $i)).
% 2.14/2.32 tff(type_type, type, (
% 2.14/2.32 type: ( $i * $i ) > $o)).
% 2.14/2.32 tff(and_type, type, (
% 2.14/2.32 and: $i)).
% 2.14/2.32 tff(halfadder_type, type, (
% 2.14/2.32 halfadder: $i)).
% 2.14/2.32 tff(fulladder_type, type, (
% 2.14/2.32 fulladder: $i)).
% 2.14/2.32 tff(nbit_adder_type, type, (
% 2.14/2.32 nbit_adder: $i > $i)).
% 2.14/2.32 tff(abnormal_type, type, (
% 2.14/2.32 abnormal: $i)).
% 2.14/2.32 tff(connection_type, type, (
% 2.14/2.32 connection: ( $i * $i ) > $o)).
% 2.14/2.32 tff(b2_type, type, (
% 2.14/2.32 b2: $i)).
% 2.14/2.32 tff(n0_type, type, (
% 2.14/2.32 n0: $i)).
% 2.14/2.32 tff(equal_value_type, type, (
% 2.14/2.32 equal_value: ( $i * $i ) > $o)).
% 2.14/2.32 tff(or_type, type, (
% 2.14/2.32 or: $i)).
% 2.14/2.32 tff(a2_type, type, (
% 2.14/2.32 a2: $i)).
% 2.14/2.32 tff(1,assumption,(value(out(c, h1(f(n2, a))), n1)), introduced(assumption)).
% 2.14/2.32 tff(2,plain,
% 2.14/2.32 (type(a, nbit_adder(n2)) <=> type(a, nbit_adder(n2))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(3,axiom,(type(a, nbit_adder(n2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_isa_2bit_adder')).
% 2.14/2.32 tff(4,plain,
% 2.14/2.32 (type(a, nbit_adder(n2))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[3, 2])).
% 2.14/2.32 tff(5,plain,
% 2.14/2.32 (^[X: $i] : refl(((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder)) <=> ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder)))),
% 2.14/2.32 inference(bind,[status(th)],[])).
% 2.14/2.32 tff(6,plain,
% 2.14/2.32 (![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder)) <=> ![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))),
% 2.14/2.32 inference(quant_intro,[status(thm)],[5])).
% 2.14/2.32 tff(7,plain,
% 2.14/2.32 (![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder)) <=> ![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(8,axiom,(![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nbit_adder_fulladder2')).
% 2.14/2.32 tff(9,plain,
% 2.14/2.32 (![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[8, 7])).
% 2.14/2.32 tff(10,plain,(
% 2.14/2.32 ![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))),
% 2.14/2.32 inference(skolemize,[status(sab)],[9])).
% 2.14/2.32 tff(11,plain,
% 2.14/2.32 (![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[10, 6])).
% 2.14/2.32 tff(12,plain,
% 2.14/2.32 (((~![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))) | ((~type(a, nbit_adder(n2))) | type(f(n2, a), fulladder))) <=> ((~![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))) | (~type(a, nbit_adder(n2))) | type(f(n2, a), fulladder))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(13,plain,
% 2.14/2.32 ((~![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))) | ((~type(a, nbit_adder(n2))) | type(f(n2, a), fulladder))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(14,plain,
% 2.14/2.32 ((~![X: $i] : ((~type(X, nbit_adder(n2))) | type(f(n2, X), fulladder))) | (~type(a, nbit_adder(n2))) | type(f(n2, a), fulladder)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[13, 12])).
% 2.14/2.32 tff(15,plain,
% 2.14/2.32 (type(f(n2, a), fulladder)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[14, 11, 4])).
% 2.14/2.32 tff(16,plain,
% 2.14/2.32 (^[X: $i] : refl(((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ((~type(X, fulladder)) | type(h1(X), halfadder)))),
% 2.14/2.32 inference(bind,[status(th)],[])).
% 2.14/2.32 tff(17,plain,
% 2.14/2.32 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 2.14/2.32 inference(quant_intro,[status(thm)],[16])).
% 2.14/2.32 tff(18,plain,
% 2.14/2.32 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(19,axiom,(![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_halfadder1')).
% 2.14/2.32 tff(20,plain,
% 2.14/2.32 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[19, 18])).
% 2.14/2.32 tff(21,plain,(
% 2.14/2.32 ![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 2.14/2.32 inference(skolemize,[status(sab)],[20])).
% 2.14/2.32 tff(22,plain,
% 2.14/2.32 (![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[21, 17])).
% 2.14/2.32 tff(23,plain,
% 2.14/2.32 (((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | ((~type(f(n2, a), fulladder)) | type(h1(f(n2, a)), halfadder))) <=> ((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | (~type(f(n2, a), fulladder)) | type(h1(f(n2, a)), halfadder))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(24,plain,
% 2.14/2.32 ((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | ((~type(f(n2, a), fulladder)) | type(h1(f(n2, a)), halfadder))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(25,plain,
% 2.14/2.32 ((~![X: $i] : ((~type(X, fulladder)) | type(h1(X), halfadder))) | (~type(f(n2, a), fulladder)) | type(h1(f(n2, a)), halfadder)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[24, 23])).
% 2.14/2.32 tff(26,plain,
% 2.14/2.32 (type(h1(f(n2, a)), halfadder)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[25, 22, 15])).
% 2.14/2.32 tff(27,plain,
% 2.14/2.32 (^[X: $i] : refl(((~type(X, halfadder)) | type(and2(X), and)) <=> ((~type(X, halfadder)) | type(and2(X), and)))),
% 2.14/2.32 inference(bind,[status(th)],[])).
% 2.14/2.32 tff(28,plain,
% 2.14/2.32 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 2.14/2.32 inference(quant_intro,[status(thm)],[27])).
% 2.14/2.32 tff(29,plain,
% 2.14/2.32 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and)) <=> ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(30,axiom,(![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_and2')).
% 2.14/2.32 tff(31,plain,
% 2.14/2.32 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[30, 29])).
% 2.14/2.32 tff(32,plain,(
% 2.14/2.32 ![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 2.14/2.32 inference(skolemize,[status(sab)],[31])).
% 2.14/2.32 tff(33,plain,
% 2.14/2.32 (![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[32, 28])).
% 2.14/2.32 tff(34,plain,
% 2.14/2.32 (((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h1(f(n2, a)), halfadder)) | type(and2(h1(f(n2, a))), and))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h1(f(n2, a)), halfadder)) | type(and2(h1(f(n2, a))), and))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(35,plain,
% 2.14/2.32 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h1(f(n2, a)), halfadder)) | type(and2(h1(f(n2, a))), and))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(36,plain,
% 2.14/2.32 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h1(f(n2, a)), halfadder)) | type(and2(h1(f(n2, a))), and)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[35, 34])).
% 2.14/2.32 tff(37,plain,
% 2.14/2.32 ((~type(h1(f(n2, a)), halfadder)) | type(and2(h1(f(n2, a))), and)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[36, 33])).
% 2.14/2.32 tff(38,plain,
% 2.14/2.32 (type(and2(h1(f(n2, a))), and)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[37, 26])).
% 2.14/2.32 tff(39,plain,
% 2.14/2.32 ((~mode(and2(h1(f(n2, a))), abnormal)) <=> (~mode(and2(h1(f(n2, a))), abnormal))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(40,axiom,(~mode(and2(h1(f(n2, a))), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_and2h2f2a')).
% 2.14/2.32 tff(41,plain,
% 2.14/2.32 (~mode(and2(h1(f(n2, a))), abnormal)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[40, 39])).
% 2.14/2.32 tff(42,plain,
% 2.14/2.32 (^[Any: $i, K: $i] : refl((mode(K, abnormal) | mode(K, ok) | (~type(K, Any))) <=> (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))))),
% 2.14/2.32 inference(bind,[status(th)],[])).
% 2.14/2.32 tff(43,plain,
% 2.14/2.32 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))) <=> ![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 2.14/2.32 inference(quant_intro,[status(thm)],[42])).
% 2.14/2.32 tff(44,plain,
% 2.14/2.32 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))) <=> ![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(45,plain,
% 2.14/2.32 (^[Any: $i, K: $i] : rewrite((((~type(K, Any)) | mode(K, ok)) | mode(K, abnormal)) <=> (mode(K, abnormal) | mode(K, ok) | (~type(K, Any))))),
% 2.14/2.32 inference(bind,[status(th)],[])).
% 2.14/2.32 tff(46,plain,
% 2.14/2.32 (![Any: $i, K: $i] : (((~type(K, Any)) | mode(K, ok)) | mode(K, abnormal)) <=> ![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 2.14/2.32 inference(quant_intro,[status(thm)],[45])).
% 2.14/2.32 tff(47,axiom,(![Any: $i, K: $i] : (((~type(K, Any)) | mode(K, ok)) | mode(K, abnormal))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','ok_or_abnormal')).
% 2.14/2.32 tff(48,plain,
% 2.14/2.32 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[47, 46])).
% 2.14/2.32 tff(49,plain,
% 2.14/2.32 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[48, 44])).
% 2.14/2.32 tff(50,plain,(
% 2.14/2.32 ![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 2.14/2.32 inference(skolemize,[status(sab)],[49])).
% 2.14/2.32 tff(51,plain,
% 2.14/2.32 (![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[50, 43])).
% 2.14/2.32 tff(52,plain,
% 2.14/2.32 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h1(f(n2, a))), abnormal) | mode(and2(h1(f(n2, a))), ok) | (~type(and2(h1(f(n2, a))), and)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h1(f(n2, a))), abnormal) | mode(and2(h1(f(n2, a))), ok) | (~type(and2(h1(f(n2, a))), and)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(53,plain,
% 2.14/2.32 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h1(f(n2, a))), abnormal) | mode(and2(h1(f(n2, a))), ok) | (~type(and2(h1(f(n2, a))), and)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(54,plain,
% 2.14/2.32 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h1(f(n2, a))), abnormal) | mode(and2(h1(f(n2, a))), ok) | (~type(and2(h1(f(n2, a))), and))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[53, 52])).
% 2.14/2.32 tff(55,plain,
% 2.14/2.32 (mode(and2(h1(f(n2, a))), ok)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[54, 51, 41, 38])).
% 2.14/2.32 tff(56,plain,
% 2.14/2.32 (^[X: $i] : refl(((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X)))) <=> ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X)))))),
% 2.14/2.32 inference(bind,[status(th)],[])).
% 2.14/2.32 tff(57,plain,
% 2.14/2.32 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))),
% 2.14/2.32 inference(quant_intro,[status(thm)],[56])).
% 2.14/2.32 tff(58,plain,
% 2.14/2.32 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(59,axiom,(![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nbit_adder_connection_inb2_in2f2')).
