%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN078+1 : TPTP v9.2.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.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 0.62s 1.62s
% Output : CNFRefutation 0.73s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 20)
% Comments :
%------------------------------------------------------------------------------
fof(pel56,conjecture,
( ! [X1] :
( ? [X2] :
( big_p(X2)
& X1 = f(X2) )
=> big_p(X1) )
<=> ! [X3] :
( big_p(X3)
=> big_p(f(X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel56) ).
fof(i_0_1,negated_conjecture,
~ ( ! [X1] :
( ? [X2] :
( big_p(X2)
& X1 = f(X2) )
=> big_p(X1) )
<=> ! [X3] :
( big_p(X3)
=> big_p(f(X3)) ) ),
inference(assume_negation,[status(cth)],[pel56]) ).
fof(i_0_2,negated_conjecture,
! [X10,X11,X12] :
( ( big_p(esk3_0)
| big_p(esk2_0) )
& ( ~ big_p(f(esk3_0))
| big_p(esk2_0) )
& ( big_p(esk3_0)
| esk1_0 = f(esk2_0) )
& ( ~ big_p(f(esk3_0))
| esk1_0 = f(esk2_0) )
& ( big_p(esk3_0)
| ~ big_p(esk1_0) )
& ( ~ big_p(f(esk3_0))
| ~ big_p(esk1_0) )
& ( ~ big_p(X11)
| X10 != f(X11)
| big_p(X10)
| ~ big_p(X12)
| big_p(f(X12)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1])])])])]) ).
cnf(i_0_3,negated_conjecture,
( big_p(X2)
| big_p(f(X3))
| ~ big_p(X1)
| X2 != f(X1)
| ~ big_p(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_4,negated_conjecture,
( ~ big_p(f(esk3_0))
| ~ big_p(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_5,negated_conjecture,
( big_p(esk2_0)
| ~ big_p(f(esk3_0)) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_6,negated_conjecture,
( esk1_0 = f(esk2_0)
| ~ big_p(f(esk3_0)) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_7,negated_conjecture,
( big_p(esk3_0)
| ~ big_p(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_8,negated_conjecture,
( big_p(esk3_0)
| big_p(esk2_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_9,negated_conjecture,
( big_p(esk3_0)
| esk1_0 = f(esk2_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_10,axiom,
X1 = X1 ).
cnf(i_0_11,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_12,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_13,axiom,
( X1 != X2
| f(X1) = f(X2) ) ).
cnf(i_0_14,axiom,
( X1 != X2
| ~ big_p(X1)
| big_p(X2) ) ).
cnf(i_0_10_001,axiom,
X1 = X1 ).
cnf(i_0_11_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_12_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_13_004,axiom,
( X1 != X2
| f(X1) = f(X2) ) ).
cnf(i_0_14_005,axiom,
( X1 != X2
| ~ big_p(X1)
| big_p(X2) ) ).
cnf(i_0_15,plain,
( ~ big_p(X1)
| big_p(f(X2))
| ~ big_p(X2)
| big_p(f(X1)) ),
inference(equality_inference,[],[3]) ).
cnf(i_0_16,plain,
( f(esk2_0) = esk1_0
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_11,i_0_6]) ).
cnf(i_0_17,plain,
( f(esk1_0) = f(f(esk2_0))
| big_p(esk3_0) ),
inference(scs_inference,[],[i_0_13,i_0_9]) ).
cnf(i_0_18,plain,
( big_p(f(esk3_0))
| ~ big_p(esk1_0) ),
inference(scs_inference,[],[i_0_7,i_0_15]) ).
cnf(i_0_19,plain,
( big_p(f(esk3_0))
| big_p(esk2_0) ),
inference(scs_inference,[],[i_0_8,i_0_15]) ).
cnf(i_0_20,plain,
( ~ big_p(X1)
| X1 != esk1_0
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_4,i_0_14]) ).
cnf(i_0_21,plain,
( ~ big_p(esk1_0)
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[20]) ).
cnf(i_0_22,plain,
( big_p(f(esk2_0))
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_5,i_0_15]) ).
