%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : HWV001-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:47:16 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.53s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 32
% Syntax : Number of clauses : 170 ( 170 unt; 0 nHn; 106 RR)
% Number of literals : 170 ( 164 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 17 con; 0-2 aty)
% Number of variables : 108 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(not_canonicalization1,axiom,
not(and(X1,X2)) = or(not(X1),not(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_canonicalization1) ).
cnf(constructor14,negated_conjecture,
f2 = not(i2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor14) ).
cnf(or_commutativity,axiom,
or(X1,X2) = or(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_commutativity) ).
cnf(not_simplification,axiom,
not(not(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_simplification) ).
cnf(constructor10,negated_conjecture,
d2 = not(e2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor10) ).
cnf(constructor4,negated_conjecture,
b2 = not(d2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor4) ).
cnf(constructor13,negated_conjecture,
f1 = not(i1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor13) ).
cnf(constructor15,negated_conjecture,
f3 = and(i1,i2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor15) ).
cnf(constructor12,negated_conjecture,
e2 = or(f2,f3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor12) ).
cnf(and_simplification2,axiom,
and(and(X1,X2),X2) = and(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_simplification2) ).
cnf(and_commutativity,axiom,
and(X1,X2) = and(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_commutativity) ).
cnf(constructor7,negated_conjecture,
c2 = or(d2,d3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor7) ).
cnf(constructor8,negated_conjecture,
d3 = f3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor8) ).
cnf(and_or_not_simplification1,axiom,
or(and(X1,X2),and(X1,not(X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_or_not_simplification1) ).
cnf(constructor9,negated_conjecture,
d1 = not(e1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor9) ).
cnf(constructor3,negated_conjecture,
b1 = not(d1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor3) ).
cnf(constructor11,negated_conjecture,
e1 = or(f1,f3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor11) ).
cnf(or_simplification3,axiom,
or(or(X1,X2),X1) = or(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_simplification3) ).
cnf(or_simplification2,axiom,
or(or(X1,X2),X2) = or(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_simplification2) ).
cnf(and_or_not_simplification2,axiom,
or(and(X1,X2),and(X2,not(X1))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_or_not_simplification2) ).
cnf(and_or_canonicalization,axiom,
and(or(X1,X2),X3) = or(and(X1,X3),and(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_or_canonicalization) ).
cnf(and_simplification3,axiom,
and(and(X1,X2),X1) = and(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_simplification3) ).
cnf(constructor6,negated_conjecture,
c1 = or(d1,d3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor6) ).
cnf(and_associativity,axiom,
and(X1,and(X2,X3)) = and(and(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_associativity) ).
cnf(constructor5,negated_conjecture,
b3 = or(c1,c2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor5) ).
cnf(not_canonicalization2,axiom,
not(or(X1,X2)) = and(not(X1),not(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_canonicalization2) ).
cnf(and_simplification1,axiom,
and(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_simplification1) ).
cnf(or_associativity,axiom,
or(X1,or(X2,X3)) = or(or(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_associativity) ).
cnf(constructor1,negated_conjecture,
a1 = and(b1,b3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor1) ).
cnf(constructor2,negated_conjecture,
a2 = and(b2,b3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',constructor2) ).
cnf(prove_interchange,negated_conjecture,
~ circuit(input(i1,i2),output(i2,i1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_interchange) ).
cnf(circuit_description,negated_conjecture,
circuit(input(i1,i2),output(a1,a2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',circuit_description) ).
cnf(c_0_32,axiom,
not(and(X1,X2)) = or(not(X1),not(X2)),
not_canonicalization1 ).
cnf(c_0_33,negated_conjecture,
f2 = not(i2),
constructor14 ).
cnf(c_0_34,axiom,
or(X1,X2) = or(X2,X1),
or_commutativity ).
cnf(c_0_35,axiom,
not(not(X1)) = X1,
not_simplification ).
