%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL927-1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 01:17:44 PM UTC 2026
% Result : Unsatisfiable 173.46s 25.79s
% Output : CNFRefutation 173.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 7
% Syntax : Number of clauses : 176 ( 65 unt; 0 nHn; 81 RR)
% Number of literals : 316 ( 0 equ; 145 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 481 ( 25 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(modus_ponens,axiom,
( ~ p(X1)
| ~ p(i(X1,X2))
| p(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
cnf(axBp,axiom,
p(i(i(X1,X2),i(i(X2,X3),i(X1,X3)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axBp) ).
cnf(axTO,axiom,
p(i(i(i(X1,X2),i(X2,X1)),i(X2,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axTO) ).
cnf(axL,axiom,
p(i(i(i(X1,X2),X2),i(i(X2,X1),X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axL) ).
cnf(resid2,axiom,
( ~ p(i(X1,i(X2,X3)))
| p(i(f(X1,X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',resid2) ).
cnf(resid1,axiom,
( ~ p(i(f(X1,X2),X3))
| p(i(X1,i(X2,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',resid1) ).
cnf(axK_axC,negated_conjecture,
( ~ p(i(i(X1,i(X2,X3)),i(X2,i(X1,X3))))
| ~ p(i(c1,i(c2,c1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axK_axC) ).
cnf(c_0_7,plain,
( ~ p(X1)
| ~ p(i(X1,X2))
| p(X2) ),
inference(fof_simplification,[status(thm)],[modus_ponens]) ).
cnf(c_0_8,plain,
( ~ p(X1)
| ~ p(i(X1,X2))
| p(X2) ),
c_0_7 ).
cnf(c_0_9,axiom,
p(i(i(X1,X2),i(i(X2,X3),i(X1,X3)))),
axBp ).
cnf(c_0_10,plain,
( ~ p(i(X3,X1))
| p(i(i(X1,X2),i(X3,X2))) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,plain,
( ~ p(i(X1,X3))
| ~ p(i(X3,X2))
| p(i(X1,X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_10]) ).
cnf(c_0_12,axiom,
p(i(i(i(X1,X2),i(X2,X1)),i(X2,X1))),
axTO ).
cnf(c_0_13,plain,
( ~ p(i(X2,X4))
| ~ p(i(X1,i(X4,X3)))
| p(i(X1,i(X2,X3))) ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_14,plain,
( ~ p(i(X1,i(i(X3,X2),i(X2,X3))))
| p(i(X1,i(X2,X3))) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( ~ p(i(X4,X1))
| ~ p(i(X3,X4))
| p(i(i(X1,X2),i(X3,X2))) ),
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_16,plain,
( ~ p(i(i(X2,X1),i(X1,X2)))
| p(i(X1,X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_17,plain,
p(i(i(X1,X1),i(X1,X1))),
inference(spm,[status(thm)],[c_0_14,c_0_9]) ).
cnf(c_0_18,plain,
( ~ p(i(i(i(X4,X5),i(X3,X5)),X1))
| p(i(i(X1,X2),i(i(X3,X4),X2))) ),
inference(spm,[status(thm)],[c_0_15,c_0_9]) ).
cnf(c_0_19,plain,
p(i(X1,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( ~ p(i(i(X3,X2),X1))
| p(i(i(X1,i(X2,X3)),i(X2,X3))) ),
inference(spm,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_21,plain,
p(i(i(i(i(X1,X2),i(X3,X2)),X4),i(i(X3,X1),X4))),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( ~ p(i(i(X2,X1),X3))
| ~ p(i(X3,i(X1,X2)))
| p(i(X1,X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_20]) ).
cnf(c_0_23,axiom,
p(i(i(i(X1,X2),X2),i(i(X2,X1),X1))),
axL ).
cnf(c_0_24,plain,
( ~ p(i(i(i(X2,X4),i(X1,X4)),X3))
| p(i(i(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_8,c_0_21]) ).
cnf(c_0_25,plain,
( ~ p(i(i(X2,i(X1,X2)),i(i(X2,X1),X1)))
| p(i(i(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
p(i(i(X1,i(X2,X3)),i(i(X4,X2),i(X1,i(X4,X3))))),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_27,plain,
p(i(i(i(X1,i(X1,X1)),X1),X1)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,plain,
( ~ p(i(X1,i(X2,X3)))
| p(i(f(X1,X2),X3)) ),
inference(fof_simplification,[status(thm)],[resid2]) ).
cnf(c_0_29,plain,
( ~ p(i(X1,i(X4,X2)))
| p(i(X1,i(i(X2,X3),i(X4,X3)))) ),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_30,plain,
( ~ p(i(X1,i(i(X2,i(X2,X2)),X2)))
| p(i(X1,X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_27]) ).
cnf(c_0_31,plain,
( ~ p(i(X1,i(X2,X3)))
| p(i(f(X1,X2),X3)) ),
c_0_28 ).
