%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN074+1 : TPTP v9.2.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n028.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 : Tue May 5 05:36:04 PM UTC 2026
% Result : Theorem 1.12s 1.61s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 24)
% Comments :
%------------------------------------------------------------------------------
fof(pel51,conjecture,
? [X1] :
! [X3] :
( ? [X2] :
! [X4] :
( big_f(X3,X4)
<=> X4 = X2 )
<=> X3 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel51) ).
fof(pel51_1,axiom,
? [X1,X2] :
! [X3,X4] :
( big_f(X3,X4)
<=> ( X3 = X1
& X4 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel51_1) ).
fof(i_0_2,negated_conjecture,
~ ? [X1] :
! [X3] :
( ? [X2] :
! [X4] :
( big_f(X3,X4)
<=> X4 = X2 )
<=> X3 = X1 ),
inference(assume_negation,[status(cth)],[pel51]) ).
fof(i_0_3,negated_conjecture,
! [X17,X19,X22,X23] :
( ( ~ big_f(esk3_1(X17),esk4_2(X17,X19))
| esk4_2(X17,X19) != X19
| esk3_1(X17) != X17 )
& ( big_f(esk3_1(X17),esk4_2(X17,X19))
| esk4_2(X17,X19) = X19
| esk3_1(X17) != X17 )
& ( ~ big_f(esk3_1(X17),X22)
| X22 = esk5_1(X17)
| esk3_1(X17) = X17 )
& ( X23 != esk5_1(X17)
| big_f(esk3_1(X17),X23)
| esk3_1(X17) = X17 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_2])])])])])]) ).
fof(i_0_4,plain,
! [X15,X16] :
( ( X15 = esk1_0
| ~ big_f(X15,X16) )
& ( X16 = esk2_0
| ~ big_f(X15,X16) )
& ( X15 != esk1_0
| X16 != esk2_0
| big_f(X15,X16) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pel51_1])])])]) ).
cnf(i_0_5,negated_conjecture,
( ~ big_f(esk3_1(X1),esk4_2(X1,X2))
| esk4_2(X1,X2) != X2
| esk3_1(X1) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_6,negated_conjecture,
( big_f(esk3_1(X1),esk4_2(X1,X2))
| esk4_2(X1,X2) = X2
| esk3_1(X1) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_7,negated_conjecture,
( X2 = esk5_1(X1)
| esk3_1(X1) = X1
| ~ big_f(esk3_1(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_8,negated_conjecture,
( big_f(esk3_1(X2),X1)
| esk3_1(X2) = X2
| X1 != esk5_1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_9,plain,
( X1 = esk2_0
| ~ big_f(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_10,plain,
( X1 = esk1_0
| ~ big_f(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_11,plain,
( big_f(X1,X2)
| X1 != esk1_0
| X2 != esk2_0 ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_12,axiom,
X1 = X1 ).
cnf(i_0_13,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_14,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_15,axiom,
( X1 != X2
| esk3_1(X1) = esk3_1(X2) ) ).
cnf(i_0_16,axiom,
( X1 != X2
| esk4_2(X1,X3) = esk4_2(X2,X3) ) ).
cnf(i_0_17,axiom,
( X1 != X2
| esk4_2(X3,X1) = esk4_2(X3,X2) ) ).
cnf(i_0_18,axiom,
( X1 != X2
| esk5_1(X1) = esk5_1(X2) ) ).
cnf(i_0_19,axiom,
( X1 != X2
| ~ big_f(X1,X3)
| big_f(X2,X3) ) ).
cnf(i_0_20,axiom,
( X1 != X2
| ~ big_f(X3,X1)
| big_f(X3,X2) ) ).
cnf(i_0_12_001,axiom,
X1 = X1 ).
cnf(i_0_13_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_14_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_15_004,axiom,
( X1 != X2
| esk3_1(X1) = esk3_1(X2) ) ).
cnf(i_0_16_005,axiom,
( X1 != X2
| esk4_2(X1,X3) = esk4_2(X2,X3) ) ).
cnf(i_0_17_006,axiom,
( X1 != X2
| esk4_2(X3,X1) = esk4_2(X3,X2) ) ).
cnf(i_0_18_007,axiom,
( X1 != X2
| esk5_1(X1) = esk5_1(X2) ) ).
cnf(i_0_19_008,axiom,
( X1 != X2
| ~ big_f(X1,X3)
| big_f(X2,X3) ) ).
cnf(i_0_20_009,axiom,
( X1 != X2
| ~ big_f(X3,X1)
| big_f(X3,X2) ) ).
cnf(i_0_21,plain,
( esk3_1(X1) = X1
| big_f(esk3_1(X1),esk5_1(X1)) ),
inference(equality_inference,[],[8]) ).
cnf(i_0_22,plain,
( esk2_0 = X1
| ~ big_f(X2,X1) ),
inference(scs_inference,[],[i_0_13,i_0_9]) ).