cnf(c_0_36,negated_conjecture,
d2 = not(e2),
constructor10 ).
cnf(c_0_37,negated_conjecture,
b2 = not(d2),
constructor4 ).
cnf(c_0_38,negated_conjecture,
or(f2,not(X1)) = not(and(X1,i2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_39,negated_conjecture,
f1 = not(i1),
constructor13 ).
cnf(c_0_40,negated_conjecture,
f3 = and(i1,i2),
constructor15 ).
cnf(c_0_41,negated_conjecture,
e2 = or(f2,f3),
constructor12 ).
cnf(c_0_42,negated_conjecture,
e2 = b2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_43,negated_conjecture,
not(f3) = or(f1,f2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_34]) ).
cnf(c_0_44,negated_conjecture,
or(f2,f3) = b2,
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,axiom,
and(and(X1,X2),X2) = and(X1,X2),
and_simplification2 ).
cnf(c_0_46,axiom,
and(X1,X2) = and(X2,X1),
and_commutativity ).
cnf(c_0_47,negated_conjecture,
not(or(f1,f2)) = f3,
inference(spm,[status(thm)],[c_0_35,c_0_43]) ).
cnf(c_0_48,negated_conjecture,
or(f3,f2) = b2,
inference(rw,[status(thm)],[c_0_44,c_0_34]) ).
cnf(c_0_49,negated_conjecture,
c2 = or(d2,d3),
constructor7 ).
cnf(c_0_50,negated_conjecture,
d3 = f3,
constructor8 ).
cnf(c_0_51,plain,
and(X1,and(X2,X1)) = and(X2,X1),
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,negated_conjecture,
not(and(i2,or(f1,f2))) = b2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_47]),c_0_34]),c_0_48]),c_0_46]) ).
cnf(c_0_53,negated_conjecture,
not(b2) = d2,
inference(spm,[status(thm)],[c_0_35,c_0_37]) ).
cnf(c_0_54,negated_conjecture,
or(d2,f3) = c2,
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,axiom,
or(and(X1,X2),and(X1,not(X2))) = X1,
and_or_not_simplification1 ).
cnf(c_0_56,negated_conjecture,
and(i2,f3) = f3,
inference(spm,[status(thm)],[c_0_51,c_0_40]) ).
cnf(c_0_57,negated_conjecture,
and(i2,or(f1,f2)) = d2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_52]),c_0_53]) ).
cnf(c_0_58,negated_conjecture,
or(f3,d2) = c2,
inference(rw,[status(thm)],[c_0_54,c_0_34]) ).
cnf(c_0_59,negated_conjecture,
d1 = not(e1),
constructor9 ).
cnf(c_0_60,negated_conjecture,
b1 = not(d1),
constructor3 ).
cnf(c_0_61,negated_conjecture,
or(d2,not(X1)) = not(and(X1,b2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_53]),c_0_34]) ).
cnf(c_0_62,negated_conjecture,
c2 = i2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_43]),c_0_57]),c_0_58]) ).
cnf(c_0_63,negated_conjecture,
e1 = or(f1,f3),
constructor11 ).
cnf(c_0_64,negated_conjecture,
e1 = b1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_59]),c_0_60]) ).
cnf(c_0_65,axiom,
or(or(X1,X2),X1) = or(X1,X2),
or_simplification3 ).
cnf(c_0_66,negated_conjecture,
not(and(b2,or(f1,f2))) = i2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_47]),c_0_34]),c_0_58]),c_0_62]),c_0_46]) ).
cnf(c_0_67,axiom,
or(or(X1,X2),X2) = or(X1,X2),
or_simplification2 ).
cnf(c_0_68,axiom,
or(and(X1,X2),and(X2,not(X1))) = X2,
and_or_not_simplification2 ).
cnf(c_0_69,negated_conjecture,
or(f1,f3) = b1,
inference(rw,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_70,plain,
or(X1,or(X1,X2)) = or(X1,X2),
inference(rw,[status(thm)],[c_0_65,c_0_34]) ).