cnf(c_0_32,plain,
( ~ p(X4)
| ~ p(i(X4,i(X3,X1)))
| p(i(i(X1,X2),i(X3,X2))) ),
inference(spm,[status(thm)],[c_0_8,c_0_29]) ).
cnf(c_0_33,plain,
( ~ p(i(f(X1,X2),X3))
| p(i(X1,i(X2,X3))) ),
inference(fof_simplification,[status(thm)],[resid1]) ).
cnf(c_0_34,plain,
( ~ p(i(X1,i(X2,i(i(X3,i(X3,X3)),X3))))
| p(i(f(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
( ~ p(i(X3,i(X2,X4)))
| p(i(i(X1,X2),i(X3,i(X1,X4)))) ),
inference(spm,[status(thm)],[c_0_13,c_0_9]) ).
cnf(c_0_36,plain,
( ~ p(i(X1,X4))
| p(i(i(i(X1,X2),X3),i(i(X4,X2),X3))) ),
inference(spm,[status(thm)],[c_0_32,c_0_9]) ).
cnf(c_0_37,plain,
( ~ p(i(f(X1,X2),X3))
| p(i(X1,i(X2,X3))) ),
c_0_33 ).
cnf(c_0_38,plain,
p(i(f(i(i(X1,i(X1,X1)),X2),i(X2,X1)),X1)),
inference(spm,[status(thm)],[c_0_34,c_0_9]) ).
cnf(c_0_39,plain,
( ~ p(i(i(X3,X1),i(X2,X3)))
| p(i(i(X1,X2),i(X1,X3))) ),
inference(spm,[status(thm)],[c_0_14,c_0_35]) ).
cnf(c_0_40,plain,
( ~ p(i(X4,X1))
| ~ p(i(i(X4,X2),X3))
| p(i(i(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_8,c_0_36]) ).
cnf(c_0_41,plain,
p(i(i(i(X1,i(X1,X1)),X2),i(i(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
( ~ p(i(X2,X1))
| p(i(i(X1,X2),i(X1,X1))) ),
inference(spm,[status(thm)],[c_0_39,c_0_10]) ).
cnf(c_0_43,plain,
( ~ p(i(X1,X3))
| p(i(i(i(X1,X2),i(X2,X3)),i(X2,X3))) ),
inference(spm,[status(thm)],[c_0_14,c_0_36]) ).
cnf(c_0_44,plain,
( ~ p(i(i(X3,i(X3,X3)),X1))
| p(i(i(X1,X2),i(i(X2,X3),X3))) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
( ~ p(i(X2,i(X1,X1)))
| p(i(i(i(X1,X1),X2),i(X1,X1))) ),
inference(spm,[status(thm)],[c_0_14,c_0_42]) ).
cnf(c_0_46,plain,
( ~ p(i(X3,X2))
| ~ p(i(i(X3,X1),i(X1,X2)))
| p(i(X1,X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_43]) ).
cnf(c_0_47,plain,
( ~ p(i(X1,i(i(X3,X2),X2)))
| p(i(X1,i(i(X2,X3),X3))) ),
inference(spm,[status(thm)],[c_0_11,c_0_23]) ).
cnf(c_0_48,plain,
p(i(i(i(X1,X1),X2),i(i(X2,i(X1,X1)),i(X1,X1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_12])]) ).
cnf(c_0_49,plain,
( ~ p(i(X1,i(X1,X3)))
| ~ p(i(X2,i(X2,X3)))
| p(i(X1,i(X2,X3))) ),
inference(spm,[status(thm)],[c_0_46,c_0_35]) ).
cnf(c_0_50,plain,
p(i(i(i(X1,X1),X2),i(i(i(X1,X1),X2),X2))),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,plain,
( ~ p(i(X1,i(X1,X3)))
| p(i(X1,i(i(i(X2,X2),X3),X3))) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_52,plain,
( ~ p(i(i(X3,X2),X1))
| p(i(i(X1,X2),i(i(X2,X3),X3))) ),
inference(spm,[status(thm)],[c_0_47,c_0_10]) ).
cnf(c_0_53,plain,
p(i(i(i(X1,X1),X2),i(i(i(X3,X3),X2),X2))),
inference(spm,[status(thm)],[c_0_51,c_0_50]) ).
cnf(c_0_54,plain,
( ~ p(i(X3,X1))
| ~ p(i(i(X2,X1),X3))
| p(i(i(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_52]) ).
cnf(c_0_55,plain,
( ~ p(i(i(X2,X1),X1))
| p(i(i(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_23]) ).
cnf(c_0_56,plain,
( ~ p(i(X3,i(i(X4,X4),X2)))
| p(i(i(i(X1,X1),X2),i(X3,X2))) ),
inference(spm,[status(thm)],[c_0_13,c_0_53]) ).