% 2.14/2.32 tff(60,plain,
% 2.14/2.32 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[59, 58])).
% 2.14/2.32 tff(61,plain,(
% 2.14/2.32 ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))),
% 2.14/2.32 inference(skolemize,[status(sab)],[60])).
% 2.14/2.32 tff(62,plain,
% 2.14/2.32 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[61, 57])).
% 2.14/2.32 tff(63,plain,
% 2.14/2.32 (((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))) | ((~type(a, nbit_adder(n2))) | connection(in(b2, a), in(n2, f(n2, a))))) <=> ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))) | (~type(a, nbit_adder(n2))) | connection(in(b2, a), in(n2, f(n2, a))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(64,plain,
% 2.14/2.32 ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))) | ((~type(a, nbit_adder(n2))) | connection(in(b2, a), in(n2, f(n2, a))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(65,plain,
% 2.14/2.32 ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(b2, X), in(n2, f(n2, X))))) | (~type(a, nbit_adder(n2))) | connection(in(b2, a), in(n2, f(n2, a)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[64, 63])).
% 2.14/2.32 tff(66,plain,
% 2.14/2.32 (connection(in(b2, a), in(n2, f(n2, a)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[65, 62, 4])).
% 2.14/2.32 tff(67,plain,
% 2.14/2.32 (value(in(b2, a), n0) <=> value(in(b2, a), n0)),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(68,axiom,(value(in(b2, a), n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','inb2_0')).
% 2.14/2.32 tff(69,plain,
% 2.14/2.32 (value(in(b2, a), n0)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[68, 67])).
% 2.14/2.32 tff(70,plain,
% 2.14/2.32 ((~equal_value(n1, n0)) <=> (~equal_value(n1, n0))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(71,axiom,(~equal_value(n1, n0)), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','equal_value2')).
% 2.14/2.32 tff(72,plain,
% 2.14/2.32 (~equal_value(n1, n0)),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[71, 70])).
% 2.14/2.32 tff(73,plain,
% 2.14/2.32 (^[P: $i, V1: $i, V2: $i] : refl((equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1))) <=> (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1))))),
% 2.14/2.32 inference(bind,[status(th)],[])).
% 2.14/2.32 tff(74,plain,
% 2.14/2.32 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1))) <=> ![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 2.14/2.32 inference(quant_intro,[status(thm)],[73])).
% 2.14/2.32 tff(75,plain,
% 2.14/2.32 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1))) <=> ![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(76,plain,
% 2.14/2.32 (^[P: $i, V1: $i, V2: $i] : trans(monotonicity(rewrite(((~value(P, V1)) | (~value(P, V2))) <=> ((~value(P, V2)) | (~value(P, V1)))), ((((~value(P, V1)) | (~value(P, V2))) | equal_value(V1, V2)) <=> (((~value(P, V2)) | (~value(P, V1))) | equal_value(V1, V2)))), rewrite((((~value(P, V2)) | (~value(P, V1))) | equal_value(V1, V2)) <=> (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))), ((((~value(P, V1)) | (~value(P, V2))) | equal_value(V1, V2)) <=> (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))))),
% 2.14/2.32 inference(bind,[status(th)],[])).
% 2.14/2.32 tff(77,plain,
% 2.14/2.32 (![P: $i, V1: $i, V2: $i] : (((~value(P, V1)) | (~value(P, V2))) | equal_value(V1, V2)) <=> ![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 2.14/2.32 inference(quant_intro,[status(thm)],[76])).
% 2.14/2.32 tff(78,axiom,(![P: $i, V1: $i, V2: $i] : (((~value(P, V1)) | (~value(P, V2))) | equal_value(V1, V2))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','unique_value')).
% 2.14/2.32 tff(79,plain,
% 2.14/2.32 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[78, 77])).
% 2.14/2.32 tff(80,plain,
% 2.14/2.32 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[79, 75])).
% 2.14/2.32 tff(81,plain,(
% 2.14/2.32 ![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 2.14/2.32 inference(skolemize,[status(sab)],[80])).
% 2.14/2.32 tff(82,plain,
% 2.14/2.32 (![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[81, 74])).
% 2.14/2.32 tff(83,plain,
% 2.14/2.32 (((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n1, n0) | (~value(in(b2, a), n0)) | (~value(in(b2, a), n1)))) <=> ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n1, n0) | (~value(in(b2, a), n0)) | (~value(in(b2, a), n1)))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(84,plain,
% 2.14/2.32 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n1, n0) | (~value(in(b2, a), n0)) | (~value(in(b2, a), n1)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(85,plain,
% 2.14/2.32 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n1, n0) | (~value(in(b2, a), n0)) | (~value(in(b2, a), n1))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[84, 83])).
% 2.14/2.32 tff(86,plain,
% 2.14/2.32 (~value(in(b2, a), n1)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[85, 82, 72, 69])).
% 2.14/2.32 tff(87,plain,
% 2.14/2.32 (^[V: $i, P2: $i, P1: $i] : refl((value(P1, V) | (~connection(P1, P2)) | (~value(P2, V))) <=> (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V))))),
% 2.14/2.32 inference(bind,[status(th)],[])).
% 2.14/2.32 tff(88,plain,
% 2.14/2.32 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V))) <=> ![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 2.14/2.33 inference(quant_intro,[status(thm)],[87])).
% 2.14/2.33 tff(89,plain,
% 2.14/2.33 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V))) <=> ![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(90,plain,
% 2.14/2.33 (^[V: $i, P2: $i, P1: $i] : rewrite((((~connection(P1, P2)) | (~value(P2, V))) | value(P1, V)) <=> (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V))))),
% 2.14/2.33 inference(bind,[status(th)],[])).
% 2.14/2.33 tff(91,plain,
% 2.14/2.33 (![V: $i, P2: $i, P1: $i] : (((~connection(P1, P2)) | (~value(P2, V))) | value(P1, V)) <=> ![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 2.14/2.33 inference(quant_intro,[status(thm)],[90])).
% 2.14/2.33 tff(92,axiom,(![V: $i, P2: $i, P1: $i] : (((~connection(P1, P2)) | (~value(P2, V))) | value(P1, V))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','value_propagation2')).
% 2.14/2.33 tff(93,plain,
% 2.14/2.33 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[92, 91])).
% 2.14/2.33 tff(94,plain,
% 2.14/2.33 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[93, 89])).
% 2.14/2.33 tff(95,plain,(
% 2.14/2.33 ![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 2.14/2.33 inference(skolemize,[status(sab)],[94])).
% 2.14/2.33 tff(96,plain,
% 2.14/2.33 (![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[95, 88])).
% 2.14/2.33 tff(97,plain,
% 2.14/2.33 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(b2, a), n1) | (~connection(in(b2, a), in(n2, f(n2, a)))) | (~value(in(n2, f(n2, a)), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(b2, a), n1) | (~connection(in(b2, a), in(n2, f(n2, a)))) | (~value(in(n2, f(n2, a)), n1)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(98,plain,
% 2.14/2.33 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(b2, a), n1) | (~connection(in(b2, a), in(n2, f(n2, a)))) | (~value(in(n2, f(n2, a)), n1)))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(99,plain,
% 2.14/2.33 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(b2, a), n1) | (~connection(in(b2, a), in(n2, f(n2, a)))) | (~value(in(n2, f(n2, a)), n1))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[98, 97])).
% 2.14/2.33 tff(100,plain,
% 2.14/2.33 (~value(in(n2, f(n2, a)), n1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[99, 96, 86, 66])).
% 2.14/2.33 tff(101,plain,
% 2.14/2.33 (^[X: $i] : refl(((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X)))) <=> ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X)))))),
% 2.14/2.33 inference(bind,[status(th)],[])).
% 2.14/2.33 tff(102,plain,
% 2.14/2.33 (![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 2.14/2.33 inference(quant_intro,[status(thm)],[101])).
% 2.14/2.33 tff(103,plain,
% 2.14/2.33 (![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(104,axiom,(![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_connection_in2_in1h1')).
% 2.14/2.33 tff(105,plain,
% 2.14/2.33 (![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[104, 103])).
% 2.14/2.33 tff(106,plain,(
% 2.14/2.33 ![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 2.14/2.33 inference(skolemize,[status(sab)],[105])).
% 2.14/2.33 tff(107,plain,
% 2.14/2.33 (![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[106, 102])).
% 2.14/2.33 tff(108,plain,
% 2.14/2.33 (((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | ((~type(f(n2, a), fulladder)) | connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a)))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | (~type(f(n2, a), fulladder)) | connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a)))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(109,plain,
% 2.14/2.33 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | ((~type(f(n2, a), fulladder)) | connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a)))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(110,plain,
% 2.14/2.33 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n2, X), in(n1, h1(X))))) | (~type(f(n2, a), fulladder)) | connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[109, 108])).
% 2.14/2.33 tff(111,plain,
% 2.14/2.33 (connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[110, 107, 15])).
% 2.14/2.33 tff(112,plain,
% 2.14/2.33 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, f(n2, a)), n1) | (~value(in(n1, h1(f(n2, a))), n1)) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n2, f(n2, a)), n1) | (~value(in(n1, h1(f(n2, a))), n1)) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(113,plain,
% 2.14/2.33 ((value(in(n2, f(n2, a)), n1) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))) | (~value(in(n1, h1(f(n2, a))), n1))) <=> (value(in(n2, f(n2, a)), n1) | (~value(in(n1, h1(f(n2, a))), n1)) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(114,plain,
% 2.14/2.33 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, f(n2, a)), n1) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))) | (~value(in(n1, h1(f(n2, a))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, f(n2, a)), n1) | (~value(in(n1, h1(f(n2, a))), n1)) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a)))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[113])).
% 2.14/2.33 tff(115,plain,
% 2.14/2.33 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, f(n2, a)), n1) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))) | (~value(in(n1, h1(f(n2, a))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n2, f(n2, a)), n1) | (~value(in(n1, h1(f(n2, a))), n1)) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[114, 112])).
% 2.14/2.33 tff(116,plain,
% 2.14/2.33 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n2, f(n2, a)), n1) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a))))) | (~value(in(n1, h1(f(n2, a))), n1)))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(117,plain,
% 2.14/2.33 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n2, f(n2, a)), n1) | (~value(in(n1, h1(f(n2, a))), n1)) | (~connection(in(n2, f(n2, a)), in(n1, h1(f(n2, a)))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[116, 115])).
% 2.14/2.33 tff(118,plain,
% 2.14/2.33 (~value(in(n1, h1(f(n2, a))), n1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[117, 96, 111, 100])).
% 2.14/2.33 tff(119,plain,
% 2.14/2.33 (^[X: $i] : refl(((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X)))) <=> ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X)))))),
% 2.14/2.33 inference(bind,[status(th)],[])).