cnf(c_0_71,negated_conjecture,
and(b2,or(f1,f2)) = f2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_66]),c_0_33]) ).
cnf(c_0_72,negated_conjecture,
and(d2,or(f1,f2)) = d2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_57]),c_0_46]) ).
cnf(c_0_73,negated_conjecture,
not(and(i2,b2)) = or(d2,f2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_53]),c_0_46]),c_0_34]) ).
cnf(c_0_74,plain,
or(X1,or(X2,X1)) = or(X2,X1),
inference(rw,[status(thm)],[c_0_67,c_0_34]) ).
cnf(c_0_75,negated_conjecture,
or(and(i2,X1),and(X1,f2)) = X1,
inference(spm,[status(thm)],[c_0_68,c_0_33]) ).
cnf(c_0_76,axiom,
and(or(X1,X2),X3) = or(and(X1,X3),and(X2,X3)),
and_or_canonicalization ).
cnf(c_0_77,negated_conjecture,
or(f1,not(X1)) = not(and(X1,i1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_39]),c_0_34]) ).
cnf(c_0_78,negated_conjecture,
or(f3,f1) = b1,
inference(rw,[status(thm)],[c_0_69,c_0_34]) ).
cnf(c_0_79,axiom,
and(and(X1,X2),X1) = and(X1,X2),
and_simplification3 ).
cnf(c_0_80,negated_conjecture,
c1 = or(d1,d3),
constructor6 ).
cnf(c_0_81,plain,
or(X1,and(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_68]),c_0_34]) ).
cnf(c_0_82,axiom,
and(X1,and(X2,X3)) = and(and(X1,X2),X3),
and_associativity ).
cnf(c_0_83,negated_conjecture,
or(f1,f2) = or(d2,f2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_71]),c_0_53]),c_0_46]),c_0_72]),c_0_34]) ).
cnf(c_0_84,negated_conjecture,
not(or(d2,f2)) = and(i2,b2),
inference(spm,[status(thm)],[c_0_35,c_0_73]) ).
cnf(c_0_85,negated_conjecture,
or(b2,f2) = b2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_48]),c_0_34]) ).
cnf(c_0_86,negated_conjecture,
not(f1) = i1,
inference(spm,[status(thm)],[c_0_35,c_0_39]) ).
cnf(c_0_87,negated_conjecture,
and(or(i2,f2),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_46]),c_0_76]) ).
cnf(c_0_88,negated_conjecture,
not(and(i1,or(f1,f2))) = b1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_47]),c_0_34]),c_0_78]),c_0_46]) ).
cnf(c_0_89,negated_conjecture,
not(b1) = d1,
inference(spm,[status(thm)],[c_0_35,c_0_60]) ).
cnf(c_0_90,plain,
and(X1,and(X1,X2)) = and(X1,X2),
inference(rw,[status(thm)],[c_0_79,c_0_46]) ).
cnf(c_0_91,negated_conjecture,
or(d1,f3) = c1,
inference(rw,[status(thm)],[c_0_80,c_0_50]) ).
cnf(c_0_92,plain,
or(X1,and(X2,and(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_93,negated_conjecture,
and(i2,b2) = f3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_83]),c_0_84]) ).
cnf(c_0_94,negated_conjecture,
not(and(i2,d2)) = b2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_37]),c_0_34]),c_0_85]),c_0_46]) ).
cnf(c_0_95,negated_conjecture,
or(i1,not(X1)) = not(and(X1,f1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_86]),c_0_34]) ).
cnf(c_0_96,negated_conjecture,
or(X1,not(X1)) = or(i2,f2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_87]),c_0_87]) ).
cnf(c_0_97,negated_conjecture,
not(and(i1,f1)) = or(i1,f1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_86]),c_0_46]),c_0_34]) ).