cnf(i_0_23,plain,
( f(esk2_0) = esk1_0
| ~ big_p(esk1_0) ),
inference(scs_inference,[],[i_0_18,i_0_16]) ).
cnf(i_0_24,plain,
( big_p(f(esk2_0))
| big_p(esk2_0) ),
inference(scs_inference,[],[i_0_19,i_0_22]) ).
cnf(i_0_25,plain,
( big_p(f(f(esk2_0)))
| big_p(esk2_0) ),
inference(scs_inference,[],[i_0_24,i_0_15]) ).
cnf(i_0_26,plain,
( esk1_0 = f(esk2_0)
| ~ big_p(esk1_0) ),
inference(scs_inference,[],[i_0_23,i_0_11]) ).
cnf(i_0_27,plain,
( big_p(X1)
| f(f(esk2_0)) != X1
| big_p(esk2_0) ),
inference(scs_inference,[],[i_0_25,i_0_14]) ).
cnf(i_0_28,plain,
( big_p(f(f(esk2_0)))
| big_p(esk2_0) ),
inference(equality_inference,[],[27]) ).
cnf(i_0_29,plain,
( f(esk1_0) = f(f(esk2_0))
| ~ big_p(esk1_0) ),
inference(scs_inference,[],[i_0_26,i_0_13]) ).
cnf(i_0_30,plain,
( f(f(esk2_0)) = f(esk1_0)
| big_p(esk3_0) ),
inference(scs_inference,[],[i_0_17,i_0_11]) ).
cnf(i_0_31,plain,
( f(f(esk2_0)) = f(esk1_0)
| ~ big_p(esk1_0) ),
inference(scs_inference,[],[i_0_29,i_0_11]) ).
cnf(i_0_32,plain,
( f(f(f(esk2_0))) = f(f(esk1_0))
| big_p(esk3_0) ),
inference(scs_inference,[],[i_0_30,i_0_13]) ).
cnf(i_0_33,plain,
( f(f(f(esk2_0))) = f(f(esk1_0))
| ~ big_p(esk1_0) ),
inference(scs_inference,[],[i_0_31,i_0_13]) ).
cnf(i_0_34,plain,
( X1 = esk1_0
| X1 != f(esk2_0)
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_12,i_0_16]) ).
cnf(i_0_35,plain,
( f(esk2_0) = esk1_0
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[34]) ).
cnf(i_0_36,plain,
( X1 != X2
| f(X2) = f(X1) ),
inference(scs_inference,[],[i_0_11,i_0_13]) ).
cnf(i_0_37,plain,
f(X1) = f(X1),
inference(equality_inference,[],[36]) ).
cnf(i_0_38,plain,
( f(esk2_0) = esk1_0
| big_p(esk3_0) ),
inference(scs_inference,[],[i_0_11,i_0_9]) ).
cnf(i_0_39,plain,
( big_p(esk1_0)
| ~ big_p(f(esk2_0))
| big_p(esk3_0) ),
inference(scs_inference,[],[i_0_38,i_0_14]) ).
cnf(i_0_40,plain,
( big_p(esk1_0)
| big_p(esk3_0)
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_39,i_0_22]) ).
cnf(i_0_41,plain,
( big_p(f(esk1_0))
| big_p(esk3_0)
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_40,i_0_15]) ).
cnf(i_0_42,plain,
( f(esk1_0) != esk1_0
| big_p(esk3_0)
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_41,i_0_20]) ).
cnf(i_0_43,plain,
( esk1_0 != f(esk1_0)
| big_p(esk3_0)
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_42,i_0_11]) ).
cnf(i_0_44,plain,
( X1 != X2
| X1 != X3
| X2 = X3 ),
inference(scs_inference,[],[i_0_11,i_0_12]) ).
cnf(i_0_45,plain,
( X1 != X2
| X1 != X3
| f(X2) = f(X3) ),
inference(scs_inference,[],[i_0_44,i_0_13]) ).