% 2.14/2.33 tff(120,plain,
% 2.14/2.33 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 2.14/2.33 inference(quant_intro,[status(thm)],[119])).
% 2.14/2.33 tff(121,plain,
% 2.14/2.33 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(122,axiom,(![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_connection_in1_in1and2')).
% 2.14/2.33 tff(123,plain,
% 2.14/2.33 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[122, 121])).
% 2.14/2.33 tff(124,plain,(
% 2.14/2.33 ![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 2.14/2.33 inference(skolemize,[status(sab)],[123])).
% 2.14/2.33 tff(125,plain,
% 2.14/2.33 (![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[124, 120])).
% 2.14/2.33 tff(126,plain,
% 2.14/2.33 (((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h1(f(n2, a)), halfadder)) | connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a))))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h1(f(n2, a)), halfadder)) | connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(127,plain,
% 2.14/2.33 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h1(f(n2, a)), halfadder)) | connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a))))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(128,plain,
% 2.14/2.33 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h1(f(n2, a)), halfadder)) | connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[127, 126])).
% 2.14/2.33 tff(129,plain,
% 2.14/2.33 ((~type(h1(f(n2, a)), halfadder)) | connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[128, 125])).
% 2.14/2.33 tff(130,plain,
% 2.14/2.33 (connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[129, 26])).
% 2.14/2.33 tff(131,plain,
% 2.14/2.33 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h1(f(n2, a))), n1) | (~value(in(n1, and2(h1(f(n2, a)))), n1)) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h1(f(n2, a))), n1) | (~value(in(n1, and2(h1(f(n2, a)))), n1)) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(132,plain,
% 2.14/2.33 ((value(in(n1, h1(f(n2, a))), n1) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))) | (~value(in(n1, and2(h1(f(n2, a)))), n1))) <=> (value(in(n1, h1(f(n2, a))), n1) | (~value(in(n1, and2(h1(f(n2, a)))), n1)) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(133,plain,
% 2.14/2.33 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h1(f(n2, a))), n1) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))) | (~value(in(n1, and2(h1(f(n2, a)))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h1(f(n2, a))), n1) | (~value(in(n1, and2(h1(f(n2, a)))), n1)) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a))))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[132])).
% 2.14/2.33 tff(134,plain,
% 2.14/2.33 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h1(f(n2, a))), n1) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))) | (~value(in(n1, and2(h1(f(n2, a)))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h1(f(n2, a))), n1) | (~value(in(n1, and2(h1(f(n2, a)))), n1)) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[133, 131])).
% 2.14/2.33 tff(135,plain,
% 2.14/2.33 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h1(f(n2, a))), n1) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a)))))) | (~value(in(n1, and2(h1(f(n2, a)))), n1)))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(136,plain,
% 2.14/2.33 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h1(f(n2, a))), n1) | (~value(in(n1, and2(h1(f(n2, a)))), n1)) | (~connection(in(n1, h1(f(n2, a))), in(n1, and2(h1(f(n2, a))))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[135, 134])).
% 2.14/2.33 tff(137,plain,
% 2.14/2.33 (~value(in(n1, and2(h1(f(n2, a)))), n1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[136, 96, 130, 118])).
% 2.14/2.33 tff(138,plain,
% 2.14/2.33 (^[K: $i] : refl(((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1)))),
% 2.14/2.33 inference(bind,[status(th)],[])).
% 2.14/2.33 tff(139,plain,
% 2.14/2.33 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 2.14/2.33 inference(quant_intro,[status(thm)],[138])).
% 2.14/2.33 tff(140,plain,
% 2.14/2.33 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(141,plain,
% 2.14/2.33 (^[K: $i] : trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and))) | value(in(n1, K), n1)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and))) | value(in(n1, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))), (((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))))),
% 2.14/2.33 inference(bind,[status(th)],[])).
% 2.14/2.33 tff(142,plain,
% 2.14/2.33 (![K: $i] : ((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 2.14/2.33 inference(quant_intro,[status(thm)],[141])).
% 2.14/2.33 tff(143,axiom,(![K: $i] : ((((~mode(K, ok)) | (~type(K, and))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','and_1_1x')).
% 2.14/2.33 tff(144,plain,
% 2.14/2.33 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[143, 142])).
% 2.14/2.33 tff(145,plain,
% 2.14/2.33 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[144, 140])).
% 2.14/2.33 tff(146,plain,(
% 2.14/2.33 ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 2.14/2.33 inference(skolemize,[status(sab)],[145])).
% 2.14/2.33 tff(147,plain,
% 2.14/2.33 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[146, 139])).
% 2.14/2.33 tff(148,plain,
% 2.14/2.33 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and2(h1(f(n2, a))), ok)) | (~type(and2(h1(f(n2, a))), and)) | (~value(out(n1, and2(h1(f(n2, a)))), n1)) | value(in(n1, and2(h1(f(n2, a)))), n1))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | (~mode(and2(h1(f(n2, a))), ok)) | (~type(and2(h1(f(n2, a))), and)) | (~value(out(n1, and2(h1(f(n2, a)))), n1)) | value(in(n1, and2(h1(f(n2, a)))), n1))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(149,plain,
% 2.14/2.33 (((~mode(and2(h1(f(n2, a))), ok)) | (~value(out(n1, and2(h1(f(n2, a)))), n1)) | (~type(and2(h1(f(n2, a))), and)) | value(in(n1, and2(h1(f(n2, a)))), n1)) <=> ((~mode(and2(h1(f(n2, a))), ok)) | (~type(and2(h1(f(n2, a))), and)) | (~value(out(n1, and2(h1(f(n2, a)))), n1)) | value(in(n1, and2(h1(f(n2, a)))), n1))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(150,plain,
% 2.14/2.33 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and2(h1(f(n2, a))), ok)) | (~value(out(n1, and2(h1(f(n2, a)))), n1)) | (~type(and2(h1(f(n2, a))), and)) | value(in(n1, and2(h1(f(n2, a)))), n1))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and2(h1(f(n2, a))), ok)) | (~type(and2(h1(f(n2, a))), and)) | (~value(out(n1, and2(h1(f(n2, a)))), n1)) | value(in(n1, and2(h1(f(n2, a)))), n1)))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[149])).
% 2.14/2.33 tff(151,plain,
% 2.14/2.33 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and2(h1(f(n2, a))), ok)) | (~value(out(n1, and2(h1(f(n2, a)))), n1)) | (~type(and2(h1(f(n2, a))), and)) | value(in(n1, and2(h1(f(n2, a)))), n1))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | (~mode(and2(h1(f(n2, a))), ok)) | (~type(and2(h1(f(n2, a))), and)) | (~value(out(n1, and2(h1(f(n2, a)))), n1)) | value(in(n1, and2(h1(f(n2, a)))), n1))),
% 2.14/2.33 inference(transitivity,[status(thm)],[150, 148])).
% 2.14/2.33 tff(152,plain,
% 2.14/2.33 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and2(h1(f(n2, a))), ok)) | (~value(out(n1, and2(h1(f(n2, a)))), n1)) | (~type(and2(h1(f(n2, a))), and)) | value(in(n1, and2(h1(f(n2, a)))), n1))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(153,plain,
% 2.14/2.33 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | (~mode(and2(h1(f(n2, a))), ok)) | (~type(and2(h1(f(n2, a))), and)) | (~value(out(n1, and2(h1(f(n2, a)))), n1)) | value(in(n1, and2(h1(f(n2, a)))), n1)),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[152, 151])).
% 2.14/2.33 tff(154,plain,
% 2.14/2.33 ((~mode(and2(h1(f(n2, a))), ok)) | (~value(out(n1, and2(h1(f(n2, a)))), n1)) | value(in(n1, and2(h1(f(n2, a)))), n1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[153, 147, 38])).
% 2.14/2.33 tff(155,plain,
% 2.14/2.33 (~value(out(n1, and2(h1(f(n2, a)))), n1)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[154, 137, 55])).
% 2.14/2.33 tff(156,plain,
% 2.14/2.33 (^[X: $i] : refl(((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X)))) <=> ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X)))))),
% 2.14/2.33 inference(bind,[status(th)],[])).
% 2.14/2.33 tff(157,plain,
% 2.14/2.33 (![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 2.14/2.33 inference(quant_intro,[status(thm)],[156])).
% 2.14/2.33 tff(158,plain,
% 2.14/2.33 (![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X)))) <=> ![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(159,axiom,(![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-1.ax','halfadder_connection_outc_out1and2')).
% 2.14/2.33 tff(160,plain,
% 2.14/2.33 (![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[159, 158])).
% 2.14/2.33 tff(161,plain,(
% 2.14/2.33 ![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 2.14/2.33 inference(skolemize,[status(sab)],[160])).
% 2.14/2.33 tff(162,plain,
% 2.14/2.33 (![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[161, 157])).
% 2.14/2.33 tff(163,plain,
% 2.14/2.33 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h1(f(n2, a)), halfadder)) | connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a))))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h1(f(n2, a)), halfadder)) | connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(164,plain,
% 2.14/2.33 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h1(f(n2, a)), halfadder)) | connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a))))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(165,plain,
% 2.14/2.33 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h1(f(n2, a)), halfadder)) | connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[164, 163])).
% 2.14/2.33 tff(166,plain,
% 2.14/2.33 ((~type(h1(f(n2, a)), halfadder)) | connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[165, 162])).
% 2.14/2.33 tff(167,plain,
% 2.14/2.33 (connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[166, 26])).
% 2.14/2.33 tff(168,plain,
% 2.14/2.33 (^[V: $i, P2: $i, P1: $i] : refl((value(P2, V) | (~value(P1, V)) | (~connection(P1, P2))) <=> (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2))))),
% 2.14/2.33 inference(bind,[status(th)],[])).
% 2.14/2.33 tff(169,plain,
% 2.14/2.33 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2))) <=> ![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 2.14/2.33 inference(quant_intro,[status(thm)],[168])).
% 2.14/2.33 tff(170,plain,
% 2.14/2.33 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2))) <=> ![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(171,plain,
% 2.14/2.33 (^[V: $i, P2: $i, P1: $i] : rewrite((((~connection(P1, P2)) | (~value(P1, V))) | value(P2, V)) <=> (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2))))),
% 2.14/2.33 inference(bind,[status(th)],[])).
% 2.14/2.33 tff(172,plain,
% 2.14/2.33 (![V: $i, P2: $i, P1: $i] : (((~connection(P1, P2)) | (~value(P1, V))) | value(P2, V)) <=> ![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 2.14/2.33 inference(quant_intro,[status(thm)],[171])).