cnf(c_0_98,negated_conjecture,
b3 = or(c1,c2),
constructor5 ).
cnf(c_0_99,negated_conjecture,
and(i1,or(f1,f2)) = d1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_88]),c_0_89]) ).
cnf(c_0_100,negated_conjecture,
and(i1,f3) = f3,
inference(spm,[status(thm)],[c_0_90,c_0_40]) ).
cnf(c_0_101,negated_conjecture,
or(f3,d1) = c1,
inference(rw,[status(thm)],[c_0_91,c_0_34]) ).
cnf(c_0_102,axiom,
not(or(X1,X2)) = and(not(X1),not(X2)),
not_canonicalization2 ).
cnf(c_0_103,negated_conjecture,
not(f2) = i2,
inference(spm,[status(thm)],[c_0_35,c_0_33]) ).
cnf(c_0_104,negated_conjecture,
or(b2,and(X1,f3)) = b2,
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_105,negated_conjecture,
and(i1,and(i2,X1)) = and(f3,X1),
inference(spm,[status(thm)],[c_0_82,c_0_40]) ).
cnf(c_0_106,negated_conjecture,
and(i2,d2) = d2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_94]),c_0_53]) ).
cnf(c_0_107,negated_conjecture,
or(i2,f2) = or(i1,f1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]) ).
cnf(c_0_108,negated_conjecture,
or(i2,c1) = b3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_62]),c_0_34]) ).
cnf(c_0_109,negated_conjecture,
c1 = i1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_99]),c_0_47]),c_0_100]),c_0_34]),c_0_101]) ).
cnf(c_0_110,axiom,
and(X1,X1) = X1,
and_simplification1 ).
cnf(c_0_111,plain,
not(and(X1,not(X2))) = or(not(X1),X2),
inference(spm,[status(thm)],[c_0_32,c_0_35]) ).
cnf(c_0_112,negated_conjecture,
not(or(X1,f2)) = and(i2,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_46]) ).
cnf(c_0_113,negated_conjecture,
not(or(i1,X1)) = and(f1,not(X1)),
inference(spm,[status(thm)],[c_0_102,c_0_39]) ).
cnf(c_0_114,negated_conjecture,
or(b2,and(f3,X1)) = b2,
inference(spm,[status(thm)],[c_0_104,c_0_46]) ).
cnf(c_0_115,negated_conjecture,
and(f3,d2) = and(i1,d2),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_116,negated_conjecture,
not(or(d2,X1)) = and(b2,not(X1)),
inference(spm,[status(thm)],[c_0_102,c_0_37]) ).
cnf(c_0_117,negated_conjecture,
or(X1,not(X1)) = or(i1,f1),
inference(rw,[status(thm)],[c_0_96,c_0_107]) ).
cnf(c_0_118,negated_conjecture,
not(or(X1,f1)) = and(i1,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_86]),c_0_46]) ).
cnf(c_0_119,negated_conjecture,
or(i1,i2) = b3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109]),c_0_34]) ).
cnf(c_0_120,plain,
and(X1,or(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_110]),c_0_81]),c_0_46]) ).
cnf(c_0_121,negated_conjecture,
not(and(b2,f1)) = or(i1,d2),
inference(spm,[status(thm)],[c_0_95,c_0_53]) ).
cnf(c_0_122,negated_conjecture,
or(i2,not(X1)) = not(and(X1,f2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_103]),c_0_34]) ).
cnf(c_0_123,negated_conjecture,
or(and(i2,f2),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_87]),c_0_35]),c_0_112]),c_0_33]) ).
cnf(c_0_124,negated_conjecture,
and(i2,f2) = and(i1,f1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_96]),c_0_112]),c_0_33]),c_0_39]),c_0_86]),c_0_46]) ).
cnf(c_0_125,plain,
and(X1,or(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_110]),c_0_34]),c_0_81]),c_0_46]) ).