cnf(i_0_23,plain,
( ~ big_f(X1,X2)
| esk3_1(X1) = esk3_1(esk1_0) ),
inference(scs_inference,[],[i_0_15,i_0_10]) ).
cnf(i_0_24,plain,
( X1 != X2
| esk4_2(esk4_2(X3,X1),X4) = esk4_2(esk4_2(X3,X2),X4) ),
inference(scs_inference,[],[i_0_16,i_0_17]) ).
cnf(i_0_25,plain,
esk4_2(esk4_2(X1,X2),X3) = esk4_2(esk4_2(X1,X2),X3),
inference(equality_inference,[],[24]) ).
cnf(i_0_26,plain,
( big_f(esk3_1(X1),esk5_1(X1))
| esk5_1(esk3_1(X1)) = esk5_1(X1) ),
inference(scs_inference,[],[i_0_18,i_0_21]) ).
cnf(i_0_27,plain,
( esk5_1(esk3_1(X1)) = esk5_1(X1)
| esk2_0 = esk5_1(X1) ),
inference(scs_inference,[],[i_0_22,i_0_26]) ).
cnf(i_0_28,plain,
( esk3_1(X1) = X1
| esk3_1(esk3_1(X1)) = esk3_1(esk1_0) ),
inference(scs_inference,[],[i_0_23,i_0_21]) ).
cnf(i_0_29,plain,
( esk5_1(X1) = esk5_1(esk3_1(X1))
| esk2_0 = esk5_1(X1) ),
inference(scs_inference,[],[i_0_27,i_0_13]) ).
cnf(i_0_30,plain,
( esk3_1(esk3_1(X1)) = esk3_1(esk1_0)
| esk3_1(esk3_1(X1)) = esk3_1(X1) ),
inference(scs_inference,[],[i_0_28,i_0_15]) ).
cnf(i_0_31,plain,
( esk4_2(esk5_1(X1),X2) = esk4_2(esk5_1(esk3_1(X1)),X2)
| esk2_0 = esk5_1(X1) ),
inference(scs_inference,[],[i_0_29,i_0_16]) ).
cnf(i_0_32,plain,
( esk3_1(esk3_1(X1)) = esk3_1(esk1_0)
| esk4_2(X2,esk3_1(esk3_1(X1))) = esk4_2(X2,esk3_1(X1)) ),
inference(scs_inference,[],[i_0_30,i_0_17]) ).
cnf(i_0_33,plain,
( big_f(esk3_1(X1),esk5_1(X1))
| X2 = X1
| X2 != esk3_1(X1) ),
inference(scs_inference,[],[i_0_14,i_0_21]) ).
cnf(i_0_34,plain,
( big_f(esk3_1(X1),esk5_1(X1))
| esk3_1(X1) = X1 ),
inference(equality_inference,[],[33]) ).
cnf(i_0_35,plain,
( X1 != X2
| ~ big_f(X1,X3)
| X2 = esk1_0 ),
inference(scs_inference,[],[i_0_19,i_0_10]) ).
cnf(i_0_36,plain,
( ~ big_f(X1,X2)
| X1 = esk1_0 ),
inference(equality_inference,[],[35]) ).
cnf(i_0_37,plain,
( X1 != X2
| ~ big_f(X3,X1)
| X2 = esk2_0 ),
inference(scs_inference,[],[i_0_20,i_0_9]) ).
cnf(i_0_38,plain,
( ~ big_f(X1,X2)
| X2 = esk2_0 ),
inference(equality_inference,[],[37]) ).
cnf(i_0_39,plain,
( X1 != esk1_0
| X2 != esk2_0
| X2 = esk2_0 ),
inference(scs_inference,[],[i_0_11,i_0_9]) ).
cnf(i_0_40,plain,
( X1 = esk3_1(X1)
| ~ big_f(esk3_1(X1),X2)
| X2 = esk5_1(X1) ),
inference(scs_inference,[],[i_0_7,i_0_13]) ).
cnf(i_0_41,plain,
( X1 = esk3_1(X1)
| ~ big_f(esk3_1(X1),X2)
| esk3_1(X2) = esk3_1(esk5_1(X1)) ),
inference(scs_inference,[],[i_0_40,i_0_15]) ).
cnf(i_0_42,plain,
( X1 = esk3_1(X1)
| ~ big_f(esk3_1(X1),X2)
| esk4_2(esk3_1(X2),X3) = esk4_2(esk3_1(esk5_1(X1)),X3) ),
inference(scs_inference,[],[i_0_41,i_0_16]) ).
cnf(i_0_43,plain,
( ~ big_f(esk3_1(esk3_1(esk1_0)),esk4_2(esk3_1(esk1_0),X1))
| esk4_2(esk3_1(esk1_0),X1) != X1 ),
inference(scs_inference,[],[i_0_5,i_0_30]) ).