% 2.14/2.33 tff(173,axiom,(![V: $i, P2: $i, P1: $i] : (((~connection(P1, P2)) | (~value(P1, V))) | value(P2, V))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','value_propagation1')).
% 2.14/2.33 tff(174,plain,
% 2.14/2.33 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[173, 172])).
% 2.14/2.33 tff(175,plain,
% 2.14/2.33 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[174, 170])).
% 2.14/2.33 tff(176,plain,(
% 2.14/2.33 ![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 2.14/2.33 inference(skolemize,[status(sab)],[175])).
% 2.14/2.33 tff(177,plain,
% 2.14/2.33 (![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[176, 169])).
% 2.14/2.33 tff(178,plain,
% 2.14/2.33 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and2(h1(f(n2, a)))), n1) | (~value(out(c, h1(f(n2, a))), n1)) | (~connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, and2(h1(f(n2, a)))), n1) | (~value(out(c, h1(f(n2, a))), n1)) | (~connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(179,plain,
% 2.14/2.34 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and2(h1(f(n2, a)))), n1) | (~value(out(c, h1(f(n2, a))), n1)) | (~connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a)))))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(180,plain,
% 2.14/2.34 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, and2(h1(f(n2, a)))), n1) | (~value(out(c, h1(f(n2, a))), n1)) | (~connection(out(c, h1(f(n2, a))), out(n1, and2(h1(f(n2, a))))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[179, 178])).
% 2.14/2.34 tff(181,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[180, 177, 167, 155, 1])).
% 2.14/2.34 tff(182,plain,(~value(out(c, h1(f(n2, a))), n1)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(183,plain,
% 2.14/2.34 (^[X: $i] : refl(((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X)))) <=> ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X)))))),
% 2.14/2.34 inference(bind,[status(th)],[])).
% 2.14/2.34 tff(184,plain,
% 2.14/2.34 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 2.14/2.34 inference(quant_intro,[status(thm)],[183])).
% 2.14/2.34 tff(185,plain,
% 2.14/2.34 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(186,axiom,(![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_connection_outch1_in2or1')).
% 2.14/2.34 tff(187,plain,
% 2.14/2.34 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[186, 185])).
% 2.14/2.34 tff(188,plain,(
% 2.14/2.34 ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 2.14/2.34 inference(skolemize,[status(sab)],[187])).
% 2.14/2.34 tff(189,plain,
% 2.14/2.34 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[188, 184])).
% 2.14/2.34 tff(190,plain,
% 2.14/2.34 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))) | ((~type(f(n2, a), fulladder)) | connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a)))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))) | (~type(f(n2, a), fulladder)) | connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a)))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(191,plain,
% 2.14/2.34 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))) | ((~type(f(n2, a), fulladder)) | connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a)))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(192,plain,
% 2.14/2.34 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h1(X)), in(n2, or1(X))))) | (~type(f(n2, a), fulladder)) | connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[191, 190])).
% 2.14/2.34 tff(193,plain,
% 2.14/2.34 (connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[192, 189, 15])).
% 2.14/2.34 tff(194,plain,
% 2.14/2.34 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n2, or1(f(n2, a))), n1)) | value(out(c, h1(f(n2, a))), n1) | (~connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, or1(f(n2, a))), n1)) | value(out(c, h1(f(n2, a))), n1) | (~connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(195,plain,
% 2.14/2.34 ((value(out(c, h1(f(n2, a))), n1) | (~connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a))))) | (~value(in(n2, or1(f(n2, a))), n1))) <=> ((~value(in(n2, or1(f(n2, a))), n1)) | value(out(c, h1(f(n2, a))), n1) | (~connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(196,plain,
% 2.19/2.34 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h1(f(n2, a))), n1) | (~connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a))))) | (~value(in(n2, or1(f(n2, a))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n2, or1(f(n2, a))), n1)) | value(out(c, h1(f(n2, a))), n1) | (~connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a)))))))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[195])).
% 2.19/2.34 tff(197,plain,
% 2.19/2.34 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h1(f(n2, a))), n1) | (~connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a))))) | (~value(in(n2, or1(f(n2, a))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, or1(f(n2, a))), n1)) | value(out(c, h1(f(n2, a))), n1) | (~connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a))))))),
% 2.19/2.34 inference(transitivity,[status(thm)],[196, 194])).
% 2.19/2.34 tff(198,plain,
% 2.19/2.34 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h1(f(n2, a))), n1) | (~connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a))))) | (~value(in(n2, or1(f(n2, a))), n1)))),
% 2.19/2.34 inference(quant_inst,[status(thm)],[])).
% 2.19/2.34 tff(199,plain,
% 2.19/2.34 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n2, or1(f(n2, a))), n1)) | value(out(c, h1(f(n2, a))), n1) | (~connection(out(c, h1(f(n2, a))), in(n2, or1(f(n2, a)))))),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[198, 197])).
% 2.19/2.34 tff(200,plain,
% 2.19/2.34 ((~value(in(n2, or1(f(n2, a))), n1)) | value(out(c, h1(f(n2, a))), n1)),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[199, 96, 193])).
% 2.19/2.34 tff(201,plain,
% 2.19/2.34 (~value(in(n2, or1(f(n2, a))), n1)),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[200, 182])).
% 2.19/2.34 tff(202,plain,
% 2.19/2.34 (^[X: $i] : refl(((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X)))) <=> ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X)))))),
% 2.19/2.34 inference(bind,[status(th)],[])).
% 2.19/2.34 tff(203,plain,
% 2.19/2.34 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))),
% 2.19/2.34 inference(quant_intro,[status(thm)],[202])).
% 2.19/2.34 tff(204,plain,
% 2.19/2.34 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))),
% 2.19/2.34 inference(rewrite,[status(thm)],[])).
% 2.19/2.34 tff(205,axiom,(![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nbit_adder_connection_outc_outcf1')).
% 2.19/2.34 tff(206,plain,
% 2.19/2.34 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[205, 204])).
% 2.19/2.34 tff(207,plain,(
% 2.19/2.34 ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))),
% 2.19/2.34 inference(skolemize,[status(sab)],[206])).
% 2.19/2.34 tff(208,plain,
% 2.19/2.34 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[207, 203])).
% 2.19/2.34 tff(209,plain,
% 2.19/2.34 (((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))) | ((~type(a, nbit_adder(n2))) | connection(out(c, a), out(c, f(n2, a))))) <=> ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))) | (~type(a, nbit_adder(n2))) | connection(out(c, a), out(c, f(n2, a))))),
% 2.19/2.34 inference(rewrite,[status(thm)],[])).
% 2.19/2.34 tff(210,plain,
% 2.19/2.34 ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))) | ((~type(a, nbit_adder(n2))) | connection(out(c, a), out(c, f(n2, a))))),
% 2.19/2.34 inference(quant_inst,[status(thm)],[])).
% 2.19/2.34 tff(211,plain,
% 2.19/2.34 ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(out(c, X), out(c, f(n2, X))))) | (~type(a, nbit_adder(n2))) | connection(out(c, a), out(c, f(n2, a)))),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[210, 209])).
% 2.19/2.34 tff(212,plain,
% 2.19/2.34 (connection(out(c, a), out(c, f(n2, a)))),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[211, 208, 4])).
% 2.19/2.34 tff(213,plain,
% 2.19/2.34 (value(out(c, a), n1) <=> value(out(c, a), n1)),
% 2.19/2.34 inference(rewrite,[status(thm)],[])).
% 2.19/2.34 tff(214,axiom,(value(out(c, a), n1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','outc_1')).
% 2.19/2.34 tff(215,plain,
% 2.19/2.34 (value(out(c, a), n1)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[214, 213])).
% 2.19/2.34 tff(216,plain,
% 2.19/2.34 (((~![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, f(n2, a)))) | value(out(c, f(n2, 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, f(n2, a)))) | value(out(c, f(n2, a)), n1))),
% 2.19/2.34 inference(rewrite,[status(thm)],[])).
% 2.19/2.34 tff(217,plain,
% 2.19/2.34 ((value(out(c, f(n2, a)), n1) | (~value(out(c, a), n1)) | (~connection(out(c, a), out(c, f(n2, a))))) <=> ((~value(out(c, a), n1)) | (~connection(out(c, a), out(c, f(n2, a)))) | value(out(c, f(n2, a)), n1))),
% 2.19/2.34 inference(rewrite,[status(thm)],[])).
% 2.19/2.34 tff(218,plain,
% 2.19/2.34 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(c, f(n2, a)), n1) | (~value(out(c, a), n1)) | (~connection(out(c, a), out(c, f(n2, 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, f(n2, a)))) | value(out(c, f(n2, a)), n1)))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[217])).
% 2.19/2.34 tff(219,plain,
% 2.19/2.34 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(c, f(n2, a)), n1) | (~value(out(c, a), n1)) | (~connection(out(c, a), out(c, f(n2, 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, f(n2, a)))) | value(out(c, f(n2, a)), n1))),
% 2.19/2.34 inference(transitivity,[status(thm)],[218, 216])).
% 2.19/2.34 tff(220,plain,
% 2.19/2.34 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(c, f(n2, a)), n1) | (~value(out(c, a), n1)) | (~connection(out(c, a), out(c, f(n2, a)))))),
% 2.19/2.34 inference(quant_inst,[status(thm)],[])).
% 2.19/2.34 tff(221,plain,
% 2.19/2.34 ((~![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, f(n2, a)))) | value(out(c, f(n2, a)), n1)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[220, 219])).
% 2.19/2.34 tff(222,plain,
% 2.19/2.34 (value(out(c, f(n2, a)), n1)),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[221, 177, 215, 212])).
% 2.19/2.34 tff(223,assumption,(~value(out(n1, or1(f(n2, a))), n1)), introduced(assumption)).
% 2.19/2.34 tff(224,plain,
% 2.19/2.34 (^[X: $i] : refl(((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X)))) <=> ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X)))))),
% 2.19/2.34 inference(bind,[status(th)],[])).
% 2.19/2.34 tff(225,plain,
% 2.19/2.34 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 2.19/2.34 inference(quant_intro,[status(thm)],[224])).
% 2.19/2.34 tff(226,plain,
% 2.19/2.34 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 2.19/2.34 inference(rewrite,[status(thm)],[])).
% 2.19/2.34 tff(227,axiom,(![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_connection_outc_out1or1')).
% 2.19/2.34 tff(228,plain,
% 2.19/2.34 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[227, 226])).
% 2.19/2.34 tff(229,plain,(
% 2.19/2.34 ![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 2.19/2.34 inference(skolemize,[status(sab)],[228])).
% 2.19/2.34 tff(230,plain,
% 2.19/2.34 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[229, 225])).