cnf(i_0_46,plain,
( f(f(X1)) = f(f(X2))
| X3 != X2
| X3 != X1 ),
inference(scs_inference,[],[i_0_45,i_0_36]) ).
cnf(i_0_47,plain,
( X1 != X2
| X2 = X3
| X3 != X1 ),
inference(scs_inference,[],[i_0_11,i_0_12]) ).
cnf(i_0_48,plain,
( f(esk2_0) != X1
| X1 = esk1_0
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_47,i_0_6]) ).
cnf(i_0_49,plain,
( f(esk2_0) = esk1_0
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[48]) ).
cnf(i_0_50,plain,
( X1 != X2
| big_p(X1)
| ~ big_p(X2) ),
inference(scs_inference,[],[i_0_11,i_0_14]) ).
cnf(i_0_51,plain,
( big_p(X1)
| ~ big_p(X1) ),
inference(equality_inference,[],[50]) ).
cnf(i_0_52,plain,
( esk1_0 = X1
| X1 != f(esk2_0)
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_11,i_0_34]) ).
cnf(i_0_53,plain,
( esk1_0 = f(esk2_0)
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[52]) ).
cnf(i_0_54,plain,
( X1 != X2
| X3 = X1
| X3 != X2 ),
inference(scs_inference,[],[i_0_11,i_0_12]) ).
cnf(i_0_55,plain,
( esk1_0 = X1
| f(esk2_0) != X1
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_11,i_0_48]) ).
cnf(i_0_56,plain,
( esk1_0 = f(esk2_0)
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[55]) ).
cnf(i_0_57,plain,
( esk1_0 != X1
| ~ big_p(X1)
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_11,i_0_20]) ).
cnf(i_0_58,plain,
( ~ big_p(esk1_0)
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[57]) ).
cnf(i_0_59,plain,
( X1 != f(f(esk2_0))
| big_p(X1)
| big_p(esk2_0) ),
inference(scs_inference,[],[i_0_11,i_0_27]) ).
cnf(i_0_60,plain,
( big_p(f(f(esk2_0)))
| big_p(esk2_0) ),
inference(equality_inference,[],[59]) ).
cnf(i_0_61,plain,
( X1 != X2
| f(X1) = f(X3)
| X2 != X3 ),
inference(scs_inference,[],[i_0_11,i_0_45]) ).
cnf(i_0_62,plain,
( X1 != f(esk2_0)
| f(X1) = f(esk1_0)
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_61,i_0_16]) ).
cnf(i_0_63,plain,
( f(f(esk2_0)) = f(esk1_0)
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[62]) ).
cnf(i_0_64,plain,
( f(f(f(esk2_0))) = f(f(esk1_0))
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_63,i_0_13]) ).
cnf(i_0_65,plain,
( f(esk1_0) = f(f(esk2_0))
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_11,i_0_63]) ).
cnf(i_0_66,plain,
( f(f(esk1_0)) = f(f(f(esk2_0)))
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_65,i_0_13]) ).
cnf(i_0_67,plain,
( X1 != X2
| f(X2) = f(X3)
| X3 != X1 ),
inference(scs_inference,[],[i_0_11,i_0_61]) ).
cnf(i_0_68,plain,
( esk1_0 != X1
| f(X1) = f(f(esk2_0))
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_67,i_0_16]) ).
cnf(i_0_69,plain,
( f(esk1_0) = f(f(esk2_0))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[68]) ).
cnf(i_0_70,plain,
( f(esk1_0) = f(X1)
| X1 != f(esk2_0)
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_11,i_0_62]) ).
cnf(i_0_71,plain,
( f(esk1_0) = f(f(esk2_0))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[70]) ).
cnf(i_0_72,plain,
( X1 != esk1_0
| f(X1) = f(f(esk2_0))
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_11,i_0_68]) ).
cnf(i_0_73,plain,
( f(esk1_0) = f(f(esk2_0))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[72]) ).
cnf(i_0_74,plain,
( f(f(esk2_0)) = f(X1)
| X1 != esk1_0
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_11,i_0_72]) ).