cnf(i_0_44,plain,
( big_f(esk3_1(esk3_1(esk1_0)),esk4_2(esk3_1(esk1_0),X1))
| esk4_2(esk3_1(esk1_0),X1) = X1 ),
inference(scs_inference,[],[i_0_6,i_0_30]) ).
cnf(i_0_45,plain,
( X1 != X2
| esk3_1(X2) = esk3_1(X1) ),
inference(scs_inference,[],[i_0_13,i_0_15]) ).
cnf(i_0_46,plain,
esk3_1(X1) = esk3_1(X1),
inference(equality_inference,[],[45]) ).
cnf(i_0_47,plain,
( esk1_0 = X1
| ~ big_f(X1,X2) ),
inference(scs_inference,[],[i_0_13,i_0_10]) ).
cnf(i_0_48,plain,
( esk3_1(X1) = X1
| esk1_0 = esk3_1(X1) ),
inference(scs_inference,[],[i_0_47,i_0_21]) ).
cnf(i_0_49,plain,
( esk4_2(esk3_1(X1),X2) = esk4_2(X1,X2)
| esk1_0 = esk3_1(X1) ),
inference(scs_inference,[],[i_0_48,i_0_16]) ).
cnf(i_0_50,plain,
( esk4_2(X1,esk4_2(esk3_1(X2),X3)) = esk4_2(X1,esk4_2(X2,X3))
| esk1_0 = esk3_1(X2) ),
inference(scs_inference,[],[i_0_49,i_0_17]) ).
cnf(i_0_51,plain,
( X1 != X2
| esk4_2(X2,X3) = esk4_2(X1,X3) ),
inference(scs_inference,[],[i_0_13,i_0_16]) ).
cnf(i_0_52,plain,
esk4_2(X1,X2) = esk4_2(X1,X2),
inference(equality_inference,[],[51]) ).
cnf(i_0_53,plain,
( esk4_2(X1,X2) = esk4_2(X1,X3)
| X3 != X2 ),
inference(scs_inference,[],[i_0_13,i_0_17]) ).
cnf(i_0_54,plain,
esk4_2(X1,X2) = esk4_2(X1,X2),
inference(equality_inference,[],[53]) ).
cnf(i_0_55,plain,
( X1 != X2
| esk5_1(X2) = esk5_1(X1) ),
inference(scs_inference,[],[i_0_13,i_0_18]) ).
cnf(i_0_56,plain,
esk5_1(X1) = esk5_1(X1),
inference(equality_inference,[],[55]) ).
cnf(i_0_57,plain,
( big_f(esk3_1(X1),esk5_1(X1))
| X1 = esk3_1(X1) ),
inference(scs_inference,[],[i_0_13,i_0_21]) ).
cnf(i_0_58,plain,
( X1 = esk3_1(X1)
| esk5_1(X1) = esk2_0 ),
inference(scs_inference,[],[i_0_57,i_0_9]) ).
cnf(i_0_59,plain,
( esk5_1(X1) = esk2_0
| esk3_1(X1) = esk3_1(esk3_1(X1)) ),
inference(scs_inference,[],[i_0_58,i_0_15]) ).
cnf(i_0_60,plain,
( esk3_1(esk3_1(esk3_1(X1))) = esk3_1(esk3_1(X1))
| esk5_1(X1) = esk2_0 ),
inference(scs_inference,[],[i_0_59,i_0_45]) ).
cnf(i_0_61,plain,
( X1 != esk4_2(X2,X1)
| esk3_1(X2) != X2
| ~ big_f(esk3_1(X2),esk4_2(X2,X1)) ),
inference(scs_inference,[],[i_0_13,i_0_5]) ).
cnf(i_0_62,plain,
( X1 != esk4_2(esk3_1(esk1_0),X1)
| ~ big_f(esk3_1(esk3_1(esk1_0)),esk4_2(esk3_1(esk1_0),X1)) ),
inference(scs_inference,[],[i_0_61,i_0_30]) ).
cnf(i_0_63,plain,
( esk3_1(esk1_0) = esk3_1(X1)
| ~ big_f(X1,X2) ),
inference(scs_inference,[],[i_0_13,i_0_23]) ).
cnf(i_0_64,plain,
( esk3_1(X1) = X1
| esk3_1(esk1_0) = esk3_1(esk3_1(X1)) ),
inference(scs_inference,[],[i_0_63,i_0_21]) ).
cnf(i_0_65,plain,
( esk3_1(esk1_0) = esk3_1(esk3_1(X1))
| esk3_1(esk3_1(X1)) = esk3_1(X1) ),
inference(scs_inference,[],[i_0_64,i_0_15]) ).
cnf(i_0_66,plain,
( esk3_1(esk1_0) = esk3_1(esk3_1(X1))
| esk4_2(esk3_1(esk3_1(X1)),X2) = esk4_2(esk3_1(X1),X2) ),
inference(scs_inference,[],[i_0_65,i_0_16]) ).