cnf(c_0_126,negated_conjecture,
or(b2,and(i1,d2)) = b2,
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_127,negated_conjecture,
and(d2,b2) = and(i1,f1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]),c_0_39]),c_0_37]),c_0_53]),c_0_46]) ).
cnf(c_0_128,negated_conjecture,
or(i1,d2) = b3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_66]),c_0_119]),c_0_82]),c_0_46]),c_0_120]),c_0_121]) ).
cnf(c_0_129,negated_conjecture,
not(and(f1,f2)) = b3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_86]),c_0_34]),c_0_119]) ).
cnf(c_0_130,negated_conjecture,
or(and(i1,f1),X1) = X1,
inference(rw,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_131,negated_conjecture,
and(i1,f1) = and(i1,d2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_82]),c_0_127]),c_0_90]) ).
cnf(c_0_132,negated_conjecture,
not(and(b2,f1)) = b3,
inference(rw,[status(thm)],[c_0_121,c_0_128]) ).
cnf(c_0_133,negated_conjecture,
not(b3) = and(f1,f2),
inference(spm,[status(thm)],[c_0_35,c_0_129]) ).
cnf(c_0_134,axiom,
or(X1,or(X2,X3)) = or(or(X1,X2),X3),
or_associativity ).
cnf(c_0_135,negated_conjecture,
or(i2,f3) = i2,
inference(spm,[status(thm)],[c_0_81,c_0_40]) ).
cnf(c_0_136,plain,
or(and(X1,X2),and(not(X2),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_35]),c_0_34]) ).
cnf(c_0_137,negated_conjecture,
or(and(i1,d2),X1) = X1,
inference(rw,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_138,negated_conjecture,
and(f1,f2) = and(b2,f1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_132]),c_0_133]) ).
cnf(c_0_139,negated_conjecture,
a1 = and(b1,b3),
constructor1 ).
cnf(c_0_140,negated_conjecture,
or(i2,or(f3,X1)) = or(i2,X1),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_141,negated_conjecture,
or(f3,d1) = i1,
inference(rw,[status(thm)],[c_0_101,c_0_109]) ).
cnf(c_0_142,negated_conjecture,
or(f3,d2) = i2,
inference(rw,[status(thm)],[c_0_58,c_0_62]) ).
cnf(c_0_143,negated_conjecture,
not(and(i1,b2)) = or(d2,f1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_53]),c_0_46]),c_0_34]) ).
cnf(c_0_144,negated_conjecture,
and(i1,b2) = i1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_37]),c_0_46]) ).
cnf(c_0_145,negated_conjecture,
or(d1,not(X1)) = not(and(X1,b1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_89]),c_0_34]) ).
cnf(c_0_146,negated_conjecture,
not(b3) = and(b2,f1),
inference(rw,[status(thm)],[c_0_133,c_0_138]) ).
cnf(c_0_147,negated_conjecture,
and(b3,b1) = a1,
inference(rw,[status(thm)],[c_0_139,c_0_46]) ).
cnf(c_0_148,negated_conjecture,
not(or(X1,d1)) = and(b1,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_60]),c_0_46]) ).
cnf(c_0_149,negated_conjecture,
or(i2,d1) = b3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_34]),c_0_119]) ).
cnf(c_0_150,negated_conjecture,
a2 = and(b2,b3),
constructor2 ).
cnf(c_0_151,negated_conjecture,
or(f3,or(d2,X1)) = or(i2,X1),
inference(spm,[status(thm)],[c_0_134,c_0_142]) ).
cnf(c_0_152,negated_conjecture,
or(d2,f1) = f1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_144]),c_0_39]) ).
cnf(c_0_153,negated_conjecture,
or(i2,f1) = or(i2,b1),
inference(spm,[status(thm)],[c_0_140,c_0_78]) ).
cnf(c_0_154,negated_conjecture,
or(d1,and(b2,f1)) = not(a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_147]) ).
