%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : HWV001-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 12:48:41 PM UTC 2026
% Result : Unsatisfiable 0.79s 0.50s
% Output : CNFRefutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 35
% Syntax : Number of clauses : 201 ( 201 unt; 0 nHn; 138 RR)
% Number of literals : 201 ( 195 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 : 24 ( 24 usr; 19 con; 0-2 aty)
% Number of variables : 105 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(not_canonicalization1,axiom,
not(and(X1,X2)) = or(not(X1),not(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_canonicalization1) ).
cnf(constructor14,negated_conjecture,
f2 = not(i2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor14) ).
cnf(or_commutativity,axiom,
or(X1,X2) = or(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_commutativity) ).
cnf(constructor13,negated_conjecture,
f1 = not(i1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor13) ).
cnf(constructor15,negated_conjecture,
f3 = and(i1,i2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor15) ).
cnf(constructor12,negated_conjecture,
e2 = or(f2,f3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor12) ).
cnf(not_simplification,axiom,
not(not(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_simplification) ).
cnf(constructor10,negated_conjecture,
d2 = not(e2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor10) ).
cnf(constructor4,negated_conjecture,
b2 = not(d2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor4) ).
cnf(and_not_simplification3,axiom,
and(and(X1,X2),not(X1)) = n0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_not_simplification3) ).
cnf(and_associativity,axiom,
and(X1,and(X2,X3)) = and(and(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_associativity) ).
cnf(and_commutativity,axiom,
and(X1,X2) = and(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_commutativity) ).
cnf(or_definition1,axiom,
or(X1,n0) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',or_definition1) ).
cnf(and_or_not_simplification2,axiom,
or(and(X1,X2),and(X2,not(X1))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_not_simplification2) ).
cnf(and_simplification2,axiom,
and(and(X1,X2),X2) = and(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_simplification2) ).
cnf(constructor11,negated_conjecture,
e1 = or(f1,f3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor11) ).
cnf(constructor9,negated_conjecture,
d1 = not(e1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor9) ).
cnf(constructor3,negated_conjecture,
b1 = not(d1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor3) ).
cnf(constructor7,negated_conjecture,
c2 = or(d2,d3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor7) ).
cnf(constructor8,negated_conjecture,
d3 = f3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor8) ).
cnf(and_or_not_simplification1,axiom,
or(and(X1,X2),and(X1,not(X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_or_not_simplification1) ).
cnf(and_simplification3,axiom,
and(and(X1,X2),X1) = and(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_simplification3) ).
cnf(constructor6,negated_conjecture,
c1 = or(d1,d3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor6) ).
cnf(constructor5,negated_conjecture,
b3 = or(c1,c2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor5) ).
cnf(not_canonicalization2,axiom,
not(or(X1,X2)) = and(not(X1),not(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_canonicalization2) ).
cnf(or_simplification3,axiom,
or(or(X1,X2),X1) = or(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_simplification3) ).
cnf(or_simplification2,axiom,
or(or(X1,X2),X2) = or(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_simplification2) ).
cnf(or_not_simplification3,axiom,
or(or(X1,X2),not(X1)) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_not_simplification3) ).
cnf(or_associativity,axiom,
or(X1,or(X2,X3)) = or(or(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_associativity) ).
cnf(constructor1,negated_conjecture,
a1 = and(b1,b3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor1) ).
cnf(or_not_simplification1,axiom,
or(X1,not(X1)) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_not_simplification1) ).
cnf(not_definition2,axiom,
not(n1) = n0,
file('/export/starexec/sandbox2/benchmark/Axioms/HWC002-0.ax',not_definition2) ).
cnf(constructor2,negated_conjecture,
a2 = and(b2,b3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',constructor2) ).
cnf(prove_interchange,negated_conjecture,
~ circuit(input(i1,i2),output(i2,i1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_interchange) ).
cnf(circuit_description,negated_conjecture,
circuit(input(i1,i2),output(a1,a2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',circuit_description) ).