cnf(i_0_67,plain,
( X1 != esk3_1(X1)
| esk4_2(X1,X2) != X2
| ~ big_f(esk3_1(X1),esk4_2(X1,X2)) ),
inference(scs_inference,[],[i_0_13,i_0_5]) ).
cnf(i_0_68,plain,
( esk4_2(esk3_1(X1),X2) != X2
| ~ big_f(esk3_1(esk3_1(X1)),esk4_2(esk3_1(X1),X2))
| X1 != esk3_1(X1) ),
inference(scs_inference,[],[i_0_67,i_0_15]) ).
cnf(i_0_69,plain,
( big_f(esk3_1(X1),esk5_1(X1))
| esk5_1(X1) = esk5_1(esk3_1(X1)) ),
inference(scs_inference,[],[i_0_13,i_0_26]) ).
cnf(i_0_70,plain,
( esk5_1(X1) = esk5_1(esk3_1(X1))
| esk5_1(X1) = esk2_0 ),
inference(scs_inference,[],[i_0_69,i_0_9]) ).
cnf(i_0_71,plain,
( esk3_1(esk5_1(X1)) = esk3_1(esk5_1(esk3_1(X1)))
| esk5_1(X1) = esk2_0 ),
inference(scs_inference,[],[i_0_70,i_0_15]) ).
cnf(i_0_72,plain,
( X1 != esk3_1(X1)
| big_f(esk3_1(X1),esk4_2(X1,X2))
| esk4_2(X1,X2) = X2 ),
inference(scs_inference,[],[i_0_13,i_0_6]) ).
cnf(i_0_73,plain,
( big_f(esk3_1(esk3_1(X1)),esk4_2(esk3_1(X1),X2))
| esk4_2(esk3_1(X1),X2) = X2
| X1 != esk3_1(X1) ),
inference(scs_inference,[],[i_0_72,i_0_15]) ).
cnf(i_0_74,plain,
( esk5_1(esk3_1(X1)) = esk5_1(X1)
| esk5_1(X1) = esk2_0 ),
inference(scs_inference,[],[i_0_13,i_0_27]) ).
cnf(i_0_75,plain,
( esk5_1(X1) = esk2_0
| esk3_1(esk5_1(esk3_1(X1))) = esk3_1(esk5_1(X1)) ),
inference(scs_inference,[],[i_0_74,i_0_15]) ).
cnf(i_0_76,plain,
( esk5_1(X1) != X2
| esk3_1(X1) = X1
| big_f(esk3_1(X1),X2) ),
inference(scs_inference,[],[i_0_13,i_0_8]) ).
cnf(i_0_77,plain,
( esk3_1(X1) = X1
| big_f(esk3_1(X1),esk5_1(X1)) ),
inference(equality_inference,[],[76]) ).
cnf(i_0_78,plain,
( X1 = esk3_1(X1)
| esk3_1(esk3_1(X1)) = esk3_1(esk1_0) ),
inference(scs_inference,[],[i_0_13,i_0_28]) ).
cnf(i_0_79,plain,
( esk3_1(esk3_1(X1)) = esk3_1(esk1_0)
| esk3_1(X1) = esk3_1(esk3_1(X1)) ),
inference(scs_inference,[],[i_0_78,i_0_15]) ).
cnf(i_0_80,plain,
( esk3_1(esk3_1(X1)) = esk3_1(esk1_0)
| esk4_2(esk3_1(X1),X2) = esk4_2(esk3_1(esk3_1(X1)),X2) ),
inference(scs_inference,[],[i_0_79,i_0_16]) ).
cnf(i_0_81,plain,
( esk1_0 != X1
| big_f(X1,X2)
| X2 != esk2_0 ),
inference(scs_inference,[],[i_0_13,i_0_11]) ).
cnf(i_0_82,plain,
( X1 != esk2_0
| esk1_0 != X2
| X1 = esk2_0 ),
inference(scs_inference,[],[i_0_81,i_0_9]) ).
cnf(i_0_83,plain,
( X1 = esk3_1(X1)
| esk1_0 = esk3_1(X1) ),
inference(scs_inference,[],[i_0_13,i_0_48]) ).
cnf(i_0_84,plain,
( esk1_0 = esk3_1(X1)
| esk3_1(X1) = esk3_1(esk3_1(X1)) ),
inference(scs_inference,[],[i_0_83,i_0_15]) ).
cnf(i_0_85,plain,
( esk4_2(esk3_1(X1),X2) = esk4_2(esk3_1(esk3_1(X1)),X2)
| esk1_0 = esk3_1(X1) ),
inference(scs_inference,[],[i_0_84,i_0_16]) ).
cnf(i_0_86,plain,
( esk2_0 != X1
| big_f(X2,X1)
| X2 != esk1_0 ),
inference(scs_inference,[],[i_0_13,i_0_11]) ).