cnf(i_0_75,plain,
( f(f(esk2_0)) = f(esk1_0)
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[74]) ).
cnf(i_0_76,plain,
( f(esk2_0) != X1
| f(esk1_0) = f(X1)
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_11,i_0_70]) ).
cnf(i_0_77,plain,
( f(esk1_0) = f(f(esk2_0))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[76]) ).
cnf(i_0_78,plain,
( f(X1) = f(esk1_0)
| f(esk2_0) != X1
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_11,i_0_76]) ).
cnf(i_0_79,plain,
( f(f(esk2_0)) = f(esk1_0)
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[78]) ).
cnf(i_0_80,plain,
( esk1_0 != X1
| f(f(esk2_0)) = f(X1)
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_11,i_0_74]) ).
cnf(i_0_81,plain,
( f(f(esk2_0)) = f(esk1_0)
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[80]) ).
cnf(i_0_82,plain,
( X1 != X2
| X3 != X2
| f(X3) = f(X1) ),
inference(scs_inference,[],[i_0_11,i_0_61]) ).
cnf(i_0_83,plain,
( X1 != X2
| X3 != X2
| f(f(X3)) = f(f(X1)) ),
inference(scs_inference,[],[i_0_82,i_0_13]) ).
cnf(i_0_84,plain,
( f(f(X1)) = f(f(X2))
| X2 != X1 ),
inference(scs_inference,[],[i_0_13,i_0_36]) ).
cnf(i_0_85,plain,
f(f(X1)) = f(f(X1)),
inference(equality_inference,[],[84]) ).
cnf(i_0_86,plain,
( X1 != X2
| X3 != X1
| f(f(X3)) = f(f(X2)) ),
inference(scs_inference,[],[i_0_13,i_0_61]) ).
cnf(i_0_87,plain,
( big_p(f(X1))
| ~ big_p(f(X2))
| X2 != X1 ),
inference(scs_inference,[],[i_0_13,i_0_14]) ).
cnf(i_0_88,plain,
( big_p(f(f(esk2_0)))
| ~ big_p(f(esk1_0))
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_87,i_0_6]) ).
cnf(i_0_89,plain,
( big_p(f(f(f(esk2_0))))
| ~ big_p(f(esk1_0))
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_88,i_0_15]) ).
cnf(i_0_90,plain,
( X1 != f(esk2_0)
| f(f(X1)) = f(f(esk1_0))
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_62]) ).
cnf(i_0_91,plain,
( f(f(f(esk2_0))) = f(f(esk1_0))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[90]) ).
cnf(i_0_92,plain,
( esk2_0 != X1
| f(X1) = esk1_0
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_48]) ).
cnf(i_0_93,plain,
( f(esk2_0) = esk1_0
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[92]) ).
cnf(i_0_94,plain,
( X1 != X2
| X2 != X3
| f(f(X3)) = f(f(X1)) ),
inference(scs_inference,[],[i_0_13,i_0_67]) ).
cnf(i_0_95,plain,
( esk2_0 != X1
| esk1_0 = f(X1)
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_55]) ).
cnf(i_0_96,plain,
( esk1_0 = f(esk2_0)
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[95]) ).
cnf(i_0_97,plain,
( f(f(X1)) = f(f(f(esk2_0)))
| esk1_0 != X1
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_68]) ).
cnf(i_0_98,plain,
( f(f(esk1_0)) = f(f(f(esk2_0)))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[97]) ).
cnf(i_0_99,plain,
( big_p(f(X1))
| X1 != f(esk2_0)
| big_p(esk2_0) ),
inference(scs_inference,[],[i_0_13,i_0_59]) ).
cnf(i_0_100,plain,
( big_p(f(f(esk2_0)))
| big_p(esk2_0) ),
inference(equality_inference,[],[99]) ).
cnf(i_0_101,plain,
( X1 != f(esk2_0)
| f(f(esk1_0)) = f(f(X1))
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_70]) ).
cnf(i_0_102,plain,
( f(f(esk1_0)) = f(f(f(esk2_0)))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[101]) ).