% 2.19/2.34 tff(231,plain,
% 2.19/2.34 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | ((~type(f(n2, a), fulladder)) | connection(out(c, f(n2, a)), out(n1, or1(f(n2, a)))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | (~type(f(n2, a), fulladder)) | connection(out(c, f(n2, a)), out(n1, or1(f(n2, a)))))),
% 2.19/2.34 inference(rewrite,[status(thm)],[])).
% 2.19/2.34 tff(232,plain,
% 2.19/2.34 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | ((~type(f(n2, a), fulladder)) | connection(out(c, f(n2, a)), out(n1, or1(f(n2, a)))))),
% 2.19/2.34 inference(quant_inst,[status(thm)],[])).
% 2.19/2.34 tff(233,plain,
% 2.19/2.34 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, X), out(n1, or1(X))))) | (~type(f(n2, a), fulladder)) | connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[232, 231])).
% 2.19/2.34 tff(234,plain,
% 2.19/2.34 (connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[233, 230, 15])).
% 2.19/2.34 tff(235,plain,
% 2.19/2.34 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, or1(f(n2, a))), n1) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))) | (~value(out(c, f(n2, a)), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, or1(f(n2, a))), n1) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))) | (~value(out(c, f(n2, a)), n1)))),
% 2.19/2.34 inference(rewrite,[status(thm)],[])).
% 2.19/2.34 tff(236,plain,
% 2.19/2.34 ((value(out(n1, or1(f(n2, a))), n1) | (~value(out(c, f(n2, a)), n1)) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a)))))) <=> (value(out(n1, or1(f(n2, a))), n1) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))) | (~value(out(c, f(n2, a)), n1)))),
% 2.19/2.34 inference(rewrite,[status(thm)],[])).
% 2.19/2.34 tff(237,plain,
% 2.19/2.34 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, or1(f(n2, a))), n1) | (~value(out(c, f(n2, a)), n1)) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, or1(f(n2, a))), n1) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))) | (~value(out(c, f(n2, a)), n1))))),
% 2.19/2.34 inference(monotonicity,[status(thm)],[236])).
% 2.19/2.34 tff(238,plain,
% 2.19/2.34 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, or1(f(n2, a))), n1) | (~value(out(c, f(n2, a)), n1)) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, or1(f(n2, a))), n1) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))) | (~value(out(c, f(n2, a)), n1)))),
% 2.19/2.34 inference(transitivity,[status(thm)],[237, 235])).
% 2.19/2.34 tff(239,plain,
% 2.19/2.34 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, or1(f(n2, a))), n1) | (~value(out(c, f(n2, a)), n1)) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))))),
% 2.19/2.34 inference(quant_inst,[status(thm)],[])).
% 2.19/2.34 tff(240,plain,
% 2.19/2.34 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, or1(f(n2, a))), n1) | (~connection(out(c, f(n2, a)), out(n1, or1(f(n2, a))))) | (~value(out(c, f(n2, a)), n1))),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[239, 238])).
% 2.19/2.34 tff(241,plain,
% 2.19/2.34 ($false),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[240, 177, 234, 223, 222])).
% 2.19/2.34 tff(242,plain,(value(out(n1, or1(f(n2, a))), n1)), inference(lemma,lemma(discharge,[]))).
% 2.19/2.34 tff(243,plain,
% 2.19/2.34 (^[X: $i] : refl(((~type(X, fulladder)) | type(or1(X), or)) <=> ((~type(X, fulladder)) | type(or1(X), or)))),
% 2.19/2.34 inference(bind,[status(th)],[])).
% 2.19/2.34 tff(244,plain,
% 2.19/2.34 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 2.19/2.34 inference(quant_intro,[status(thm)],[243])).
% 2.19/2.34 tff(245,plain,
% 2.19/2.34 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or)) <=> ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 2.19/2.34 inference(rewrite,[status(thm)],[])).
% 2.19/2.34 tff(246,axiom,(![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_or1')).
% 2.19/2.34 tff(247,plain,
% 2.19/2.34 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[246, 245])).
% 2.19/2.34 tff(248,plain,(
% 2.19/2.34 ![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 2.19/2.34 inference(skolemize,[status(sab)],[247])).
% 2.19/2.34 tff(249,plain,
% 2.19/2.34 (![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[248, 244])).
% 2.19/2.34 tff(250,plain,
% 2.19/2.34 (((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | ((~type(f(n2, a), fulladder)) | type(or1(f(n2, a)), or))) <=> ((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | (~type(f(n2, a), fulladder)) | type(or1(f(n2, a)), or))),
% 2.19/2.34 inference(rewrite,[status(thm)],[])).
% 2.19/2.34 tff(251,plain,
% 2.19/2.34 ((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | ((~type(f(n2, a), fulladder)) | type(or1(f(n2, a)), or))),
% 2.19/2.34 inference(quant_inst,[status(thm)],[])).
% 2.19/2.34 tff(252,plain,
% 2.19/2.34 ((~![X: $i] : ((~type(X, fulladder)) | type(or1(X), or))) | (~type(f(n2, a), fulladder)) | type(or1(f(n2, a)), or)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[251, 250])).
% 2.19/2.34 tff(253,plain,
% 2.19/2.34 (type(or1(f(n2, a)), or)),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[252, 249, 15])).
% 2.19/2.34 tff(254,plain,
% 2.19/2.34 ((~mode(or1(f(n2, a)), abnormal)) <=> (~mode(or1(f(n2, a)), abnormal))),
% 2.19/2.34 inference(rewrite,[status(thm)],[])).
% 2.19/2.34 tff(255,axiom,(~mode(or1(f(n2, a)), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_or1f2a')).
% 2.19/2.34 tff(256,plain,
% 2.19/2.34 (~mode(or1(f(n2, a)), abnormal)),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[255, 254])).
% 2.19/2.34 tff(257,plain,
% 2.19/2.34 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(or1(f(n2, a)), abnormal) | mode(or1(f(n2, a)), ok) | (~type(or1(f(n2, a)), or)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(or1(f(n2, a)), abnormal) | mode(or1(f(n2, a)), ok) | (~type(or1(f(n2, a)), or)))),
% 2.19/2.34 inference(rewrite,[status(thm)],[])).
% 2.19/2.34 tff(258,plain,
% 2.19/2.34 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(or1(f(n2, a)), abnormal) | mode(or1(f(n2, a)), ok) | (~type(or1(f(n2, a)), or)))),
% 2.19/2.34 inference(quant_inst,[status(thm)],[])).
% 2.19/2.34 tff(259,plain,
% 2.19/2.34 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(or1(f(n2, a)), abnormal) | mode(or1(f(n2, a)), ok) | (~type(or1(f(n2, a)), or))),
% 2.19/2.34 inference(modus_ponens,[status(thm)],[258, 257])).
% 2.19/2.34 tff(260,plain,
% 2.19/2.34 (mode(or1(f(n2, a)), ok)),
% 2.19/2.34 inference(unit_resolution,[status(thm)],[259, 51, 256, 253])).
% 2.19/2.34 tff(261,plain,
% 2.19/2.34 (^[K: $i] : refl(((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or))))),
% 2.19/2.34 inference(bind,[status(th)],[])).
% 2.19/2.34 tff(262,plain,
% 2.19/2.34 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or))) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 2.19/2.34 inference(quant_intro,[status(thm)],[261])).
% 2.19/2.34 tff(263,plain,
% 2.19/2.34 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or))) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 2.19/2.34 inference(rewrite,[status(thm)],[])).
% 2.19/2.34 tff(264,plain,
% 2.19/2.34 (^[K: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, or)))), (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, or))) | value(in(n1, K), n1)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, or))) | value(in(n1, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n1) | (~type(K, or)))), (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n1) | (~type(K, or))))), ((((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) | value(in(n2, K), n1)) <=> (((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n1) | (~type(K, or))) | value(in(n2, K), n1)))), rewrite((((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n1, K), n1) | (~type(K, or))) | value(in(n2, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))), ((((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) | value(in(n2, K), n1)) <=> ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))))),
% 2.19/2.35 inference(bind,[status(th)],[])).
% 2.19/2.35 tff(265,plain,
% 2.19/2.35 (![K: $i] : (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) | value(in(n2, K), n1)) <=> ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 2.19/2.35 inference(quant_intro,[status(thm)],[264])).
% 2.19/2.35 tff(266,axiom,(![K: $i] : (((((~mode(K, ok)) | (~type(K, or))) | (~value(out(n1, K), n1))) | value(in(n1, K), n1)) | value(in(n2, K), n1))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-0.ax','or_1_11')).
% 2.19/2.35 tff(267,plain,
% 2.19/2.35 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[266, 265])).
% 2.19/2.35 tff(268,plain,
% 2.19/2.35 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[267, 263])).
% 2.19/2.35 tff(269,plain,(
% 2.19/2.35 ![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 2.19/2.35 inference(skolemize,[status(sab)],[268])).
% 2.19/2.35 tff(270,plain,
% 2.19/2.35 (![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | value(in(n2, K), n1) | value(in(n1, K), n1) | (~type(K, or)))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[269, 262])).
% 2.19/2.35 tff(271,plain,
% 2.19/2.35 (((~![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(f(n2, a)), ok)) | value(in(n1, or1(f(n2, a))), n1) | (~type(or1(f(n2, a)), or)) | (~value(out(n1, or1(f(n2, a))), n1)) | value(in(n2, or1(f(n2, 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(f(n2, a)), ok)) | value(in(n1, or1(f(n2, a))), n1) | (~type(or1(f(n2, a)), or)) | (~value(out(n1, or1(f(n2, a))), n1)) | value(in(n2, or1(f(n2, a))), n1))),
% 2.19/2.35 inference(rewrite,[status(thm)],[])).
% 2.19/2.35 tff(272,plain,
% 2.19/2.35 (((~mode(or1(f(n2, a)), ok)) | (~value(out(n1, or1(f(n2, a))), n1)) | value(in(n2, or1(f(n2, a))), n1) | value(in(n1, or1(f(n2, a))), n1) | (~type(or1(f(n2, a)), or))) <=> ((~mode(or1(f(n2, a)), ok)) | value(in(n1, or1(f(n2, a))), n1) | (~type(or1(f(n2, a)), or)) | (~value(out(n1, or1(f(n2, a))), n1)) | value(in(n2, or1(f(n2, a))), n1))),
% 2.19/2.35 inference(rewrite,[status(thm)],[])).
% 2.19/2.35 tff(273,plain,
% 2.19/2.35 (((~![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(f(n2, a)), ok)) | (~value(out(n1, or1(f(n2, a))), n1)) | value(in(n2, or1(f(n2, a))), n1) | value(in(n1, or1(f(n2, a))), n1) | (~type(or1(f(n2, 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(f(n2, a)), ok)) | value(in(n1, or1(f(n2, a))), n1) | (~type(or1(f(n2, a)), or)) | (~value(out(n1, or1(f(n2, a))), n1)) | value(in(n2, or1(f(n2, a))), n1)))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[272])).