cnf(i_0_87,plain,
( X1 != esk1_0
| esk2_0 != X2
| X1 = esk1_0 ),
inference(scs_inference,[],[i_0_86,i_0_10]) ).
cnf(i_0_88,plain,
( esk3_1(X1) = X1
| esk3_1(X1) = esk1_0 ),
inference(scs_inference,[],[i_0_13,i_0_48]) ).
cnf(i_0_89,plain,
( esk3_1(esk3_1(X1)) = esk3_1(X1)
| esk3_1(X1) = esk1_0 ),
inference(scs_inference,[],[i_0_88,i_0_15]) ).
cnf(i_0_90,plain,
( esk4_2(esk3_1(esk3_1(X1)),X2) = esk4_2(esk3_1(X1),X2)
| esk3_1(X1) = esk1_0 ),
inference(scs_inference,[],[i_0_89,i_0_16]) ).
cnf(i_0_91,plain,
( X1 != X2
| X1 != X3
| X2 = X3 ),
inference(scs_inference,[],[i_0_13,i_0_14]) ).
cnf(i_0_92,plain,
( X1 != X2
| X1 != X3
| esk3_1(X2) = esk3_1(X3) ),
inference(scs_inference,[],[i_0_91,i_0_15]) ).
cnf(i_0_93,plain,
( X1 != X2
| X1 != X3
| esk4_2(esk3_1(X2),X4) = esk4_2(esk3_1(X3),X4) ),
inference(scs_inference,[],[i_0_92,i_0_16]) ).
cnf(i_0_94,plain,
( esk4_2(X1,X2) = esk4_2(esk3_1(X1),X2)
| esk1_0 = esk3_1(X1) ),
inference(scs_inference,[],[i_0_13,i_0_49]) ).
cnf(i_0_95,plain,
( esk1_0 = esk3_1(X1)
| esk3_1(esk4_2(X1,X2)) = esk3_1(esk4_2(esk3_1(X1),X2)) ),
inference(scs_inference,[],[i_0_94,i_0_15]) ).
cnf(i_0_96,plain,
( X1 != X2
| X3 = X1
| X3 != X2 ),
inference(scs_inference,[],[i_0_13,i_0_14]) ).
cnf(i_0_97,plain,
( big_f(esk3_1(X1),esk5_1(X1))
| X2 != X1
| esk3_1(X1) = X2 ),
inference(scs_inference,[],[i_0_96,i_0_21]) ).
cnf(i_0_98,plain,
( big_f(esk3_1(X1),esk5_1(X1))
| esk3_1(X1) = X1 ),
inference(equality_inference,[],[97]) ).
cnf(i_0_99,plain,
( esk4_2(esk3_1(X1),X2) = esk4_2(X1,X2)
| esk3_1(X1) = esk1_0 ),
inference(scs_inference,[],[i_0_13,i_0_49]) ).
cnf(i_0_100,plain,
( esk3_1(esk4_2(esk3_1(X1),X2)) = esk3_1(esk4_2(X1,X2))
| esk3_1(X1) = esk1_0 ),
inference(scs_inference,[],[i_0_99,i_0_15]) ).
cnf(i_0_101,plain,
( X1 != X2
| big_f(X1,X3)
| ~ big_f(X2,X3) ),
inference(scs_inference,[],[i_0_13,i_0_19]) ).
cnf(i_0_102,plain,
( ~ big_f(X1,X2)
| big_f(X1,X2) ),
inference(equality_inference,[],[101]) ).
cnf(i_0_103,plain,
( esk3_1(X1) = X1
| esk5_1(X1) = esk2_0 ),
inference(scs_inference,[],[i_0_13,i_0_58]) ).
cnf(i_0_104,plain,
( esk5_1(X1) = esk2_0
| esk3_1(esk3_1(X1)) = esk3_1(X1) ),
inference(scs_inference,[],[i_0_103,i_0_15]) ).
cnf(i_0_105,plain,
( esk4_2(esk3_1(esk3_1(X1)),X2) = esk4_2(esk3_1(X1),X2)
| esk5_1(X1) = esk2_0 ),
inference(scs_inference,[],[i_0_104,i_0_16]) ).
cnf(i_0_106,plain,
( X1 != X2
| big_f(X3,X1)
| ~ big_f(X3,X2) ),
inference(scs_inference,[],[i_0_13,i_0_20]) ).
cnf(i_0_107,plain,
( ~ big_f(X1,X2)
| big_f(X1,X2) ),
inference(equality_inference,[],[106]) ).
cnf(i_0_108,plain,
( X1 = esk3_1(X1)
| esk2_0 = esk5_1(X1) ),
inference(scs_inference,[],[i_0_13,i_0_58]) ).
cnf(i_0_109,plain,
( esk2_0 = esk5_1(X1)
| esk3_1(X1) = esk3_1(esk3_1(X1)) ),
inference(scs_inference,[],[i_0_108,i_0_15]) ).