cnf(c_0_57,plain,
( ~ p(i(i(i(X1,X3),i(X2,X3)),X1))
| p(i(i(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_54,c_0_9]) ).
cnf(c_0_58,plain,
( ~ p(i(i(X2,X1),X3))
| p(i(i(i(X1,X2),X3),X3)) ),
inference(spm,[status(thm)],[c_0_55,c_0_20]) ).
cnf(c_0_59,plain,
p(i(i(i(X1,X1),i(X2,X3)),i(i(X2,X3),i(X2,X3)))),
inference(spm,[status(thm)],[c_0_56,c_0_9]) ).
cnf(c_0_60,plain,
( ~ p(i(i(X2,i(X1,X2)),i(X1,X2)))
| p(i(i(i(X1,X2),X1),X1)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_61,plain,
( ~ p(i(i(i(X1,X2),X2),X1))
| p(i(i(X1,i(X2,X1)),i(X2,X1))) ),
inference(spm,[status(thm)],[c_0_54,c_0_23]) ).
cnf(c_0_62,plain,
p(i(i(i(i(X1,X2),i(X1,X2)),X3),i(i(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_18,c_0_59]) ).
cnf(c_0_63,plain,
( ~ p(i(i(i(X2,X1),X1),X2))
| p(i(i(i(X1,X2),X1),X1)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_64,plain,
( ~ p(i(i(i(X1,X2),i(X1,X2)),X3))
| p(i(i(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_8,c_0_62]) ).
cnf(c_0_65,plain,
( ~ p(i(X2,i(i(X2,X1),X1)))
| p(i(i(i(X1,i(X2,X1)),X1),X1)) ),
inference(spm,[status(thm)],[c_0_63,c_0_10]) ).
cnf(c_0_66,plain,
p(i(i(X1,i(X1,X1)),i(i(i(X1,i(X1,X1)),X1),X1))),
inference(spm,[status(thm)],[c_0_64,c_0_41]) ).
cnf(c_0_67,plain,
p(i(i(i(X1,i(X1,X1)),X2),i(i(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_47,c_0_41]) ).
cnf(c_0_68,plain,
( ~ p(i(i(X3,X2),i(X1,X3)))
| p(i(i(X1,X2),i(X1,X3))) ),
inference(spm,[status(thm)],[c_0_24,c_0_58]) ).
cnf(c_0_69,plain,
p(i(i(i(X1,i(i(X1,i(X1,X1)),X1)),X1),X1)),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,plain,
( ~ p(i(i(X2,X1),i(i(X1,X2),X2)))
| p(i(i(i(X1,X2),X1),X1)) ),
inference(spm,[status(thm)],[c_0_57,c_0_20]) ).
cnf(c_0_71,plain,
p(i(X1,i(X2,f(X1,X2)))),
inference(spm,[status(thm)],[c_0_37,c_0_19]) ).
cnf(c_0_72,plain,
( ~ p(i(i(i(X4,X3),X3),X1))
| p(i(i(X1,X2),i(i(i(X3,X4),X4),X2))) ),
inference(spm,[status(thm)],[c_0_15,c_0_23]) ).
cnf(c_0_73,plain,
( ~ p(i(i(X3,i(X3,X3)),X1))
| p(i(i(X1,X2),i(i(X3,X2),X2))) ),
inference(spm,[status(thm)],[c_0_40,c_0_67]) ).
cnf(c_0_74,plain,
( ~ p(i(i(i(X2,X1),X1),X2))
| p(i(i(X1,i(X1,X2)),i(X1,X2))) ),
inference(spm,[status(thm)],[c_0_68,c_0_61]) ).
cnf(c_0_75,plain,
( ~ p(i(i(X2,i(i(X2,i(X2,X2)),X2)),X1))
| p(i(i(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_40,c_0_69]) ).
cnf(c_0_76,plain,
p(i(i(i(X1,i(X2,X2)),X1),X1)),
inference(spm,[status(thm)],[c_0_70,c_0_48]) ).
cnf(c_0_77,plain,
( ~ p(i(X1,X3))
| p(i(X1,i(X2,f(X3,X2)))) ),
inference(spm,[status(thm)],[c_0_11,c_0_71]) ).
cnf(c_0_78,plain,
p(i(i(i(i(X1,X2),X2),X3),i(i(i(X2,X1),X1),X3))),
inference(spm,[status(thm)],[c_0_72,c_0_19]) ).
cnf(c_0_79,plain,
( ~ p(i(i(i(X1,X1),X1),X1))
| p(i(i(i(X1,X1),X2),i(i(X1,X2),X2))) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_80,plain,
p(i(i(i(X1,X1),X1),X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_42]),c_0_76])]) ).