cnf(c_0_155,negated_conjecture,
and(b2,f1) = and(b1,f2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_133]),c_0_138]),c_0_33]) ).
cnf(c_0_156,negated_conjecture,
and(b3,b2) = a2,
inference(rw,[status(thm)],[c_0_150,c_0_46]) ).
cnf(c_0_157,plain,
or(and(not(X1),X2),not(or(X1,X2))) = not(X1),
inference(spm,[status(thm)],[c_0_55,c_0_102]) ).
cnf(c_0_158,negated_conjecture,
or(i2,b1) = b1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_78]),c_0_153]) ).
cnf(c_0_159,negated_conjecture,
or(d1,and(b1,f2)) = not(a1),
inference(rw,[status(thm)],[c_0_154,c_0_155]) ).
cnf(c_0_160,negated_conjecture,
and(d2,f1) = d2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_137]),c_0_39]) ).
cnf(c_0_161,negated_conjecture,
or(d2,and(b2,f1)) = not(a2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_146]),c_0_156]) ).
cnf(c_0_162,negated_conjecture,
not(a1) = f2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_33]),c_0_46]),c_0_89]),c_0_34]),c_0_159]),c_0_33]) ).
cnf(c_0_163,negated_conjecture,
not(a2) = f1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_160]),c_0_37]),c_0_46]),c_0_161]) ).
cnf(c_0_164,negated_conjecture,
~ circuit(input(i1,i2),output(i2,i1)),
inference(fof_simplification,[status(thm)],[prove_interchange]) ).
cnf(c_0_165,negated_conjecture,
circuit(input(i1,i2),output(a1,a2)),
circuit_description ).
cnf(c_0_166,negated_conjecture,
a1 = i2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_162]),c_0_103]) ).
cnf(c_0_167,negated_conjecture,
a2 = i1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_163]),c_0_86]) ).
cnf(c_0_168,negated_conjecture,
~ circuit(input(i1,i2),output(i2,i1)),
c_0_164 ).
cnf(c_0_169,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_167]),c_0_168]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV001-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.39 % Computer : n005.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Sun Sep 20 20:47:24 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.44 Running first-order theorem proving
% 0.15/5.44 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.53 % Version: 3.5.1
% 0.15/5.53 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.15/5.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.15/5.53 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.53 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.53 % Starting sh5l with 300s (1) cores
% 0.15/5.53 % new_bool_1 with pid 1742950 completed with status 0
% 0.15/5.53 % Result found by new_bool_1
% 0.15/5.53 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.15/5.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.15/5.53 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.53 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.53 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.53 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.53 % Search class: FUUSM-FFMM21-MFFFFFNN
% 0.15/5.53 % partial match(1): FGUSM-FFMM21-MFFFFFNN
% 0.15/5.53 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.53 % Starting SubtermCWHack with 31s (1) cores
% 0.15/5.53 % SubtermCWHack with pid 1742957 completed with status 0
% 0.15/5.53 % Result found by SubtermCWHack
% 0.15/5.53 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.15/5.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.53 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.15/5.53 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.53 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.53 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.15/5.53 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.15/5.53 % Search class: FUUSM-FFMM21-MFFFFFNN
% 0.15/5.53 % partial match(1): FGUSM-FFMM21-MFFFFFNN
% 0.15/5.53 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.15/5.53 % Starting SubtermCWHack with 31s (1) cores
% 0.15/5.53 % Preprocessing time : 0.001 s
% 0.15/5.53
% 0.15/5.53 % Proof found!