cnf(i_0_110,plain,
( esk4_2(esk3_1(X1),X2) = esk4_2(esk3_1(esk3_1(X1)),X2)
| esk2_0 = esk5_1(X1) ),
inference(scs_inference,[],[i_0_109,i_0_16]) ).
cnf(i_0_111,plain,
( esk3_1(X1) != X2
| big_f(esk3_1(X1),esk5_1(X1))
| X2 = X1 ),
inference(scs_inference,[],[i_0_13,i_0_33]) ).
cnf(i_0_112,plain,
( esk3_1(X1) = X1
| big_f(esk3_1(X1),esk5_1(X1)) ),
inference(equality_inference,[],[111]) ).
cnf(i_0_113,plain,
( X1 = esk3_1(X1)
| esk3_1(esk1_0) = esk3_1(esk3_1(X1)) ),
inference(scs_inference,[],[i_0_13,i_0_64]) ).
cnf(i_0_114,plain,
( esk3_1(esk1_0) = esk3_1(esk3_1(X1))
| esk3_1(X1) = esk3_1(esk3_1(X1)) ),
inference(scs_inference,[],[i_0_113,i_0_15]) ).
cnf(i_0_115,plain,
( esk3_1(esk1_0) = esk3_1(esk3_1(X1))
| esk4_2(esk3_1(X1),X2) = esk4_2(esk3_1(esk3_1(X1)),X2) ),
inference(scs_inference,[],[i_0_114,i_0_16]) ).
cnf(i_0_116,plain,
( X1 != X2
| ~ big_f(X2,X3)
| X1 = esk1_0 ),
inference(scs_inference,[],[i_0_13,i_0_35]) ).
cnf(i_0_117,plain,
( ~ big_f(X1,X2)
| X1 = esk1_0 ),
inference(equality_inference,[],[116]) ).
cnf(i_0_118,plain,
( X1 = esk3_1(X1)
| esk3_1(X1) = esk1_0 ),
inference(scs_inference,[],[i_0_13,i_0_83]) ).
cnf(i_0_119,plain,
( esk3_1(X1) = esk1_0
| esk3_1(X1) = esk3_1(esk3_1(X1)) ),
inference(scs_inference,[],[i_0_118,i_0_15]) ).
cnf(i_0_120,plain,
( esk4_2(esk3_1(X1),X2) = esk4_2(esk3_1(esk3_1(X1)),X2)
| esk3_1(X1) = esk1_0 ),
inference(scs_inference,[],[i_0_119,i_0_16]) ).
cnf(i_0_121,plain,
( X1 != X2
| ~ big_f(X3,X2)
| X1 = esk2_0 ),
inference(scs_inference,[],[i_0_13,i_0_37]) ).
cnf(i_0_122,plain,
( ~ big_f(X1,X2)
| X2 = esk2_0 ),
inference(equality_inference,[],[121]) ).
cnf(i_0_123,plain,
( esk3_1(esk3_1(X1)) = esk3_1(X1)
| esk1_0 = esk3_1(X1) ),
inference(scs_inference,[],[i_0_13,i_0_84]) ).
cnf(i_0_124,plain,
( esk3_1(esk3_1(esk3_1(X1))) = esk3_1(esk3_1(X1))
| esk1_0 = esk3_1(X1) ),
inference(scs_inference,[],[i_0_123,i_0_15]) ).
cnf(i_0_125,plain,
( X1 != esk3_1(X1)
| X2 != esk4_2(X1,X2)
| ~ big_f(esk3_1(X1),esk4_2(X1,X2)) ),
inference(scs_inference,[],[i_0_13,i_0_61]) ).
cnf(i_0_126,plain,
( ~ big_f(esk3_1(esk1_0),esk4_2(esk1_0,X1))
| X1 != esk4_2(esk1_0,X1) ),
inference(scs_inference,[],[i_0_125,i_0_83]) ).
cnf(i_0_127,plain,
( X1 != esk4_2(esk1_0,X1)
| ~ big_f(esk3_1(esk1_0),esk4_2(esk1_0,esk4_2(esk1_0,X1))) ),
inference(scs_inference,[],[i_0_126,i_0_17]) ).
cnf(i_0_128,plain,
( ~ big_f(X1,esk4_2(esk1_0,esk2_0))
| ~ big_f(esk3_1(esk1_0),esk4_2(esk1_0,esk4_2(esk1_0,esk2_0))) ),
inference(scs_inference,[],[i_0_127,i_0_22]) ).
cnf(i_0_129,plain,
( ~ big_f(esk3_1(esk1_0),esk4_2(esk1_0,esk4_2(esk1_0,esk2_0)))
| esk3_1(esk1_0) != esk1_0
| esk4_2(esk1_0,esk2_0) = esk2_0 ),
inference(scs_inference,[],[i_0_128,i_0_6]) ).