cnf(c_0_35,axiom,
not(and(X1,X2)) = or(not(X1),not(X2)),
not_canonicalization1 ).
cnf(c_0_36,negated_conjecture,
f2 = not(i2),
constructor14 ).
cnf(c_0_37,axiom,
or(X1,X2) = or(X2,X1),
or_commutativity ).
cnf(c_0_38,negated_conjecture,
or(f2,not(X1)) = not(and(X1,i2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
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,axiom,
not(not(X1)) = X1,
not_simplification ).
cnf(c_0_43,negated_conjecture,
d2 = not(e2),
constructor10 ).
cnf(c_0_44,negated_conjecture,
b2 = not(d2),
constructor4 ).
cnf(c_0_45,axiom,
and(and(X1,X2),not(X1)) = n0,
and_not_simplification3 ).
cnf(c_0_46,axiom,
and(X1,and(X2,X3)) = and(and(X1,X2),X3),
and_associativity ).
cnf(c_0_47,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_37]) ).
cnf(c_0_48,negated_conjecture,
or(f3,f2) = e2,
inference(rw,[status(thm)],[c_0_41,c_0_37]) ).
cnf(c_0_49,negated_conjecture,
e2 = b2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_50,plain,
and(X1,and(X2,not(X1))) = n0,
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
not(f2) = i2,
inference(spm,[status(thm)],[c_0_42,c_0_36]) ).
cnf(c_0_52,negated_conjecture,
not(or(f1,f2)) = f3,
inference(spm,[status(thm)],[c_0_42,c_0_47]) ).
cnf(c_0_53,negated_conjecture,
or(f3,f2) = b2,
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,axiom,
and(X1,X2) = and(X2,X1),
and_commutativity ).
cnf(c_0_55,negated_conjecture,
and(f2,and(X1,i2)) = n0,
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,axiom,
or(X1,n0) = X1,
or_definition1 ).
cnf(c_0_57,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_52]),c_0_37]),c_0_53]),c_0_54]) ).
cnf(c_0_58,negated_conjecture,
not(b2) = d2,
inference(spm,[status(thm)],[c_0_42,c_0_44]) ).
cnf(c_0_59,axiom,
or(and(X1,X2),and(X2,not(X1))) = X2,
and_or_not_simplification2 ).
cnf(c_0_60,negated_conjecture,
and(f3,f2) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_40]),c_0_54]) ).
cnf(c_0_61,plain,
or(n0,X1) = X1,
inference(spm,[status(thm)],[c_0_56,c_0_37]) ).
cnf(c_0_62,negated_conjecture,
and(i2,or(f1,f2)) = d2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_57]),c_0_58]) ).
cnf(c_0_63,negated_conjecture,
and(f2,or(f1,f2)) = f2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_47]),c_0_61]) ).
cnf(c_0_64,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_58]),c_0_54]),c_0_37]) ).
cnf(c_0_65,axiom,
and(and(X1,X2),X2) = and(X1,X2),
and_simplification2 ).
cnf(c_0_66,negated_conjecture,
or(f1,f2) = or(d2,f2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_62]),c_0_36]),c_0_54]),c_0_63]) ).
cnf(c_0_67,negated_conjecture,
not(or(d2,f2)) = and(i2,b2),
inference(spm,[status(thm)],[c_0_42,c_0_64]) ).
cnf(c_0_68,negated_conjecture,
e1 = or(f1,f3),
constructor11 ).
cnf(c_0_69,negated_conjecture,
d1 = not(e1),
constructor9 ).
cnf(c_0_70,negated_conjecture,
b1 = not(d1),
constructor3 ).
cnf(c_0_71,plain,
and(X1,and(X2,X1)) = and(X2,X1),
inference(rw,[status(thm)],[c_0_65,c_0_54]) ).
cnf(c_0_72,negated_conjecture,
c2 = or(d2,d3),
constructor7 ).
cnf(c_0_73,negated_conjecture,
d3 = f3,
constructor8 ).