cnf(c_0_81,plain,
( ~ p(X3)
| ~ p(i(X3,X2))
| p(i(X1,f(X2,X1))) ),
inference(spm,[status(thm)],[c_0_8,c_0_77]) ).
cnf(c_0_82,plain,
( ~ p(i(X4,i(i(X2,X1),X1)))
| p(i(i(i(i(X1,X2),X2),X3),i(X4,X3))) ),
inference(spm,[status(thm)],[c_0_13,c_0_78]) ).
cnf(c_0_83,plain,
p(i(i(i(X1,X1),X2),i(i(X1,X2),X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]) ).
cnf(c_0_84,plain,
p(i(i(X1,i(X1,X1)),i(X1,X1))),
inference(spm,[status(thm)],[c_0_55,c_0_80]) ).
cnf(c_0_85,plain,
( ~ p(i(i(X3,X2),i(X2,X3)))
| p(i(X1,f(i(X2,X3),X1))) ),
inference(spm,[status(thm)],[c_0_81,c_0_12]) ).
cnf(c_0_86,plain,
p(i(i(i(i(X1,X2),X2),X3),i(i(i(X2,X2),X1),X3))),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_87,plain,
p(i(i(i(X1,X1),X2),i(i(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_44,c_0_84]) ).
cnf(c_0_88,plain,
( ~ p(f(X2,X3))
| ~ p(i(X2,i(X3,X1)))
| p(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_31]) ).
cnf(c_0_89,plain,
p(i(X1,f(i(X2,X2),X1))),
inference(spm,[status(thm)],[c_0_85,c_0_19]) ).
cnf(c_0_90,plain,
( ~ p(i(i(i(X2,X1),X1),X3))
| p(i(i(i(X1,X1),X2),X3)) ),
inference(spm,[status(thm)],[c_0_8,c_0_86]) ).
cnf(c_0_91,plain,
p(i(i(i(i(i(X1,X2),X2),X2),X3),i(i(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_18,c_0_87]) ).
cnf(c_0_92,plain,
( ~ p(i(X3,X1))
| ~ p(f(X3,X2))
| p(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_88,c_0_77]) ).
cnf(c_0_93,plain,
( ~ p(X2)
| p(f(i(X1,X1),X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_89]) ).
cnf(c_0_94,plain,
p(i(i(i(X1,X1),i(i(X2,X1),X1)),i(i(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_95,plain,
( ~ p(X2)
| ~ p(i(i(X3,X3),X1))
| p(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_96,plain,
p(i(i(i(i(X1,X2),X2),i(X2,X2)),i(X2,X2))),
inference(spm,[status(thm)],[c_0_55,c_0_94]) ).
cnf(c_0_97,plain,
( ~ p(f(i(X1,X3),i(X3,X2)))
| p(i(X1,X2)) ),
inference(spm,[status(thm)],[c_0_88,c_0_9]) ).
cnf(c_0_98,plain,
( ~ p(X3)
| p(f(i(X1,f(i(X2,X2),X1)),X3)) ),
inference(spm,[status(thm)],[c_0_95,c_0_71]) ).
cnf(c_0_99,plain,
( ~ p(i(i(X4,f(X3,X4)),X1))
| p(i(i(X1,X2),i(X3,X2))) ),
inference(spm,[status(thm)],[c_0_15,c_0_71]) ).
cnf(c_0_100,plain,
( ~ p(i(i(X1,X2),X1))
| p(i(i(i(X1,X1),X2),X1)) ),
inference(spm,[status(thm)],[c_0_90,c_0_58]) ).
cnf(c_0_101,plain,
p(i(i(X1,i(X2,X1)),i(X1,X1))),
inference(spm,[status(thm)],[c_0_24,c_0_96]) ).
cnf(c_0_102,plain,
( ~ p(X2)
| p(i(X1,f(X2,X1))) ),
inference(spm,[status(thm)],[c_0_8,c_0_71]) ).
cnf(c_0_103,plain,
( ~ p(i(f(i(X3,X3),X1),X2))
| p(i(X1,X2)) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_104,plain,
p(i(i(i(i(f(X1,X2),X3),i(X2,X3)),X4),i(X1,X4))),
inference(spm,[status(thm)],[c_0_99,c_0_9]) ).
cnf(c_0_105,plain,
( ~ p(i(i(X2,i(X1,X2)),X2))
| p(i(i(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_100]) ).
cnf(c_0_106,plain,
p(i(i(i(X1,X1),i(X2,i(X1,X1))),i(X1,X1))),
inference(spm,[status(thm)],[c_0_14,c_0_101]) ).
cnf(c_0_107,plain,
( ~ p(i(X3,X2))
| ~ p(f(i(X2,X1),X3))
| p(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_10]) ).
cnf(c_0_108,plain,
( ~ p(X1)
| ~ p(X2)
| p(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_102]) ).