cnf(i_0_130,plain,
( esk3_1(esk1_0) != esk1_0
| esk4_2(esk1_0,esk4_2(esk1_0,esk2_0)) != esk2_0
| esk4_2(esk1_0,esk2_0) = esk2_0 ),
inference(scs_inference,[],[i_0_129,i_0_11]) ).
cnf(i_0_131,plain,
( esk4_2(esk1_0,esk2_0) = esk2_0
| esk4_2(esk1_0,esk4_2(esk1_0,esk2_0)) != esk2_0 ),
inference(scs_inference,[],[i_0_130,i_0_88]) ).
cnf(i_0_132,plain,
( esk3_1(esk4_2(esk1_0,esk2_0)) = esk3_1(esk2_0)
| esk4_2(esk1_0,esk4_2(esk1_0,esk2_0)) != esk2_0 ),
inference(scs_inference,[],[i_0_131,i_0_15]) ).
cnf(i_0_133,plain,
( esk4_2(esk3_1(esk4_2(esk1_0,esk2_0)),X1) = esk4_2(esk3_1(esk2_0),X1)
| esk4_2(esk1_0,esk4_2(esk1_0,esk2_0)) != esk2_0 ),
inference(scs_inference,[],[i_0_132,i_0_16]) ).
cnf(i_0_134,plain,
( esk4_2(X1,X2) = esk4_2(esk3_1(X1),X2)
| esk3_1(X1) = esk1_0 ),
inference(scs_inference,[],[i_0_13,i_0_94]) ).
cnf(i_0_135,plain,
( esk3_1(X1) = esk1_0
| esk3_1(esk4_2(X1,X2)) = esk3_1(esk4_2(esk3_1(X1),X2)) ),
inference(scs_inference,[],[i_0_134,i_0_15]) ).
cnf(i_0_136,plain,
( esk4_2(esk1_0,X1) != X1
| ~ big_f(esk3_1(esk1_0),esk4_2(esk1_0,X1)) ),
inference(scs_inference,[],[i_0_13,i_0_126]) ).
cnf(i_0_137,plain,
( ~ big_f(X1,esk4_2(esk1_0,esk2_0))
| ~ big_f(esk3_1(esk1_0),esk4_2(esk1_0,esk2_0)) ),
inference(scs_inference,[],[i_0_136,i_0_9]) ).
cnf(i_0_138,plain,
~ big_f(esk3_1(esk1_0),esk4_2(esk1_0,esk2_0)),
nference(factoring_inference,[],[137]) ).
cnf(i_0_139,plain,
( esk3_1(esk1_0) != esk1_0
| esk4_2(esk1_0,esk2_0) = esk2_0 ),
inference(scs_inference,[],[i_0_138,i_0_6]) ).
cnf(i_0_140,plain,
( big_f(esk3_1(X1),esk4_2(X1,X2))
| esk3_1(X1) != X1
| esk4_2(X1,X2) = X2 ),
inference(rename_variables,[],[i_0_6]) ).
cnf(i_0_141,plain,
( esk5_1(esk1_0) != esk4_2(esk1_0,esk2_0)
| esk4_2(esk1_0,esk2_0) = esk2_0 ),
inference(scs_inference,[],[i_0_138,i_0_6,i_0_76]) ).
cnf(i_0_142,plain,
( esk3_1(X1) = X1
| big_f(esk3_1(X1),X2)
| esk5_1(X1) != X2 ),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_143,plain,
( esk4_2(esk3_1(esk1_0),X1) = esk4_2(esk1_0,X1)
| esk4_2(esk1_0,esk2_0) = esk2_0 ),
inference(scs_inference,[],[i_0_138,i_0_6,i_0_76,i_0_88,i_0_99]) ).
cnf(i_0_144,plain,
( esk3_1(X1) = esk1_0
| esk4_2(esk3_1(X1),X2) = esk4_2(X1,X2) ),
inference(rename_variables,[],[i_0_99]) ).
cnf(i_0_145,plain,
( esk4_2(esk1_0,X1) = esk4_2(esk3_1(esk1_0),X1)
| esk4_2(esk1_0,esk2_0) = esk2_0 ),
inference(scs_inference,[],[i_0_138,i_0_6,i_0_76,i_0_88,i_0_99,i_0_134]) ).
cnf(i_0_146,plain,
( esk3_1(X1) = esk1_0
| esk4_2(X1,X2) = esk4_2(esk3_1(X1),X2) ),
inference(rename_variables,[],[i_0_134]) ).
cnf(i_0_147,plain,
( ~ big_f(esk3_1(esk1_0),X1)
| esk4_2(esk1_0,esk2_0) = esk2_0 ),
inference(scs_inference,[],[i_0_138,i_0_6,i_0_76,i_0_88,i_0_99,i_0_134,i_0_10]) ).
cnf(i_0_148,plain,
( X1 = esk1_0
| ~ big_f(X1,X2) ),
inference(rename_variables,[],[i_0_10]) ).