cnf(c_0_74,negated_conjecture,
and(i2,b2) = f3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_66]),c_0_67]) ).
cnf(c_0_75,negated_conjecture,
or(f3,f1) = e1,
inference(rw,[status(thm)],[c_0_68,c_0_37]) ).
cnf(c_0_76,negated_conjecture,
e1 = b1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_69]),c_0_70]) ).
cnf(c_0_77,axiom,
or(and(X1,X2),and(X1,not(X2))) = X1,
and_or_not_simplification1 ).
cnf(c_0_78,negated_conjecture,
and(i2,f3) = f3,
inference(spm,[status(thm)],[c_0_71,c_0_40]) ).
cnf(c_0_79,negated_conjecture,
or(d2,f3) = c2,
inference(rw,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_80,negated_conjecture,
or(f1,not(X1)) = not(and(X1,i1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_39]),c_0_37]) ).
cnf(c_0_81,negated_conjecture,
not(or(d2,f2)) = f3,
inference(rw,[status(thm)],[c_0_67,c_0_74]) ).
cnf(c_0_82,negated_conjecture,
or(f3,f1) = b1,
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_83,axiom,
and(and(X1,X2),X1) = and(X1,X2),
and_simplification3 ).
cnf(c_0_84,negated_conjecture,
c1 = or(d1,d3),
constructor6 ).
cnf(c_0_85,negated_conjecture,
or(f3,and(i2,or(f1,f2))) = i2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_47]) ).
cnf(c_0_86,negated_conjecture,
or(f3,d2) = c2,
inference(rw,[status(thm)],[c_0_79,c_0_37]) ).
cnf(c_0_87,negated_conjecture,
not(and(i1,or(d2,f2))) = b1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_37]),c_0_82]),c_0_54]) ).
cnf(c_0_88,negated_conjecture,
not(b1) = d1,
inference(spm,[status(thm)],[c_0_42,c_0_70]) ).
cnf(c_0_89,plain,
and(X1,and(X1,X2)) = and(X1,X2),
inference(rw,[status(thm)],[c_0_83,c_0_54]) ).
cnf(c_0_90,negated_conjecture,
or(d1,f3) = c1,
inference(rw,[status(thm)],[c_0_84,c_0_73]) ).
cnf(c_0_91,negated_conjecture,
b3 = or(c1,c2),
constructor5 ).
cnf(c_0_92,negated_conjecture,
c2 = i2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_62]),c_0_86]) ).
cnf(c_0_93,negated_conjecture,
and(i1,or(d2,f2)) = d1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_87]),c_0_88]) ).
cnf(c_0_94,negated_conjecture,
and(i1,f3) = f3,
inference(spm,[status(thm)],[c_0_89,c_0_40]) ).
cnf(c_0_95,negated_conjecture,
or(f3,d1) = c1,
inference(rw,[status(thm)],[c_0_90,c_0_37]) ).
cnf(c_0_96,axiom,
not(or(X1,X2)) = and(not(X1),not(X2)),
not_canonicalization2 ).
cnf(c_0_97,negated_conjecture,
or(i2,c1) = b3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92]),c_0_37]) ).
cnf(c_0_98,negated_conjecture,
c1 = i1,
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_77,c_0_93]),c_0_67]),c_0_74]),c_0_94]),c_0_37]),c_0_95]) ).
cnf(c_0_99,axiom,
or(or(X1,X2),X1) = or(X1,X2),
or_simplification3 ).
cnf(c_0_100,axiom,
or(or(X1,X2),X2) = or(X1,X2),
or_simplification2 ).
cnf(c_0_101,negated_conjecture,
not(or(X1,i2)) = and(f2,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_36]),c_0_54]) ).
cnf(c_0_102,negated_conjecture,
or(i1,i2) = b3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98]),c_0_37]) ).
cnf(c_0_103,plain,
or(X1,or(X1,X2)) = or(X1,X2),
inference(rw,[status(thm)],[c_0_99,c_0_37]) ).