cnf(c_0_109,plain,
p(i(i(i(X1,f(X2,X1)),X3),i(X2,X3))),
inference(spm,[status(thm)],[c_0_99,c_0_19]) ).
cnf(c_0_110,plain,
( ~ p(i(i(X3,X3),i(X1,X2)))
| p(i(X1,X2)) ),
inference(spm,[status(thm)],[c_0_103,c_0_31]) ).
cnf(c_0_111,plain,
( ~ p(i(i(i(f(X1,X3),X4),i(X3,X4)),X2))
| p(i(X1,X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_104]) ).
cnf(c_0_112,plain,
p(i(i(X1,i(X2,X2)),i(X2,X2))),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_113,plain,
( ~ p(X2)
| ~ p(i(X3,X1))
| ~ p(i(X2,X3))
| p(X1) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_114,plain,
( ~ p(i(X1,i(i(X4,f(X2,X4)),X3)))
| p(i(X1,i(X2,X3))) ),
inference(spm,[status(thm)],[c_0_11,c_0_109]) ).
cnf(c_0_115,plain,
( ~ p(i(i(X4,X4),i(X3,X1)))
| p(i(i(X1,X2),i(X3,X2))) ),
inference(spm,[status(thm)],[c_0_110,c_0_29]) ).
cnf(c_0_116,plain,
( ~ p(i(f(i(X4,X4),X3),X1))
| p(i(i(X1,X2),i(X3,X2))) ),
inference(spm,[status(thm)],[c_0_15,c_0_89]) ).
cnf(c_0_117,plain,
p(i(X1,i(X2,X2))),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_118,plain,
( ~ p(X3)
| ~ p(i(f(i(X2,X2),X3),X1))
| p(X1) ),
inference(spm,[status(thm)],[c_0_113,c_0_89]) ).
cnf(c_0_119,plain,
( ~ p(i(i(X3,f(X1,X3)),X2))
| p(i(X1,X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_109]) ).
cnf(c_0_120,plain,
p(i(i(i(f(X1,X2),X2),X2),i(X1,f(X1,X2)))),
inference(spm,[status(thm)],[c_0_114,c_0_23]) ).
cnf(c_0_121,plain,
p(i(i(f(i(X1,X1),X2),X3),i(X2,X3))),
inference(spm,[status(thm)],[c_0_115,c_0_71]) ).
cnf(c_0_122,plain,
p(i(i(i(X1,X1),X2),i(X3,X2))),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_123,plain,
( ~ p(X3)
| ~ p(i(i(X2,X2),i(X3,X1)))
| p(X1) ),
inference(spm,[status(thm)],[c_0_118,c_0_31]) ).
cnf(c_0_124,plain,
( ~ p(i(X2,i(f(X1,X3),X4)))
| p(i(X1,i(X2,i(X3,X4)))) ),
inference(spm,[status(thm)],[c_0_119,c_0_35]) ).
cnf(c_0_125,plain,
( ~ p(i(i(f(X1,X2),X2),X2))
| p(i(X1,f(X1,X2))) ),
inference(spm,[status(thm)],[c_0_8,c_0_120]) ).
cnf(c_0_126,plain,
p(i(i(f(i(X1,X1),i(X2,X3)),i(X3,X2)),i(X3,X2))),
inference(spm,[status(thm)],[c_0_14,c_0_121]) ).
cnf(c_0_127,plain,
p(i(i(X1,X2),i(i(i(X1,X2),X2),X2))),
inference(spm,[status(thm)],[c_0_24,c_0_87]) ).
cnf(c_0_128,plain,
p(i(i(X1,X2),i(X3,i(X1,X2)))),
inference(spm,[status(thm)],[c_0_24,c_0_122]) ).
cnf(c_0_129,plain,
( ~ p(i(X4,X2))
| ~ p(i(i(X3,X3),i(X1,X4)))
| p(i(X1,X2)) ),
inference(spm,[status(thm)],[c_0_123,c_0_29]) ).
cnf(c_0_130,plain,
p(i(X1,i(i(i(X2,X2),X3),i(X4,X3)))),
inference(spm,[status(thm)],[c_0_124,c_0_122]) ).
cnf(c_0_131,plain,
( ~ p(i(X3,i(X4,X2)))
| ~ p(i(X1,f(X3,X4)))
| p(i(X1,X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_31]) ).
cnf(c_0_132,plain,
p(i(i(X1,X1),f(i(X1,X1),i(X2,X2)))),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_133,plain,
( ~ p(i(X3,i(i(X1,X2),X2)))
| p(i(i(X1,X2),i(X3,X2))) ),
inference(spm,[status(thm)],[c_0_13,c_0_127]) ).
cnf(c_0_134,plain,
p(i(i(X1,X2),i(i(i(X1,X2),X3),X3))),
inference(spm,[status(thm)],[c_0_47,c_0_128]) ).