% 2.19/2.35 tff(274,plain,
% 2.19/2.35 (((~![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(f(n2, a)), ok)) | (~value(out(n1, or1(f(n2, a))), n1)) | value(in(n2, or1(f(n2, a))), n1) | value(in(n1, or1(f(n2, a))), n1) | (~type(or1(f(n2, 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(f(n2, a)), ok)) | value(in(n1, or1(f(n2, a))), n1) | (~type(or1(f(n2, a)), or)) | (~value(out(n1, or1(f(n2, a))), n1)) | value(in(n2, or1(f(n2, a))), n1))),
% 2.19/2.35 inference(transitivity,[status(thm)],[273, 271])).
% 2.19/2.35 tff(275,plain,
% 2.19/2.35 ((~![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(f(n2, a)), ok)) | (~value(out(n1, or1(f(n2, a))), n1)) | value(in(n2, or1(f(n2, a))), n1) | value(in(n1, or1(f(n2, a))), n1) | (~type(or1(f(n2, a)), or)))),
% 2.19/2.35 inference(quant_inst,[status(thm)],[])).
% 2.19/2.35 tff(276,plain,
% 2.19/2.35 ((~![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(f(n2, a)), ok)) | value(in(n1, or1(f(n2, a))), n1) | (~type(or1(f(n2, a)), or)) | (~value(out(n1, or1(f(n2, a))), n1)) | value(in(n2, or1(f(n2, a))), n1)),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[275, 274])).
% 2.19/2.35 tff(277,plain,
% 2.19/2.35 ((~mode(or1(f(n2, a)), ok)) | value(in(n1, or1(f(n2, a))), n1) | (~value(out(n1, or1(f(n2, a))), n1)) | value(in(n2, or1(f(n2, a))), n1)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[276, 270, 253])).
% 2.19/2.35 tff(278,plain,
% 2.19/2.35 (value(in(n1, or1(f(n2, a))), n1) | (~value(out(n1, or1(f(n2, a))), n1)) | value(in(n2, or1(f(n2, a))), n1)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[277, 260])).
% 2.19/2.35 tff(279,plain,
% 2.19/2.35 (value(in(n1, or1(f(n2, a))), n1) | value(in(n2, or1(f(n2, a))), n1)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[278, 242])).
% 2.19/2.35 tff(280,plain,
% 2.19/2.35 (value(in(n1, or1(f(n2, a))), n1)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[279, 201])).
% 2.19/2.35 tff(281,plain,
% 2.19/2.35 (^[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)))))),
% 2.19/2.35 inference(bind,[status(th)],[])).
% 2.19/2.35 tff(282,plain,
% 2.19/2.35 (![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))))),
% 2.19/2.35 inference(quant_intro,[status(thm)],[281])).
% 2.19/2.35 tff(283,plain,
% 2.19/2.35 (![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))))),
% 2.19/2.35 inference(rewrite,[status(thm)],[])).
% 2.19/2.35 tff(284,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')).
% 2.19/2.35 tff(285,plain,
% 2.19/2.35 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[284, 283])).
% 2.19/2.35 tff(286,plain,(
% 2.19/2.35 ![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 2.19/2.35 inference(skolemize,[status(sab)],[285])).
% 2.19/2.35 tff(287,plain,
% 2.19/2.35 (![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[286, 282])).
% 2.19/2.35 tff(288,plain,
% 2.19/2.35 (((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | ((~type(f(n2, a), fulladder)) | connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a)))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | (~type(f(n2, a), fulladder)) | connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a)))))),
% 2.19/2.35 inference(rewrite,[status(thm)],[])).
% 2.19/2.35 tff(289,plain,
% 2.19/2.35 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | ((~type(f(n2, a), fulladder)) | connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a)))))),
% 2.19/2.35 inference(quant_inst,[status(thm)],[])).
% 2.19/2.35 tff(290,plain,
% 2.19/2.35 ((~![X: $i] : ((~type(X, fulladder)) | connection(out(c, h2(X)), in(n1, or1(X))))) | (~type(f(n2, a), fulladder)) | connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a))))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[289, 288])).
% 2.19/2.35 tff(291,plain,
% 2.19/2.35 (connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a))))),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[290, 287, 15])).
% 2.19/2.35 tff(292,plain,
% 2.19/2.35 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n1, or1(f(n2, a))), n1)) | (~connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a))))) | value(out(c, h2(f(n2, a))), n1))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, or1(f(n2, a))), n1)) | (~connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a))))) | value(out(c, h2(f(n2, a))), n1))),
% 2.19/2.35 inference(rewrite,[status(thm)],[])).
% 2.19/2.35 tff(293,plain,
% 2.19/2.35 ((value(out(c, h2(f(n2, a))), n1) | (~connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a))))) | (~value(in(n1, or1(f(n2, a))), n1))) <=> ((~value(in(n1, or1(f(n2, a))), n1)) | (~connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a))))) | value(out(c, h2(f(n2, a))), n1))),
% 2.19/2.35 inference(rewrite,[status(thm)],[])).
% 2.19/2.35 tff(294,plain,
% 2.19/2.35 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(f(n2, a))), n1) | (~connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a))))) | (~value(in(n1, or1(f(n2, a))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | ((~value(in(n1, or1(f(n2, a))), n1)) | (~connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a))))) | value(out(c, h2(f(n2, a))), n1)))),
% 2.19/2.35 inference(monotonicity,[status(thm)],[293])).
% 2.19/2.35 tff(295,plain,
% 2.19/2.35 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(f(n2, a))), n1) | (~connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a))))) | (~value(in(n1, or1(f(n2, a))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, or1(f(n2, a))), n1)) | (~connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a))))) | value(out(c, h2(f(n2, a))), n1))),
% 2.19/2.35 inference(transitivity,[status(thm)],[294, 292])).
% 2.19/2.35 tff(296,plain,
% 2.19/2.35 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(out(c, h2(f(n2, a))), n1) | (~connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a))))) | (~value(in(n1, or1(f(n2, a))), n1)))),
% 2.19/2.35 inference(quant_inst,[status(thm)],[])).
% 2.19/2.35 tff(297,plain,
% 2.19/2.35 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (~value(in(n1, or1(f(n2, a))), n1)) | (~connection(out(c, h2(f(n2, a))), in(n1, or1(f(n2, a))))) | value(out(c, h2(f(n2, a))), n1)),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[296, 295])).
% 2.19/2.35 tff(298,plain,
% 2.19/2.35 (value(out(c, h2(f(n2, a))), n1)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[297, 96, 291, 280])).
% 2.19/2.35 tff(299,plain,
% 2.19/2.35 (^[X: $i] : refl(((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ((~type(X, fulladder)) | type(h2(X), halfadder)))),
% 2.19/2.35 inference(bind,[status(th)],[])).
% 2.19/2.35 tff(300,plain,
% 2.19/2.35 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 2.19/2.35 inference(quant_intro,[status(thm)],[299])).
% 2.19/2.35 tff(301,plain,
% 2.19/2.35 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder)) <=> ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 2.19/2.35 inference(rewrite,[status(thm)],[])).
% 2.19/2.35 tff(302,axiom,(![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_halfadder2')).
% 2.19/2.35 tff(303,plain,
% 2.19/2.35 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[302, 301])).
% 2.19/2.35 tff(304,plain,(
% 2.19/2.35 ![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 2.19/2.35 inference(skolemize,[status(sab)],[303])).
% 2.19/2.35 tff(305,plain,
% 2.19/2.35 (![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[304, 300])).
% 2.19/2.35 tff(306,plain,
% 2.19/2.35 (((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | ((~type(f(n2, a), fulladder)) | type(h2(f(n2, a)), halfadder))) <=> ((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | (~type(f(n2, a), fulladder)) | type(h2(f(n2, a)), halfadder))),
% 2.19/2.35 inference(rewrite,[status(thm)],[])).
% 2.19/2.35 tff(307,plain,
% 2.19/2.35 ((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | ((~type(f(n2, a), fulladder)) | type(h2(f(n2, a)), halfadder))),
% 2.19/2.35 inference(quant_inst,[status(thm)],[])).
% 2.19/2.35 tff(308,plain,
% 2.19/2.35 ((~![X: $i] : ((~type(X, fulladder)) | type(h2(X), halfadder))) | (~type(f(n2, a), fulladder)) | type(h2(f(n2, a)), halfadder)),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[307, 306])).
% 2.19/2.35 tff(309,plain,
% 2.19/2.35 (type(h2(f(n2, a)), halfadder)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[308, 305, 15])).
% 2.19/2.35 tff(310,plain,
% 2.19/2.35 (((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h2(f(n2, a)), halfadder)) | type(and2(h2(f(n2, a))), and))) <=> ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h2(f(n2, a)), halfadder)) | type(and2(h2(f(n2, a))), and))),
% 2.19/2.35 inference(rewrite,[status(thm)],[])).
% 2.19/2.35 tff(311,plain,
% 2.19/2.35 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | ((~type(h2(f(n2, a)), halfadder)) | type(and2(h2(f(n2, a))), and))),
% 2.19/2.35 inference(quant_inst,[status(thm)],[])).
% 2.19/2.35 tff(312,plain,
% 2.19/2.35 ((~![X: $i] : ((~type(X, halfadder)) | type(and2(X), and))) | (~type(h2(f(n2, a)), halfadder)) | type(and2(h2(f(n2, a))), and)),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[311, 310])).
% 2.19/2.35 tff(313,plain,
% 2.19/2.35 ((~type(h2(f(n2, a)), halfadder)) | type(and2(h2(f(n2, a))), and)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[312, 33])).
% 2.19/2.35 tff(314,plain,
% 2.19/2.35 (type(and2(h2(f(n2, a))), and)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[313, 309])).
% 2.19/2.35 tff(315,plain,
% 2.19/2.35 ((~mode(and2(h2(f(n2, a))), abnormal)) <=> (~mode(and2(h2(f(n2, a))), abnormal))),
% 2.19/2.35 inference(rewrite,[status(thm)],[])).
% 2.19/2.35 tff(316,axiom,(~mode(and2(h2(f(n2, a))), abnormal)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diagnosis_and2h1f2a')).
% 2.19/2.35 tff(317,plain,
% 2.19/2.35 (~mode(and2(h2(f(n2, a))), abnormal)),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[316, 315])).