cnf(c_0_104,plain,
or(X1,or(X2,X1)) = or(X2,X1),
inference(rw,[status(thm)],[c_0_100,c_0_37]) ).
cnf(c_0_105,negated_conjecture,
not(b3) = and(f1,f2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_39]),c_0_54]) ).
cnf(c_0_106,plain,
or(X1,and(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_77]),c_0_37]) ).
cnf(c_0_107,negated_conjecture,
or(b1,f1) = b1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_82]),c_0_37]) ).
cnf(c_0_108,negated_conjecture,
or(b1,not(X1)) = not(and(X1,d1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_70]),c_0_37]) ).
cnf(c_0_109,negated_conjecture,
not(and(i1,b3)) = f1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_105]),c_0_106]),c_0_54]) ).
cnf(c_0_110,negated_conjecture,
not(f1) = i1,
inference(spm,[status(thm)],[c_0_42,c_0_39]) ).
cnf(c_0_111,negated_conjecture,
not(and(i1,d1)) = b1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_70]),c_0_37]),c_0_107]),c_0_54]) ).
cnf(c_0_112,negated_conjecture,
not(and(i1,f2)) = or(i2,f1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_51]),c_0_54]),c_0_37]) ).
cnf(c_0_113,negated_conjecture,
not(and(d1,b3)) = or(b1,and(f1,f2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_105]),c_0_54]) ).
cnf(c_0_114,negated_conjecture,
and(i1,b3) = i1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_109]),c_0_110]) ).
cnf(c_0_115,negated_conjecture,
and(i1,d1) = d1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_111]),c_0_88]) ).
cnf(c_0_116,axiom,
or(or(X1,X2),not(X1)) = n1,
or_not_simplification3 ).
cnf(c_0_117,axiom,
or(X1,or(X2,X3)) = or(or(X1,X2),X3),
or_associativity ).
cnf(c_0_118,negated_conjecture,
not(or(i2,f1)) = and(i1,f2),
inference(spm,[status(thm)],[c_0_42,c_0_112]) ).
cnf(c_0_119,plain,
or(X1,and(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_59]),c_0_37]) ).
cnf(c_0_120,negated_conjecture,
or(f1,or(b1,and(f1,f2))) = b1,
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_80,c_0_113]),c_0_46]),c_0_54]),c_0_114]),c_0_54]),c_0_115]),c_0_70]) ).
cnf(c_0_121,negated_conjecture,
not(or(X1,d1)) = and(b1,not(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_70]),c_0_54]) ).
cnf(c_0_122,negated_conjecture,
or(f3,d1) = i1,
inference(rw,[status(thm)],[c_0_95,c_0_98]) ).
cnf(c_0_123,plain,
or(X1,or(X2,not(X1))) = n1,
inference(rw,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_124,negated_conjecture,
not(and(i2,or(i2,f1))) = f2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_118]),c_0_119]),c_0_54]) ).
cnf(c_0_125,negated_conjecture,
a1 = and(b1,b3),
constructor1 ).
cnf(c_0_126,negated_conjecture,
or(b1,and(f1,f2)) = b1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_120]),c_0_117]),c_0_104]),c_0_37]) ).
cnf(c_0_127,axiom,
or(X1,not(X1)) = n1,
or_not_simplification1 ).
cnf(c_0_128,negated_conjecture,
not(and(i2,d1)) = or(b1,f2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_70]),c_0_54]),c_0_37]) ).
cnf(c_0_129,negated_conjecture,
and(b1,or(d2,f2)) = f1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_39]),c_0_47]),c_0_66]) ).
cnf(c_0_130,negated_conjecture,
and(d1,or(d2,f2)) = d1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_93]),c_0_54]) ).
cnf(c_0_131,negated_conjecture,
or(b1,or(X1,d1)) = n1,
inference(spm,[status(thm)],[c_0_123,c_0_88]) ).