cnf(i_0_149,plain,
esk4_2(esk1_0,esk2_0) = esk2_0,
inference(scs_inference,[],[i_0_138,i_0_6,i_0_76,i_0_88,i_0_99,i_0_134,i_0_10,i_0_7,i_0_35,i_0_91,i_0_97]) ).
cnf(i_0_150,plain,
( big_f(esk3_1(X1),esk5_1(X1))
| esk3_1(X1) = X2
| X2 != X1 ),
inference(rename_variables,[],[i_0_97]) ).
cnf(i_0_152,plain,
esk4_2(X1,esk2_0) = esk4_2(X1,esk4_2(esk1_0,esk2_0)),
inference(scs_inference,[],[i_0_149,i_0_53]) ).
cnf(i_0_153,plain,
esk2_0 = esk4_2(esk1_0,esk2_0),
inference(scs_inference,[],[i_0_149,i_0_53,i_0_13]) ).
cnf(i_0_154,plain,
esk3_1(esk1_0) != esk1_0,
inference(scs_inference,[],[i_0_138,i_0_149,i_0_53,i_0_13,i_0_11]) ).
cnf(i_0_155,plain,
( X1 != esk2_0
| X2 != esk1_0
| big_f(X2,X1) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_156,plain,
esk1_0 != esk3_1(esk1_0),
inference(scs_inference,[],[i_0_138,i_0_149,i_0_53,i_0_13,i_0_11,i_0_81]) ).
cnf(i_0_157,plain,
( X1 != esk2_0
| esk1_0 != X2
| big_f(X2,X1) ),
inference(rename_variables,[],[i_0_81]) ).
cnf(i_0_158,plain,
esk5_1(esk1_0) != esk4_2(esk1_0,esk2_0),
inference(scs_inference,[],[i_0_138,i_0_149,i_0_53,i_0_13,i_0_11,i_0_81,i_0_76]) ).
cnf(i_0_159,plain,
( esk3_1(X1) = X1
| big_f(esk3_1(X1),X2)
| esk5_1(X1) != X2 ),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_160,plain,
esk2_0 != esk5_1(esk1_0),
inference(scs_inference,[],[i_0_138,i_0_149,i_0_53,i_0_13,i_0_11,i_0_81,i_0_76,i_0_91]) ).
cnf(i_0_161,plain,
~ big_f(esk3_1(esk1_0),esk2_0),
inference(scs_inference,[],[i_0_138,i_0_149,i_0_53,i_0_13,i_0_11,i_0_81,i_0_76,i_0_91,i_0_20]) ).
cnf(i_0_162,plain,
~ big_f(X1,esk5_1(esk1_0)),
inference(scs_inference,[],[i_0_138,i_0_149,i_0_53,i_0_13,i_0_11,i_0_81,i_0_76,i_0_91,i_0_20,i_0_22]) ).
cnf(i_0_163,plain,
( esk2_0 = X1
| ~ big_f(X2,X1) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_164,plain,
esk5_1(esk3_1(esk1_0)) = esk5_1(esk1_0),
inference(scs_inference,[],[i_0_138,i_0_149,i_0_53,i_0_13,i_0_11,i_0_81,i_0_76,i_0_91,i_0_20,i_0_22,i_0_27]) ).
cnf(i_0_165,plain,
( esk2_0 = esk5_1(X1)
| esk5_1(esk3_1(X1)) = esk5_1(X1) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_166,plain,
esk5_1(esk1_0) = esk5_1(esk3_1(esk1_0)),
inference(scs_inference,[],[i_0_138,i_0_149,i_0_53,i_0_13,i_0_11,i_0_81,i_0_76,i_0_91,i_0_20,i_0_22,i_0_27,i_0_29]) ).
cnf(i_0_167,plain,
( esk2_0 = esk5_1(X1)
| esk5_1(X1) = esk5_1(esk3_1(X1)) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_168,plain,
~ big_f(esk3_1(esk1_0),X1),
inference(scs_inference,[],[i_0_138,i_0_149,i_0_53,i_0_13,i_0_11,i_0_81,i_0_76,i_0_91,i_0_20,i_0_22,i_0_27,i_0_29,i_0_47]) ).
cnf(i_0_169,plain,
( esk1_0 = X1
| ~ big_f(X1,X2) ),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_170,plain,
$false,
inference(scs_inference,[],[i_0_138,i_0_149,i_0_53,i_0_13,i_0_11,i_0_81,i_0_76,i_0_91,i_0_20,i_0_22,i_0_27,i_0_29,i_0_47,i_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN074+1 : TPTP v9.2.1. Released v2.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n028.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 08:12:15 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.12/1.61 % Version : CSE_E---1.7
% 1.12/1.61 % Problem : theBenchmark.p
% 1.12/1.61 % SZS status Theorem for theBenchmark.p
% 1.12/1.61 % SZS output start CNFRefutation
% See solution above
% 1.22/1.79 % Total time : 1.271s
%------------------------------------------------------------------------------