cnf(c_0_135,plain,
( ~ p(i(i(X4,X2),X3))
| p(i(i(i(X1,X1),X2),X3)) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_136,plain,
( ~ p(i(i(X1,X1),i(i(X3,X3),X2)))
| p(i(i(X1,X1),X2)) ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_137,plain,
( ~ p(f(i(i(X1,X2),X2),i(X2,X1)))
| p(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_23]) ).
cnf(c_0_138,plain,
p(i(i(X1,X2),i(i(i(X2,X1),X1),X2))),
inference(spm,[status(thm)],[c_0_133,c_0_23]) ).
cnf(c_0_139,plain,
p(i(i(X1,i(i(X2,X1),X2)),i(X1,X2))),
inference(spm,[status(thm)],[c_0_39,c_0_134]) ).
cnf(c_0_140,plain,
p(i(i(i(X1,X1),X2),i(X3,i(X4,X2)))),
inference(spm,[status(thm)],[c_0_135,c_0_128]) ).
cnf(c_0_141,plain,
( ~ p(i(i(X3,X3),i(X1,X2)))
| p(i(i(X1,X1),i(X1,X2))) ),
inference(spm,[status(thm)],[c_0_136,c_0_35]) ).
cnf(c_0_142,plain,
( ~ p(i(X2,X1))
| ~ p(i(i(X1,X2),X2))
| p(X1) ),
inference(spm,[status(thm)],[c_0_137,c_0_108]) ).
cnf(c_0_143,plain,
( ~ p(i(X3,i(i(X2,X1),X1)))
| p(i(i(X1,X2),i(X3,X2))) ),
inference(spm,[status(thm)],[c_0_13,c_0_138]) ).
cnf(c_0_144,plain,
p(i(i(i(X1,i(X2,X1)),X2),i(i(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_24,c_0_139]) ).
cnf(c_0_145,plain,
p(i(i(X1,X2),i(X3,i(X4,i(X1,X2))))),
inference(spm,[status(thm)],[c_0_24,c_0_140]) ).
cnf(c_0_146,plain,
( ~ p(i(X1,X2))
| p(i(i(X1,X1),i(X1,X2))) ),
inference(spm,[status(thm)],[c_0_141,c_0_10]) ).
cnf(c_0_147,plain,
( ~ p(i(f(X1,X4),X2))
| p(i(X1,i(i(X2,X3),i(X4,X3)))) ),
inference(spm,[status(thm)],[c_0_124,c_0_10]) ).
cnf(c_0_148,plain,
( ~ p(i(i(X1,X3),X3))
| p(i(i(X1,X2),i(i(X3,X1),X2))) ),
inference(spm,[status(thm)],[c_0_115,c_0_52]) ).
cnf(c_0_149,plain,
( ~ p(i(i(X3,X2),X1))
| ~ p(i(i(X2,X3),X1))
| p(X1) ),
inference(spm,[status(thm)],[c_0_142,c_0_20]) ).
cnf(c_0_150,plain,
p(i(i(X1,X2),i(i(i(X1,i(X2,X1)),X2),X2))),
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_151,plain,
p(i(i(X1,X2),i(i(i(X3,i(X1,X2)),X4),X4))),
inference(spm,[status(thm)],[c_0_47,c_0_145]) ).
cnf(c_0_152,plain,
( ~ p(i(X2,X3))
| ~ p(i(X1,i(X2,X2)))
| p(i(X1,i(X2,X3))) ),
inference(spm,[status(thm)],[c_0_11,c_0_146]) ).
cnf(c_0_153,plain,
( ~ p(i(X4,X2))
| ~ p(i(f(i(X3,X3),X1),X4))
| p(i(X1,X2)) ),
inference(spm,[status(thm)],[c_0_123,c_0_147]) ).
cnf(c_0_154,plain,
( ~ p(i(i(i(X3,X1),X1),X3))
| p(i(i(X1,X2),i(i(i(X1,X3),X1),X2))) ),
inference(spm,[status(thm)],[c_0_148,c_0_74]) ).
cnf(c_0_155,plain,
p(i(i(i(X1,i(X2,X1)),X2),X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_150]),c_0_151])]) ).
cnf(c_0_156,plain,
( ~ p(i(X2,X3))
| p(i(X1,i(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_117])]) ).
cnf(c_0_157,plain,
( ~ p(i(i(X3,X3),X2))
| p(i(X1,X2)) ),
inference(spm,[status(thm)],[c_0_153,c_0_117]) ).
cnf(c_0_158,plain,
p(i(i(X1,X2),i(i(i(X1,i(i(X3,X1),X1)),X1),X2))),
inference(spm,[status(thm)],[c_0_154,c_0_91]) ).
cnf(c_0_159,plain,
( ~ p(i(i(X2,i(X1,X2)),X1))
| p(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_155]) ).