cnf(c_0_132,negated_conjecture,
and(i1,and(i2,X1)) = and(f3,X1),
inference(spm,[status(thm)],[c_0_46,c_0_40]) ).
cnf(c_0_133,negated_conjecture,
and(i2,or(i2,f1)) = i2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_124]),c_0_51]) ).
cnf(c_0_134,negated_conjecture,
and(d1,and(X1,b1)) = n0,
inference(spm,[status(thm)],[c_0_50,c_0_70]) ).
cnf(c_0_135,negated_conjecture,
and(b3,b1) = a1,
inference(rw,[status(thm)],[c_0_125,c_0_54]) ).
cnf(c_0_136,negated_conjecture,
not(and(d1,b3)) = b1,
inference(rw,[status(thm)],[c_0_113,c_0_126]) ).
cnf(c_0_137,negated_conjecture,
or(b2,not(X1)) = not(and(X1,d2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_44]),c_0_37]) ).
cnf(c_0_138,negated_conjecture,
or(b2,f1) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_52]),c_0_117]),c_0_37]),c_0_53]),c_0_37]) ).
cnf(c_0_139,negated_conjecture,
or(f1,or(b1,f2)) = or(b1,f2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_128]),c_0_46]),c_0_54]),c_0_115]),c_0_128]) ).
cnf(c_0_140,plain,
or(X1,or(X2,X3)) = or(X3,or(X1,X2)),
inference(spm,[status(thm)],[c_0_37,c_0_117]) ).
cnf(c_0_141,negated_conjecture,
or(d2,f2) = or(d1,f1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_129]),c_0_88]),c_0_54]),c_0_130]),c_0_37]) ).
cnf(c_0_142,negated_conjecture,
or(b1,or(d1,X1)) = n1,
inference(spm,[status(thm)],[c_0_131,c_0_37]) ).
cnf(c_0_143,negated_conjecture,
and(f3,or(i2,f1)) = f3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_40]) ).
cnf(c_0_144,negated_conjecture,
and(d1,a1) = n0,
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_145,negated_conjecture,
or(a1,and(d1,b3)) = b3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_135]),c_0_88]),c_0_54]) ).
cnf(c_0_146,negated_conjecture,
and(d1,b3) = d1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_136]),c_0_88]) ).
cnf(c_0_147,negated_conjecture,
or(i1,or(X1,f1)) = n1,
inference(spm,[status(thm)],[c_0_123,c_0_39]) ).
cnf(c_0_148,negated_conjecture,
not(and(i1,d2)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_39]),c_0_138]) ).
cnf(c_0_149,axiom,
not(n1) = n0,
not_definition2 ).
cnf(c_0_150,negated_conjecture,
not(or(b1,f2)) = and(i2,d1),
inference(spm,[status(thm)],[c_0_42,c_0_128]) ).
cnf(c_0_151,negated_conjecture,
or(b1,f2) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_140]),c_0_37]),c_0_66]),c_0_141]),c_0_142]) ).
cnf(c_0_152,negated_conjecture,
not(or(i2,X1)) = and(f2,not(X1)),
inference(spm,[status(thm)],[c_0_96,c_0_36]) ).
cnf(c_0_153,negated_conjecture,
or(i2,f1) = or(i2,b1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_143]),c_0_117]),c_0_37]),c_0_82]) ).
cnf(c_0_154,negated_conjecture,
and(d1,not(a1)) = d1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_144]),c_0_61]) ).
cnf(c_0_155,negated_conjecture,
not(or(d1,X1)) = and(b1,not(X1)),
inference(spm,[status(thm)],[c_0_96,c_0_70]) ).
cnf(c_0_156,negated_conjecture,
or(d1,a1) = b3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_145,c_0_146]),c_0_37]) ).
cnf(c_0_157,negated_conjecture,
or(i1,b1) = n1,
inference(spm,[status(thm)],[c_0_147,c_0_82]) ).
cnf(c_0_158,negated_conjecture,
and(i1,d2) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_148]),c_0_149]) ).