cnf(i_0_103,plain,
( X1 != esk2_0
| f(f(X1)) = f(esk1_0)
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_62]) ).
cnf(i_0_104,plain,
( f(f(esk2_0)) = f(esk1_0)
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[103]) ).
cnf(i_0_105,plain,
( f(f(X1)) = f(f(f(esk2_0)))
| X1 != esk1_0
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_72]) ).
cnf(i_0_106,plain,
( f(f(esk1_0)) = f(f(f(esk2_0)))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[105]) ).
cnf(i_0_107,plain,
( esk2_0 != X1
| f(esk1_0) = f(f(X1))
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_76]) ).
cnf(i_0_108,plain,
( f(esk1_0) = f(f(esk2_0))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[107]) ).
cnf(i_0_109,plain,
( f(f(f(esk2_0))) = f(f(X1))
| X1 != esk1_0
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_74]) ).
cnf(i_0_110,plain,
( f(f(f(esk2_0))) = f(f(esk1_0))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[109]) ).
cnf(i_0_111,plain,
( esk2_0 != X1
| f(f(X1)) = f(esk1_0)
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_78]) ).
cnf(i_0_112,plain,
( f(f(esk2_0)) = f(esk1_0)
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[111]) ).
cnf(i_0_113,plain,
( f(f(f(esk2_0))) = f(f(X1))
| esk1_0 != X1
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_80]) ).
cnf(i_0_114,plain,
( f(f(f(esk2_0))) = f(f(esk1_0))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[113]) ).
cnf(i_0_115,plain,
( X1 != esk2_0
| f(esk1_0) = f(f(X1))
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_70]) ).
cnf(i_0_116,plain,
( f(esk1_0) = f(f(esk2_0))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[115]) ).
cnf(i_0_117,plain,
( f(f(f(X1))) = f(f(esk1_0))
| X1 != esk2_0
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_103]) ).
cnf(i_0_118,plain,
( f(f(f(esk2_0))) = f(f(esk1_0))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[117]) ).
cnf(i_0_119,plain,
( f(f(esk1_0)) = f(f(f(X1)))
| esk2_0 != X1
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_107]) ).
cnf(i_0_120,plain,
( f(f(esk1_0)) = f(f(f(esk2_0)))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[119]) ).
cnf(i_0_121,plain,
( f(f(f(X1))) = f(f(esk1_0))
| esk2_0 != X1
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_111]) ).
cnf(i_0_122,plain,
( f(f(f(esk2_0))) = f(f(esk1_0))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[121]) ).
cnf(i_0_123,plain,
( f(f(esk1_0)) = f(f(f(X1)))
| X1 != esk2_0
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_115]) ).
cnf(i_0_124,plain,
( f(f(esk1_0)) = f(f(f(esk2_0)))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[123]) ).
cnf(i_0_125,plain,
( f(esk2_0) != X1
| f(f(esk1_0)) = f(f(X1))
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_76]) ).
cnf(i_0_126,plain,
( f(f(esk1_0)) = f(f(f(esk2_0)))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[125]) ).
cnf(i_0_127,plain,
( f(esk2_0) != X1
| f(f(X1)) = f(f(esk1_0))
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_13,i_0_78]) ).
cnf(i_0_128,plain,
( f(f(f(esk2_0))) = f(f(esk1_0))
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[127]) ).
cnf(i_0_129,plain,
( ~ big_p(X1)
| X1 != esk1_0
| big_p(esk3_0) ),
inference(scs_inference,[],[i_0_7,i_0_14]) ).
cnf(i_0_130,plain,
( ~ big_p(esk1_0)
| big_p(esk3_0) ),
inference(equality_inference,[],[129]) ).
cnf(i_0_131,plain,
( ~ big_p(f(esk2_0))
| big_p(esk3_0) ),
inference(scs_inference,[],[i_0_7,i_0_39]) ).
cnf(i_0_132,plain,
( big_p(esk3_0)
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_131,i_0_22]) ).