cnf(c_0_160,plain,
( ~ p(i(X2,X3))
| p(i(i(X1,X2),i(X1,X3))) ),
inference(spm,[status(thm)],[c_0_39,c_0_156]) ).
cnf(c_0_161,plain,
p(i(X1,i(i(i(X2,i(i(X3,X2),X2)),X2),X2))),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_162,negated_conjecture,
( ~ p(i(i(X1,i(X2,X3)),i(X2,i(X1,X3))))
| ~ p(i(c1,i(c2,c1))) ),
inference(fof_simplification,[status(thm)],[axK_axC]) ).
cnf(c_0_163,plain,
p(i(i(X1,i(X2,X3)),i(i(i(X3,X2),X2),i(X1,X3)))),
inference(spm,[status(thm)],[c_0_24,c_0_78]) ).
cnf(c_0_164,plain,
( ~ p(i(i(i(X1,X2),X1),X2))
| p(i(X1,X2)) ),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_165,plain,
p(i(i(i(X1,i(i(X2,X1),X1)),X1),i(X3,X1))),
inference(spm,[status(thm)],[c_0_133,c_0_161]) ).
cnf(c_0_166,negated_conjecture,
( ~ p(i(i(X1,i(X2,X3)),i(X2,i(X1,X3))))
| ~ p(i(c1,i(c2,c1))) ),
c_0_162 ).
cnf(c_0_167,plain,
( ~ p(i(i(X3,X4),X1))
| ~ p(i(f(i(X2,X2),X3),X4))
| p(X1) ),
inference(spm,[status(thm)],[c_0_113,c_0_121]) ).
cnf(c_0_168,plain,
( ~ p(i(X4,i(i(X3,X2),X2)))
| p(i(i(X1,i(X2,X3)),i(X4,i(X1,X3)))) ),
inference(spm,[status(thm)],[c_0_13,c_0_163]) ).
cnf(c_0_169,plain,
p(i(X1,i(i(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_170,negated_conjecture,
( ~ p(i(X1,X1))
| ~ p(i(c1,i(c2,c1))) ),
inference(spm,[status(thm)],[c_0_166,c_0_10]) ).
cnf(c_0_171,plain,
( ~ p(i(i(X2,i(X3,X3)),X1))
| p(X1) ),
inference(spm,[status(thm)],[c_0_167,c_0_117]) ).
cnf(c_0_172,plain,
p(i(i(X1,i(X2,X3)),i(X2,i(X1,X3)))),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_173,negated_conjecture,
~ p(i(c1,i(c2,c1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_19])]) ).
cnf(c_0_174,plain,
p(i(X1,i(X2,X1))),
inference(spm,[status(thm)],[c_0_171,c_0_172]) ).
cnf(c_0_175,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_173,c_0_174])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL927-1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.46 % Computer : n020.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Mon Sep 21 01:13:04 UTC 2026
% 0.18/0.47 % CPUTime :
% 0.18/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.55 Running first-order theorem proving
% 0.22/0.55 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
% 173.46/25.79 % Version: 3.5.1
% 173.46/25.79 % Preprocessing class: FSSSSMSSSSSNFFN.
% 173.46/25.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 173.46/25.79 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 173.46/25.79 % Starting new_bool_3 with 300s (1) cores
% 173.46/25.79 % Starting new_bool_1 with 300s (1) cores
% 173.46/25.79 % Starting sh5l with 300s (1) cores
% 173.46/25.79 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1673417 completed with status 0
% 173.46/25.79 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 173.46/25.79 % Preprocessing class: FSSSSMSSSSSNFFN.
% 173.46/25.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 173.46/25.79 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 173.46/25.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 173.46/25.79 % No SInE strategy applied
% 173.46/25.79 % Search class: FHHNS-FFSF22-MFFFFFNN
% 173.46/25.79 % partial match(1): FHUNS-FFSF22-MFFFFFNN
% 173.46/25.79 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 173.46/25.79 % Starting SubtermCWHack with 136s (1) cores
% 173.46/25.79 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 173.46/25.79 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S00 with 136s (1) cores
% 173.46/25.79 % Starting G-E--_060_C18_F1_PI_AE_CS_SP_S0Y with 136s (1) cores
% 173.46/25.79 % Starting new_bool_3 with 136s (1) cores
% 173.46/25.79 % G-E--_060_C18_F1_PI_AE_CS_SP_S0Y with pid 1673425 completed with status 0
% 173.46/25.79 % Result found by G-E--_060_C18_F1_PI_AE_CS_SP_S0Y
% 173.46/25.79 % Preprocessing class: FSSSSMSSSSSNFFN.