cnf(c_0_159,negated_conjecture,
and(i2,d1) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_151]),c_0_149]) ).
cnf(c_0_160,negated_conjecture,
and(d1,f2) = and(i1,f2),
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_152,c_0_153]),c_0_152]),c_0_88]),c_0_54]),c_0_110]),c_0_54]) ).
cnf(c_0_161,negated_conjecture,
or(d1,and(b1,not(a1))) = not(a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_154]),c_0_70]),c_0_54]) ).
cnf(c_0_162,negated_conjecture,
and(b1,not(a1)) = and(f1,f2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_105]) ).
cnf(c_0_163,negated_conjecture,
not(and(d1,f1)) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_110]),c_0_54]),c_0_37]),c_0_157]) ).
cnf(c_0_164,negated_conjecture,
and(i1,b2) = i1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_158]),c_0_44]),c_0_61]) ).
cnf(c_0_165,negated_conjecture,
and(i1,f2) = d1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_159]),c_0_36]),c_0_160]),c_0_61]) ).
cnf(c_0_166,negated_conjecture,
or(d1,and(f1,f2)) = not(a1),
inference(rw,[status(thm)],[c_0_161,c_0_162]) ).
cnf(c_0_167,negated_conjecture,
and(d1,f1) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_163]),c_0_149]) ).
cnf(c_0_168,negated_conjecture,
and(d2,f1) = d2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_158]),c_0_39]),c_0_61]) ).
cnf(c_0_169,negated_conjecture,
not(or(i1,X1)) = and(f1,not(X1)),
inference(spm,[status(thm)],[c_0_96,c_0_39]) ).
cnf(c_0_170,negated_conjecture,
or(i1,and(b2,f1)) = b2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_164]),c_0_39]) ).
cnf(c_0_171,negated_conjecture,
not(a1) = f2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_165]),c_0_39]),c_0_54]),c_0_166]) ).
cnf(c_0_172,negated_conjecture,
and(b3,and(b1,X1)) = and(a1,X1),
inference(spm,[status(thm)],[c_0_46,c_0_135]) ).
cnf(c_0_173,negated_conjecture,
and(b1,f1) = f1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_167]),c_0_70]),c_0_61]),c_0_54]) ).
cnf(c_0_174,negated_conjecture,
not(or(d2,X1)) = and(b2,not(X1)),
inference(spm,[status(thm)],[c_0_96,c_0_44]) ).
cnf(c_0_175,negated_conjecture,
or(d2,and(b2,f1)) = f1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_168]),c_0_44]),c_0_54]) ).
cnf(c_0_176,negated_conjecture,
and(f1,not(and(b2,f1))) = d2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_58]) ).
cnf(c_0_177,negated_conjecture,
a1 = i2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_171]),c_0_51]) ).
cnf(c_0_178,negated_conjecture,
and(f1,a1) = and(b3,f1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_54]) ).
cnf(c_0_179,negated_conjecture,
and(i2,or(d2,f2)) = d2,
inference(rw,[status(thm)],[c_0_62,c_0_66]) ).
cnf(c_0_180,negated_conjecture,
a2 = and(b2,b3),
constructor2 ).
cnf(c_0_181,negated_conjecture,
and(b2,not(and(b2,f1))) = i1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_110]) ).
cnf(c_0_182,negated_conjecture,
and(d2,not(and(b2,f1))) = d2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_176]),c_0_54]) ).
cnf(c_0_183,negated_conjecture,
and(b3,and(b1,X1)) = and(i2,X1),
inference(rw,[status(thm)],[c_0_172,c_0_177]) ).
cnf(c_0_184,negated_conjecture,
and(b1,or(d1,f1)) = f1,
inference(rw,[status(thm)],[c_0_129,c_0_141]) ).
cnf(c_0_185,negated_conjecture,
and(b3,f1) = and(i2,f1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_178,c_0_177]),c_0_54]) ).