% 2.19/2.35 tff(318,plain,
% 2.19/2.35 (((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h2(f(n2, a))), abnormal) | mode(and2(h2(f(n2, a))), ok) | (~type(and2(h2(f(n2, a))), and)))) <=> ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h2(f(n2, a))), abnormal) | mode(and2(h2(f(n2, a))), ok) | (~type(and2(h2(f(n2, a))), and)))),
% 2.19/2.35 inference(rewrite,[status(thm)],[])).
% 2.19/2.35 tff(319,plain,
% 2.19/2.35 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | (mode(and2(h2(f(n2, a))), abnormal) | mode(and2(h2(f(n2, a))), ok) | (~type(and2(h2(f(n2, a))), and)))),
% 2.19/2.35 inference(quant_inst,[status(thm)],[])).
% 2.19/2.35 tff(320,plain,
% 2.19/2.35 ((~![Any: $i, K: $i] : (mode(K, abnormal) | mode(K, ok) | (~type(K, Any)))) | mode(and2(h2(f(n2, a))), abnormal) | mode(and2(h2(f(n2, a))), ok) | (~type(and2(h2(f(n2, a))), and))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[319, 318])).
% 2.19/2.35 tff(321,plain,
% 2.19/2.35 (mode(and2(h2(f(n2, a))), ok)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[320, 51, 317, 314])).
% 2.19/2.35 tff(322,plain,
% 2.19/2.35 (^[X: $i] : refl(((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X)))) <=> ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X)))))),
% 2.19/2.35 inference(bind,[status(th)],[])).
% 2.19/2.35 tff(323,plain,
% 2.19/2.35 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))),
% 2.19/2.35 inference(quant_intro,[status(thm)],[322])).
% 2.19/2.35 tff(324,plain,
% 2.19/2.35 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X)))) <=> ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))),
% 2.19/2.35 inference(rewrite,[status(thm)],[])).
% 2.19/2.35 tff(325,axiom,(![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nbit_adder_connection_ina2_in1f2')).
% 2.19/2.35 tff(326,plain,
% 2.19/2.35 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[325, 324])).
% 2.19/2.35 tff(327,plain,(
% 2.19/2.35 ![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))),
% 2.19/2.35 inference(skolemize,[status(sab)],[326])).
% 2.19/2.35 tff(328,plain,
% 2.19/2.35 (![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[327, 323])).
% 2.19/2.35 tff(329,plain,
% 2.19/2.35 (((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))) | ((~type(a, nbit_adder(n2))) | connection(in(a2, a), in(n1, f(n2, a))))) <=> ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))) | (~type(a, nbit_adder(n2))) | connection(in(a2, a), in(n1, f(n2, a))))),
% 2.19/2.35 inference(rewrite,[status(thm)],[])).
% 2.19/2.35 tff(330,plain,
% 2.19/2.35 ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))) | ((~type(a, nbit_adder(n2))) | connection(in(a2, a), in(n1, f(n2, a))))),
% 2.19/2.35 inference(quant_inst,[status(thm)],[])).
% 2.19/2.35 tff(331,plain,
% 2.19/2.35 ((~![X: $i] : ((~type(X, nbit_adder(n2))) | connection(in(a2, X), in(n1, f(n2, X))))) | (~type(a, nbit_adder(n2))) | connection(in(a2, a), in(n1, f(n2, a)))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[330, 329])).
% 2.19/2.35 tff(332,plain,
% 2.19/2.35 (connection(in(a2, a), in(n1, f(n2, a)))),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[331, 328, 4])).
% 2.19/2.35 tff(333,plain,
% 2.19/2.35 (value(in(a2, a), n0) <=> value(in(a2, a), n0)),
% 2.19/2.35 inference(rewrite,[status(thm)],[])).
% 2.19/2.35 tff(334,axiom,(value(in(a2, a), n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ina2_0')).
% 2.19/2.35 tff(335,plain,
% 2.19/2.35 (value(in(a2, a), n0)),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[334, 333])).
% 2.19/2.35 tff(336,plain,
% 2.19/2.35 (((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n1, n0) | (~value(in(a2, a), n0)) | (~value(in(a2, a), n1)))) <=> ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n1, n0) | (~value(in(a2, a), n0)) | (~value(in(a2, a), n1)))),
% 2.19/2.35 inference(rewrite,[status(thm)],[])).
% 2.19/2.35 tff(337,plain,
% 2.19/2.35 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | (equal_value(n1, n0) | (~value(in(a2, a), n0)) | (~value(in(a2, a), n1)))),
% 2.19/2.35 inference(quant_inst,[status(thm)],[])).
% 2.19/2.35 tff(338,plain,
% 2.19/2.35 ((~![P: $i, V1: $i, V2: $i] : (equal_value(V1, V2) | (~value(P, V2)) | (~value(P, V1)))) | equal_value(n1, n0) | (~value(in(a2, a), n0)) | (~value(in(a2, a), n1))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[337, 336])).
% 2.19/2.35 tff(339,plain,
% 2.19/2.35 (~value(in(a2, a), n1)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[338, 82, 72, 335])).
% 2.19/2.35 tff(340,plain,
% 2.19/2.35 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(a2, a), n1) | (~connection(in(a2, a), in(n1, f(n2, a)))) | (~value(in(n1, f(n2, a)), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(a2, a), n1) | (~connection(in(a2, a), in(n1, f(n2, a)))) | (~value(in(n1, f(n2, a)), n1)))),
% 2.19/2.35 inference(rewrite,[status(thm)],[])).
% 2.19/2.35 tff(341,plain,
% 2.19/2.35 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(a2, a), n1) | (~connection(in(a2, a), in(n1, f(n2, a)))) | (~value(in(n1, f(n2, a)), n1)))),
% 2.19/2.35 inference(quant_inst,[status(thm)],[])).
% 2.19/2.35 tff(342,plain,
% 2.19/2.35 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(a2, a), n1) | (~connection(in(a2, a), in(n1, f(n2, a)))) | (~value(in(n1, f(n2, a)), n1))),
% 2.19/2.35 inference(modus_ponens,[status(thm)],[341, 340])).
% 2.19/2.35 tff(343,plain,
% 2.19/2.35 (~value(in(n1, f(n2, a)), n1)),
% 2.19/2.35 inference(unit_resolution,[status(thm)],[342, 96, 339, 332])).
% 2.19/2.35 tff(344,plain,
% 2.19/2.35 (^[X: $i] : refl(((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X)))) <=> ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X)))))),
% 2.19/2.35 inference(bind,[status(th)],[])).
% 2.19/2.35 tff(345,plain,
% 2.19/2.35 (![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 2.19/2.36 inference(quant_intro,[status(thm)],[344])).
% 2.19/2.36 tff(346,plain,
% 2.19/2.36 (![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X)))) <=> ![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 2.19/2.36 inference(rewrite,[status(thm)],[])).
% 2.19/2.36 tff(347,axiom,(![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV001-2.ax','fulladder_connection_in1_in1h2')).
% 2.19/2.36 tff(348,plain,
% 2.19/2.36 (![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 2.19/2.36 inference(modus_ponens,[status(thm)],[347, 346])).
% 2.19/2.36 tff(349,plain,(
% 2.19/2.36 ![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 2.19/2.36 inference(skolemize,[status(sab)],[348])).
% 2.19/2.36 tff(350,plain,
% 2.19/2.36 (![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))),
% 2.19/2.36 inference(modus_ponens,[status(thm)],[349, 345])).
% 2.19/2.36 tff(351,plain,
% 2.19/2.36 (((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | ((~type(f(n2, a), fulladder)) | connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a)))))) <=> ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | (~type(f(n2, a), fulladder)) | connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a)))))),
% 2.19/2.36 inference(rewrite,[status(thm)],[])).
% 2.19/2.36 tff(352,plain,
% 2.19/2.36 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | ((~type(f(n2, a), fulladder)) | connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a)))))),
% 2.19/2.36 inference(quant_inst,[status(thm)],[])).
% 2.19/2.36 tff(353,plain,
% 2.19/2.36 ((~![X: $i] : ((~type(X, fulladder)) | connection(in(n1, X), in(n1, h2(X))))) | (~type(f(n2, a), fulladder)) | connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))),
% 2.19/2.36 inference(modus_ponens,[status(thm)],[352, 351])).
% 2.19/2.36 tff(354,plain,
% 2.19/2.36 (connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))),
% 2.19/2.36 inference(unit_resolution,[status(thm)],[353, 350, 15])).
% 2.19/2.36 tff(355,plain,
% 2.19/2.36 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, f(n2, a)), n1) | (~value(in(n1, h2(f(n2, a))), n1)) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, f(n2, a)), n1) | (~value(in(n1, h2(f(n2, a))), n1)) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))))),
% 2.19/2.36 inference(rewrite,[status(thm)],[])).
% 2.19/2.36 tff(356,plain,
% 2.19/2.36 ((value(in(n1, f(n2, a)), n1) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))) | (~value(in(n1, h2(f(n2, a))), n1))) <=> (value(in(n1, f(n2, a)), n1) | (~value(in(n1, h2(f(n2, a))), n1)) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))))),
% 2.19/2.36 inference(rewrite,[status(thm)],[])).
% 2.19/2.36 tff(357,plain,
% 2.19/2.36 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, f(n2, a)), n1) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))) | (~value(in(n1, h2(f(n2, a))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, f(n2, a)), n1) | (~value(in(n1, h2(f(n2, a))), n1)) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a)))))))),
% 2.19/2.36 inference(monotonicity,[status(thm)],[356])).
% 2.19/2.36 tff(358,plain,
% 2.19/2.36 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, f(n2, a)), n1) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))) | (~value(in(n1, h2(f(n2, a))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, f(n2, a)), n1) | (~value(in(n1, h2(f(n2, a))), n1)) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))))),
% 2.19/2.36 inference(transitivity,[status(thm)],[357, 355])).
% 2.19/2.36 tff(359,plain,
% 2.19/2.36 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, f(n2, a)), n1) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a))))) | (~value(in(n1, h2(f(n2, a))), n1)))),
% 2.19/2.36 inference(quant_inst,[status(thm)],[])).
% 2.19/2.36 tff(360,plain,
% 2.19/2.36 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, f(n2, a)), n1) | (~value(in(n1, h2(f(n2, a))), n1)) | (~connection(in(n1, f(n2, a)), in(n1, h2(f(n2, a)))))),
% 2.19/2.36 inference(modus_ponens,[status(thm)],[359, 358])).
% 2.19/2.36 tff(361,plain,
% 2.19/2.36 (~value(in(n1, h2(f(n2, a))), n1)),
% 2.19/2.36 inference(unit_resolution,[status(thm)],[360, 96, 354, 343])).
% 2.19/2.36 tff(362,plain,
% 2.19/2.36 (((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h2(f(n2, a)), halfadder)) | connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a))))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h2(f(n2, a)), halfadder)) | connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a))))))),
% 2.19/2.36 inference(rewrite,[status(thm)],[])).