% 173.46/25.79 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 173.46/25.79 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 173.46/25.79 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 173.46/25.79 % No SInE strategy applied
% 173.46/25.79 % Search class: FHHNS-FFSF22-MFFFFFNN
% 173.46/25.79 % partial match(1): FHUNS-FFSF22-MFFFFFNN
% 173.46/25.79 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 173.46/25.79 % Starting SubtermCWHack with 136s (1) cores
% 173.46/25.79 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 173.46/25.79 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S00 with 136s (1) cores
% 173.46/25.79 % Starting G-E--_060_C18_F1_PI_AE_CS_SP_S0Y with 136s (1) cores
% 173.46/25.79 % Preprocessing time : 0.002 s
% 173.46/25.79
% 173.46/25.79 % Proof found!
% 173.46/25.79 % SZS status Unsatisfiable
% 173.46/25.79 % SZS output start CNFRefutation
% See solution above
% 173.46/25.80 % Parsed axioms : 7
% 173.46/25.80 % Removed by relevancy pruning/SinE : 0
% 173.46/25.80 % Initial clauses : 7
% 173.46/25.80 % Removed in clause preprocessing : 0
% 173.46/25.80 % Initial clauses in saturation : 7
% 173.46/25.80 % Processed clauses : 39005
% 173.46/25.80 % ...of these trivial : 5399
% 173.46/25.80 % ...subsumed : 29459
% 173.46/25.80 % ...remaining for further processing : 4147
% 173.46/25.80 % Other redundant clauses eliminated : 0
% 173.46/25.80 % Clauses deleted for lack of memory : 0
% 173.46/25.80 % Backward-subsumed : 700
% 173.46/25.80 % Backward-rewritten : 895
% 173.46/25.80 % Generated clauses : 1036555
% 173.46/25.80 % ...of the previous two non-redundant : 917112
% 173.46/25.80 % ...aggressively subsumed : 0
% 173.46/25.80 % Contextual simplify-reflections : 0
% 173.46/25.80 % Paramodulations : 1036555
% 173.46/25.80 % Factorizations : 0
% 173.46/25.80 % NegExts : 0
% 173.46/25.80 % Equation resolutions : 0
% 173.46/25.80 % Disequality decompositions : 0
% 173.46/25.80 % Total rewrite steps : 165953
% 173.46/25.80 % ...of those cached : 145417
% 173.46/25.80 % Propositional unsat checks : 0
% 173.46/25.80 % Propositional check models : 0
% 173.46/25.80 % Propositional check unsatisfiable : 0
% 173.46/25.80 % Propositional clauses : 0
% 173.46/25.80 % Propositional clauses after purity: 0
% 173.46/25.80 % Propositional unsat core size : 0
% 173.46/25.80 % Propositional preprocessing time : 0.000
% 173.46/25.80 % Propositional encoding time : 0.000
% 173.46/25.80 % Propositional solver time : 0.000
% 173.46/25.80 % Success case prop preproc time : 0.000
% 173.46/25.80 % Success case prop encoding time : 0.000
% 173.46/25.80 % Success case prop solver time : 0.000
% 173.46/25.80 % Current number of processed clauses : 2552
% 173.46/25.80 % Positive orientable unit clauses : 679
% 173.46/25.80 % Positive unorientable unit clauses: 0
% 173.46/25.80 % Negative unit clauses : 2
% 173.46/25.80 % Non-unit-clauses : 1871
% 173.46/25.80 % Current number of unprocessed clauses: 849783
% 173.46/25.80 % ...number of literals in the above : 1415134
% 173.46/25.80 % Current number of archived formulas : 0
% 173.46/25.80 % Current number of archived clauses : 1595
% 173.46/25.80 % Clause-clause subsumption calls (NU) : 1318502
% 173.46/25.80 % Rec. Clause-clause subsumption calls : 1318326
% 173.46/25.80 % Non-unit clause-clause subsumptions : 30107
% 173.46/25.80 % Unit Clause-clause subsumption calls : 100981
% 173.46/25.80 % Rewrite failures with RHS unbound : 0
% 173.46/25.80 % BW rewrite match attempts : 600671
% 173.46/25.80 % BW rewrite match successes : 806
% 173.46/25.80 % Condensation attempts : 0
% 173.46/25.80 % Condensation successes : 0
% 173.46/25.80 % Termbank termtop insertions : 16594552
% 173.46/25.80 % Search garbage collected termcells : 15
% 173.46/25.80
% 173.46/25.80 % -------------------------------------------------
% 173.46/25.80 % User time : 23.601 s
% 173.46/25.80 % System time : 0.828 s
% 173.46/25.80 % Total time : 24.429 s
% 173.46/25.80 % Maximum resident set size: 3636 pages
% 173.46/25.80
% 173.46/25.80 % -------------------------------------------------
% 173.46/25.80 % User time : 118.976 s
% 173.46/25.80 % System time : 4.241 s
% 173.46/25.80 % Total time : 123.217 s
% 173.46/25.80 % Maximum resident set size: 4608 pages
% 173.46/25.80 % E exiting
%------------------------------------------------------------------------------