cnf(c_0_186,negated_conjecture,
and(i2,or(d1,f1)) = d2,
inference(rw,[status(thm)],[c_0_179,c_0_141]) ).
cnf(c_0_187,negated_conjecture,
and(b3,b2) = a2,
inference(rw,[status(thm)],[c_0_180,c_0_54]) ).
cnf(c_0_188,negated_conjecture,
not(and(b2,f1)) = or(i1,d2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_181]),c_0_58]),c_0_54]),c_0_182]) ).
cnf(c_0_189,negated_conjecture,
and(i2,f1) = d2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_184]),c_0_185]),c_0_186]) ).
cnf(c_0_190,negated_conjecture,
and(b3,and(b2,X1)) = and(a2,X1),
inference(spm,[status(thm)],[c_0_46,c_0_187]) ).
cnf(c_0_191,negated_conjecture,
and(b2,or(i1,d2)) = i1,
inference(rw,[status(thm)],[c_0_181,c_0_188]) ).
cnf(c_0_192,negated_conjecture,
and(b3,f1) = d2,
inference(rw,[status(thm)],[c_0_185,c_0_189]) ).
cnf(c_0_193,negated_conjecture,
and(a2,or(i1,d2)) = i1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_54]),c_0_114]) ).
cnf(c_0_194,negated_conjecture,
or(i1,d2) = b3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_192]),c_0_110]),c_0_54]),c_0_114]),c_0_37]) ).
cnf(c_0_195,negated_conjecture,
and(b3,a2) = a2,
inference(spm,[status(thm)],[c_0_89,c_0_187]) ).
cnf(c_0_196,negated_conjecture,
~ circuit(input(i1,i2),output(i2,i1)),
inference(fof_simplification,[status(thm)],[prove_interchange]) ).
cnf(c_0_197,negated_conjecture,
circuit(input(i1,i2),output(a1,a2)),
circuit_description ).
cnf(c_0_198,negated_conjecture,
a2 = i1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_193,c_0_194]),c_0_54]),c_0_195]) ).
cnf(c_0_199,negated_conjecture,
~ circuit(input(i1,i2),output(i2,i1)),
c_0_196 ).
cnf(c_0_200,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_198]),c_0_177]),c_0_199]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV001-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:47:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.79/0.50 % Version: 3.5.1
% 0.79/0.50 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.79/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.79/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.79/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.79/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.79/0.50 % Starting sh5l with 300s (1) cores
% 0.79/0.50 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1742756 completed with status 0
% 0.79/0.50 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.79/0.50 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.79/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.79/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.79/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.79/0.50 % No SInE strategy applied
% 0.79/0.50 % Search class: FUUSM-FFMM21-MFFFFFNN
% 0.79/0.50 % partial match(1): FGUSM-FFMM21-MFFFFFNN
% 0.79/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.79/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.79/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.79/0.50 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.79/0.50 % Starting new_bool_3 with 136s (1) cores
% 0.79/0.50 % Starting new_bool_1 with 136s (1) cores
% 0.79/0.50 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 1742762 completed with status 0
% 0.79/0.50 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.79/0.50 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.79/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.79/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.79/0.50 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.79/0.50 % No SInE strategy applied
% 0.79/0.50 % Search class: FUUSM-FFMM21-MFFFFFNN
% 0.79/0.50 % partial match(1): FGUSM-FFMM21-MFFFFFNN
% 0.79/0.50 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.79/0.50 % Starting SubtermCWHack with 136s (1) cores
% 0.79/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.79/0.50 % Preprocessing time : 0.002 s
% 0.79/0.50 % Presaturation interreduction done
% 0.79/0.50
% 0.79/0.50 % Proof found!