% 0.15/5.53 % SZS status Unsatisfiable
% 0.15/5.53 % SZS output start CNFRefutation
% See solution above
% 0.15/5.54 % Parsed axioms : 47
% 0.15/5.54 % Removed by relevancy pruning/SinE : 12
% 0.15/5.54 % Initial clauses : 35
% 0.15/5.54 % Removed in clause preprocessing : 0
% 0.15/5.54 % Initial clauses in saturation : 35
% 0.15/5.54 % Processed clauses : 1422
% 0.15/5.54 % ...of these trivial : 756
% 0.15/5.54 % ...subsumed : 102
% 0.15/5.54 % ...remaining for further processing : 564
% 0.15/5.54 % Other redundant clauses eliminated : 0
% 0.15/5.54 % Clauses deleted for lack of memory : 0
% 0.15/5.54 % Backward-subsumed : 0
% 0.15/5.54 % Backward-rewritten : 208
% 0.15/5.54 % Generated clauses : 18319
% 0.15/5.54 % ...of the previous two non-redundant : 10796
% 0.15/5.54 % ...aggressively subsumed : 0
% 0.15/5.54 % Contextual simplify-reflections : 0
% 0.15/5.54 % Paramodulations : 18319
% 0.15/5.54 % Factorizations : 0
% 0.15/5.54 % NegExts : 0
% 0.15/5.54 % Equation resolutions : 0
% 0.15/5.54 % Disequality decompositions : 0
% 0.15/5.54 % Total rewrite steps : 25148
% 0.15/5.54 % ...of those cached : 20760
% 0.15/5.54 % Propositional unsat checks : 0
% 0.15/5.54 % Propositional check models : 0
% 0.15/5.54 % Propositional check unsatisfiable : 0
% 0.15/5.54 % Propositional clauses : 0
% 0.15/5.54 % Propositional clauses after purity: 0
% 0.15/5.54 % Propositional unsat core size : 0
% 0.15/5.54 % Propositional preprocessing time : 0.000
% 0.15/5.54 % Propositional encoding time : 0.000
% 0.15/5.54 % Propositional solver time : 0.000
% 0.15/5.54 % Success case prop preproc time : 0.000
% 0.15/5.54 % Success case prop encoding time : 0.000
% 0.15/5.54 % Success case prop solver time : 0.000
% 0.15/5.54 % Current number of processed clauses : 356
% 0.15/5.54 % Positive orientable unit clauses : 350
% 0.15/5.54 % Positive unorientable unit clauses: 5
% 0.15/5.54 % Negative unit clauses : 1
% 0.15/5.54 % Non-unit-clauses : 0
% 0.15/5.54 % Current number of unprocessed clauses: 9283
% 0.15/5.54 % ...number of literals in the above : 9283
% 0.15/5.54 % Current number of archived formulas : 0
% 0.15/5.54 % Current number of archived clauses : 208
% 0.15/5.54 % Clause-clause subsumption calls (NU) : 0
% 0.15/5.54 % Rec. Clause-clause subsumption calls : 0
% 0.15/5.54 % Non-unit clause-clause subsumptions : 0
% 0.15/5.54 % Unit Clause-clause subsumption calls : 40
% 0.15/5.54 % Rewrite failures with RHS unbound : 0
% 0.15/5.54 % BW rewrite match attempts : 620
% 0.15/5.54 % BW rewrite match successes : 211
% 0.15/5.54 % Condensation attempts : 0
% 0.15/5.54 % Condensation successes : 0
% 0.15/5.54 % Termbank termtop insertions : 156261
% 0.15/5.54 % Search garbage collected termcells : 28
% 0.15/5.54
% 0.15/5.54 % -------------------------------------------------
% 0.15/5.54 % User time : 0.073 s
% 0.15/5.54 % System time : 0.009 s
% 0.15/5.54 % Total time : 0.081 s
% 0.15/5.54 % Maximum resident set size: 3660 pages
% 0.15/5.54
% 0.15/5.54 % -------------------------------------------------
% 0.15/5.54 % User time : 0.074 s
% 0.15/5.54 % System time : 0.014 s
% 0.15/5.54 % Total time : 0.088 s
% 0.15/5.54 % Maximum resident set size: 4864 pages
% 0.15/5.54 % E exiting
%------------------------------------------------------------------------------