% 2.19/2.36 tff(363,plain,
% 2.19/2.36 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | ((~type(h2(f(n2, a)), halfadder)) | connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a))))))),
% 2.19/2.36 inference(quant_inst,[status(thm)],[])).
% 2.19/2.36 tff(364,plain,
% 2.19/2.36 ((~![X: $i] : ((~type(X, halfadder)) | connection(in(n1, X), in(n1, and2(X))))) | (~type(h2(f(n2, a)), halfadder)) | connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))),
% 2.19/2.36 inference(modus_ponens,[status(thm)],[363, 362])).
% 2.19/2.36 tff(365,plain,
% 2.19/2.36 ((~type(h2(f(n2, a)), halfadder)) | connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))),
% 2.19/2.36 inference(unit_resolution,[status(thm)],[364, 125])).
% 2.19/2.36 tff(366,plain,
% 2.19/2.36 (connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))),
% 2.19/2.36 inference(unit_resolution,[status(thm)],[365, 309])).
% 2.19/2.36 tff(367,plain,
% 2.19/2.36 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h2(f(n2, a))), n1) | (~value(in(n1, and2(h2(f(n2, a)))), n1)) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h2(f(n2, a))), n1) | (~value(in(n1, and2(h2(f(n2, a)))), n1)) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))))),
% 2.19/2.36 inference(rewrite,[status(thm)],[])).
% 2.19/2.36 tff(368,plain,
% 2.19/2.36 ((value(in(n1, h2(f(n2, a))), n1) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))) | (~value(in(n1, and2(h2(f(n2, a)))), n1))) <=> (value(in(n1, h2(f(n2, a))), n1) | (~value(in(n1, and2(h2(f(n2, a)))), n1)) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))))),
% 2.19/2.36 inference(rewrite,[status(thm)],[])).
% 2.19/2.36 tff(369,plain,
% 2.19/2.36 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h2(f(n2, a))), n1) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))) | (~value(in(n1, and2(h2(f(n2, a)))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h2(f(n2, a))), n1) | (~value(in(n1, and2(h2(f(n2, a)))), n1)) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a))))))))),
% 2.19/2.36 inference(monotonicity,[status(thm)],[368])).
% 2.19/2.36 tff(370,plain,
% 2.19/2.36 (((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h2(f(n2, a))), n1) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))) | (~value(in(n1, and2(h2(f(n2, a)))), n1)))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h2(f(n2, a))), n1) | (~value(in(n1, and2(h2(f(n2, a)))), n1)) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))))),
% 2.19/2.36 inference(transitivity,[status(thm)],[369, 367])).
% 2.19/2.36 tff(371,plain,
% 2.19/2.36 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | (value(in(n1, h2(f(n2, a))), n1) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a)))))) | (~value(in(n1, and2(h2(f(n2, a)))), n1)))),
% 2.19/2.36 inference(quant_inst,[status(thm)],[])).
% 2.19/2.36 tff(372,plain,
% 2.19/2.36 ((~![V: $i, P2: $i, P1: $i] : (value(P1, V) | (~connection(P1, P2)) | (~value(P2, V)))) | value(in(n1, h2(f(n2, a))), n1) | (~value(in(n1, and2(h2(f(n2, a)))), n1)) | (~connection(in(n1, h2(f(n2, a))), in(n1, and2(h2(f(n2, a))))))),
% 2.19/2.36 inference(modus_ponens,[status(thm)],[371, 370])).
% 2.19/2.36 tff(373,plain,
% 2.19/2.36 (~value(in(n1, and2(h2(f(n2, a)))), n1)),
% 2.19/2.36 inference(unit_resolution,[status(thm)],[372, 96, 366, 361])).
% 2.19/2.36 tff(374,plain,
% 2.19/2.36 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and2(h2(f(n2, a))), ok)) | (~type(and2(h2(f(n2, a))), and)) | (~value(out(n1, and2(h2(f(n2, a)))), n1)) | value(in(n1, and2(h2(f(n2, a)))), n1))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | (~mode(and2(h2(f(n2, a))), ok)) | (~type(and2(h2(f(n2, a))), and)) | (~value(out(n1, and2(h2(f(n2, a)))), n1)) | value(in(n1, and2(h2(f(n2, a)))), n1))),
% 2.19/2.36 inference(rewrite,[status(thm)],[])).
% 2.19/2.36 tff(375,plain,
% 2.19/2.36 (((~mode(and2(h2(f(n2, a))), ok)) | (~value(out(n1, and2(h2(f(n2, a)))), n1)) | (~type(and2(h2(f(n2, a))), and)) | value(in(n1, and2(h2(f(n2, a)))), n1)) <=> ((~mode(and2(h2(f(n2, a))), ok)) | (~type(and2(h2(f(n2, a))), and)) | (~value(out(n1, and2(h2(f(n2, a)))), n1)) | value(in(n1, and2(h2(f(n2, a)))), n1))),
% 2.19/2.36 inference(rewrite,[status(thm)],[])).
% 2.19/2.36 tff(376,plain,
% 2.19/2.36 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and2(h2(f(n2, a))), ok)) | (~value(out(n1, and2(h2(f(n2, a)))), n1)) | (~type(and2(h2(f(n2, a))), and)) | value(in(n1, and2(h2(f(n2, a)))), n1))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and2(h2(f(n2, a))), ok)) | (~type(and2(h2(f(n2, a))), and)) | (~value(out(n1, and2(h2(f(n2, a)))), n1)) | value(in(n1, and2(h2(f(n2, a)))), n1)))),
% 2.19/2.36 inference(monotonicity,[status(thm)],[375])).
% 2.19/2.36 tff(377,plain,
% 2.19/2.36 (((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and2(h2(f(n2, a))), ok)) | (~value(out(n1, and2(h2(f(n2, a)))), n1)) | (~type(and2(h2(f(n2, a))), and)) | value(in(n1, and2(h2(f(n2, a)))), n1))) <=> ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | (~mode(and2(h2(f(n2, a))), ok)) | (~type(and2(h2(f(n2, a))), and)) | (~value(out(n1, and2(h2(f(n2, a)))), n1)) | value(in(n1, and2(h2(f(n2, a)))), n1))),
% 2.19/2.36 inference(transitivity,[status(thm)],[376, 374])).
% 2.19/2.36 tff(378,plain,
% 2.19/2.36 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | ((~mode(and2(h2(f(n2, a))), ok)) | (~value(out(n1, and2(h2(f(n2, a)))), n1)) | (~type(and2(h2(f(n2, a))), and)) | value(in(n1, and2(h2(f(n2, a)))), n1))),
% 2.19/2.36 inference(quant_inst,[status(thm)],[])).
% 2.19/2.36 tff(379,plain,
% 2.19/2.36 ((~![K: $i] : ((~mode(K, ok)) | (~value(out(n1, K), n1)) | (~type(K, and)) | value(in(n1, K), n1))) | (~mode(and2(h2(f(n2, a))), ok)) | (~type(and2(h2(f(n2, a))), and)) | (~value(out(n1, and2(h2(f(n2, a)))), n1)) | value(in(n1, and2(h2(f(n2, a)))), n1)),
% 2.19/2.36 inference(modus_ponens,[status(thm)],[378, 377])).
% 2.19/2.36 tff(380,plain,
% 2.19/2.36 ((~mode(and2(h2(f(n2, a))), ok)) | (~value(out(n1, and2(h2(f(n2, a)))), n1)) | value(in(n1, and2(h2(f(n2, a)))), n1)),
% 2.19/2.36 inference(unit_resolution,[status(thm)],[379, 147, 314])).
% 2.19/2.36 tff(381,plain,
% 2.19/2.36 (~value(out(n1, and2(h2(f(n2, a)))), n1)),
% 2.19/2.36 inference(unit_resolution,[status(thm)],[380, 373, 321])).
% 2.19/2.36 tff(382,plain,
% 2.19/2.36 (((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h2(f(n2, a)), halfadder)) | connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a))))))) <=> ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h2(f(n2, a)), halfadder)) | connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a))))))),
% 2.19/2.36 inference(rewrite,[status(thm)],[])).
% 2.19/2.36 tff(383,plain,
% 2.19/2.36 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | ((~type(h2(f(n2, a)), halfadder)) | connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a))))))),
% 2.19/2.36 inference(quant_inst,[status(thm)],[])).
% 2.19/2.36 tff(384,plain,
% 2.19/2.36 ((~![X: $i] : ((~type(X, halfadder)) | connection(out(c, X), out(n1, and2(X))))) | (~type(h2(f(n2, a)), halfadder)) | connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a)))))),
% 2.19/2.37 inference(modus_ponens,[status(thm)],[383, 382])).
% 2.19/2.37 tff(385,plain,
% 2.19/2.37 ((~type(h2(f(n2, a)), halfadder)) | connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a)))))),
% 2.19/2.37 inference(unit_resolution,[status(thm)],[384, 162])).
% 2.19/2.37 tff(386,plain,
% 2.19/2.37 (connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a)))))),
% 2.19/2.37 inference(unit_resolution,[status(thm)],[385, 309])).
% 2.19/2.37 tff(387,plain,
% 2.19/2.37 (((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and2(h2(f(n2, a)))), n1) | (~value(out(c, h2(f(n2, a))), n1)) | (~connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a)))))))) <=> ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, and2(h2(f(n2, a)))), n1) | (~value(out(c, h2(f(n2, a))), n1)) | (~connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a)))))))),
% 2.19/2.37 inference(rewrite,[status(thm)],[])).
% 2.19/2.37 tff(388,plain,
% 2.19/2.37 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | (value(out(n1, and2(h2(f(n2, a)))), n1) | (~value(out(c, h2(f(n2, a))), n1)) | (~connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a)))))))),
% 2.19/2.37 inference(quant_inst,[status(thm)],[])).
% 2.19/2.37 tff(389,plain,
% 2.19/2.37 ((~![V: $i, P2: $i, P1: $i] : (value(P2, V) | (~value(P1, V)) | (~connection(P1, P2)))) | value(out(n1, and2(h2(f(n2, a)))), n1) | (~value(out(c, h2(f(n2, a))), n1)) | (~connection(out(c, h2(f(n2, a))), out(n1, and2(h2(f(n2, a))))))),
% 2.19/2.37 inference(modus_ponens,[status(thm)],[388, 387])).
% 2.19/2.37 tff(390,plain,
% 2.19/2.37 ($false),
% 2.19/2.37 inference(unit_resolution,[status(thm)],[389, 177, 386, 381, 298])).
% 2.19/2.37 % SZS output end Proof
% 2.19/2.37 % E exiting
%------------------------------------------------------------------------------