% 0.79/0.50 % SZS status Unsatisfiable
% 0.79/0.50 % SZS output start CNFRefutation
% See solution above
% 0.79/0.50 % Parsed axioms : 47
% 0.79/0.50 % Removed by relevancy pruning/SinE : 0
% 0.79/0.50 % Initial clauses : 47
% 0.79/0.50 % Removed in clause preprocessing : 0
% 0.79/0.50 % Initial clauses in saturation : 47
% 0.79/0.50 % Processed clauses : 891
% 0.79/0.50 % ...of these trivial : 316
% 0.79/0.50 % ...subsumed : 12
% 0.79/0.50 % ...remaining for further processing : 563
% 0.79/0.50 % Other redundant clauses eliminated : 0
% 0.79/0.50 % Clauses deleted for lack of memory : 0
% 0.79/0.50 % Backward-subsumed : 0
% 0.79/0.50 % Backward-rewritten : 259
% 0.79/0.50 % Generated clauses : 7697
% 0.79/0.50 % ...of the previous two non-redundant : 4267
% 0.79/0.50 % ...aggressively subsumed : 0
% 0.79/0.50 % Contextual simplify-reflections : 0
% 0.79/0.50 % Paramodulations : 7697
% 0.79/0.50 % Factorizations : 0
% 0.79/0.50 % NegExts : 0
% 0.79/0.50 % Equation resolutions : 0
% 0.79/0.50 % Disequality decompositions : 0
% 0.79/0.50 % Total rewrite steps : 10019
% 0.79/0.50 % ...of those cached : 7798
% 0.79/0.50 % Propositional unsat checks : 0
% 0.79/0.50 % Propositional check models : 0
% 0.79/0.50 % Propositional check unsatisfiable : 0
% 0.79/0.50 % Propositional clauses : 0
% 0.79/0.50 % Propositional clauses after purity: 0
% 0.79/0.50 % Propositional unsat core size : 0
% 0.79/0.50 % Propositional preprocessing time : 0.000
% 0.79/0.50 % Propositional encoding time : 0.000
% 0.79/0.50 % Propositional solver time : 0.000
% 0.79/0.50 % Success case prop preproc time : 0.000
% 0.79/0.50 % Success case prop encoding time : 0.000
% 0.79/0.50 % Success case prop solver time : 0.000
% 0.79/0.50 % Current number of processed clauses : 261
% 0.79/0.50 % Positive orientable unit clauses : 255
% 0.79/0.50 % Positive unorientable unit clauses: 5
% 0.79/0.50 % Negative unit clauses : 1
% 0.79/0.50 % Non-unit-clauses : 0
% 0.79/0.50 % Current number of unprocessed clauses: 3385
% 0.79/0.50 % ...number of literals in the above : 3385
% 0.79/0.50 % Current number of archived formulas : 0
% 0.79/0.50 % Current number of archived clauses : 302
% 0.79/0.50 % Clause-clause subsumption calls (NU) : 0
% 0.79/0.50 % Rec. Clause-clause subsumption calls : 0
% 0.79/0.50 % Non-unit clause-clause subsumptions : 0
% 0.79/0.50 % Unit Clause-clause subsumption calls : 18
% 0.79/0.50 % Rewrite failures with RHS unbound : 0
% 0.79/0.50 % BW rewrite match attempts : 496
% 0.79/0.50 % BW rewrite match successes : 409
% 0.79/0.50 % Condensation attempts : 0
% 0.79/0.50 % Condensation successes : 0
% 0.79/0.50 % Termbank termtop insertions : 57559
% 0.79/0.50 % Search garbage collected termcells : 2
% 0.79/0.50
% 0.79/0.50 % -------------------------------------------------
% 0.79/0.50 % User time : 0.069 s
% 0.79/0.50 % System time : 0.011 s
% 0.79/0.50 % Total time : 0.079 s
% 0.79/0.50 % Maximum resident set size: 3608 pages
% 0.79/0.50
% 0.79/0.50 % -------------------------------------------------
% 0.79/0.50 % User time : 0.350 s
% 0.79/0.50 % System time : 0.047 s
% 0.79/0.50 % Total time : 0.397 s
% 0.79/0.50 % Maximum resident set size: 4864 pages
% 0.79/0.50 % E exiting
%------------------------------------------------------------------------------