cnf(i_0_133,plain,
( big_p(X1)
| esk3_0 != X1
| ~ big_p(f(esk3_0)) ),
inference(scs_inference,[],[i_0_132,i_0_14]) ).
cnf(i_0_134,plain,
( big_p(esk3_0)
| ~ big_p(f(esk3_0)) ),
inference(equality_inference,[],[133]) ).
cnf(i_0_135,plain,
( big_p(X1)
| esk3_0 != X1
| ~ big_p(esk1_0) ),
inference(scs_inference,[],[i_0_7,i_0_14]) ).
cnf(i_0_136,plain,
( big_p(esk3_0)
| ~ big_p(esk1_0) ),
inference(equality_inference,[],[135]) ).
cnf(i_0_137,plain,
( ~ big_p(X1)
| esk1_0 != X1
| big_p(esk3_0) ),
inference(scs_inference,[],[i_0_7,i_0_50]) ).
cnf(i_0_138,plain,
( ~ big_p(esk1_0)
| big_p(esk3_0) ),
inference(equality_inference,[],[137]) ).
cnf(i_0_139,plain,
( big_p(X1)
| X1 != esk3_0
| ~ big_p(esk1_0) ),
inference(scs_inference,[],[i_0_7,i_0_50]) ).
cnf(i_0_140,plain,
( big_p(esk3_0)
| ~ big_p(esk1_0) ),
inference(equality_inference,[],[139]) ).
cnf(i_0_141,plain,
( big_p(f(esk2_0))
| big_p(esk3_0) ),
inference(scs_inference,[],[i_0_8,i_0_15]) ).
cnf(i_0_142,plain,
big_p(esk3_0),
inference(scs_inference,[],[i_0_141,i_0_131]) ).
cnf(i_0_143,plain,
big_p(f(esk3_0)),
inference(scs_inference,[],[i_0_142,i_0_15]) ).
cnf(i_0_144,plain,
( ~ big_p(X1)
| ~ big_p(X2)
| big_p(f(X2))
| big_p(f(X1)) ),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_145,plain,
~ big_p(esk1_0),
inference(scs_inference,[],[i_0_142,i_0_15,i_0_4]) ).
cnf(i_0_146,plain,
big_p(esk2_0),
inference(scs_inference,[],[i_0_142,i_0_15,i_0_4,i_0_5]) ).
cnf(i_0_147,plain,
esk1_0 = f(esk2_0),
inference(scs_inference,[],[i_0_142,i_0_15,i_0_4,i_0_5,i_0_6]) ).
cnf(i_0_148,plain,
big_p(f(esk2_0)),
inference(scs_inference,[],[i_0_142,i_0_15,i_0_4,i_0_5,i_0_6,i_0_22]) ).
cnf(i_0_149,plain,
f(f(esk2_0)) = f(esk1_0),
inference(scs_inference,[],[i_0_142,i_0_15,i_0_4,i_0_5,i_0_6,i_0_22,i_0_36]) ).
cnf(i_0_150,plain,
f(esk2_0) = esk1_0,
inference(scs_inference,[],[i_0_142,i_0_15,i_0_4,i_0_5,i_0_6,i_0_22,i_0_36,i_0_16]) ).
cnf(i_0_151,plain,
f(esk1_0) = f(f(esk2_0)),
inference(scs_inference,[],[i_0_142,i_0_15,i_0_4,i_0_5,i_0_6,i_0_22,i_0_36,i_0_16,i_0_65]) ).
cnf(i_0_152,plain,
$false,
inference(scs_inference,[],[i_0_142,i_0_15,i_0_4,i_0_5,i_0_6,i_0_22,i_0_36,i_0_16,i_0_65,i_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN078+1 : TPTP v9.2.1. Released v2.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n022.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 08:11:36 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.62/1.62 % Version : CSE_E---1.7
% 0.62/1.62 % Problem : theBenchmark.p
% 0.62/1.62 % SZS status Theorem for theBenchmark.p
% 0.62/1.62 % SZS output start CNFRefutation
% See solution above
% 0.73/1.77 % Total time : 1.270s
%------------------------------------------------------------------------------