%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SET768+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 02:18:09 PM UTC 2026
% Result : Theorem 180.35s 26.53s
% Output : CNFRefutation 180.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 10 unt; 0 def)
% Number of atoms : 395 ( 0 equ)
% Maximal formula atoms : 207 ( 6 avg)
% Number of connectives : 468 ( 130 ~; 238 |; 79 &)
% ( 8 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 65 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 165 ( 9 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIII04,conjecture,
! [X4,X7,X1,X2] :
( ( member(X2,X4)
& member(X1,X4)
& equivalence(X7,X4) )
=> ( equal_set(equivalence_class(X1,X4,X7),equivalence_class(X2,X4,X7))
<=> apply(X7,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII04) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(equivalence_class,axiom,
! [X7,X4,X1,X3] :
( member(X3,equivalence_class(X1,X4,X7))
<=> ( apply(X7,X1,X3)
& member(X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',equivalence_class) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X2,X1)
& subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(equivalence,axiom,
! [X1,X7] :
( equivalence(X7,X1)
<=> ( ! [X3,X5,X6] :
( ( member(X6,X1)
& member(X5,X1)
& member(X3,X1) )
=> ( ( apply(X7,X5,X6)
& apply(X7,X3,X5) )
=> apply(X7,X3,X6) ) )
& ! [X3,X5] :
( ( member(X5,X1)
& member(X3,X1) )
=> ( apply(X7,X3,X5)
=> apply(X7,X5,X3) ) )
& ! [X3] :
( member(X3,X1)
=> apply(X7,X3,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',equivalence) ).
fof(c_0_5,negated_conjecture,
~ ! [X4,X7,X1,X2] :
( ( member(X2,X4)
& member(X1,X4)
& equivalence(X7,X4) )
=> ( equal_set(equivalence_class(X1,X4,X7),equivalence_class(X2,X4,X7))
<=> apply(X7,X1,X2) ) ),
inference(assume_negation,[status(cth)],[thIII04]) ).
fof(c_0_6,plain,
! [X20,X21,X22,X23,X24] :
( ( subset(X23,X24)
| ~ member(esk5_2(X23,X24),X24) )
& ( subset(X23,X24)
| member(esk5_2(X23,X24),X23) )
& ( member(X22,X21)
| ~ member(X22,X20)
| ~ subset(X20,X21) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[subset])])])])])])]) ).
fof(c_0_7,plain,
! [X14,X15,X16,X17] :
( ( member(X17,equivalence_class(X16,X15,X14))
| ~ apply(X14,X16,X17)
| ~ member(X17,X15) )
& ( ~ member(X17,equivalence_class(X16,X15,X14))
| apply(X14,X16,X17) )
& ( ~ member(X17,equivalence_class(X16,X15,X14))
| member(X17,X15) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_class])])])]) ).
fof(c_0_8,plain,
! [X12,X13] :
( ( equal_set(X12,X13)
| ~ subset(X13,X12)
| ~ subset(X12,X13) )
& ( ~ equal_set(X12,X13)
| subset(X13,X12) )
& ( ~ equal_set(X12,X13)
| subset(X12,X13) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])]) ).
fof(c_0_9,negated_conjecture,
( ( apply(esk2_0,esk3_0,esk4_0)
| equal_set(equivalence_class(esk3_0,esk1_0,esk2_0),equivalence_class(esk4_0,esk1_0,esk2_0)) )
& ( ~ apply(esk2_0,esk3_0,esk4_0)
| ~ equal_set(equivalence_class(esk3_0,esk1_0,esk2_0),equivalence_class(esk4_0,esk1_0,esk2_0)) )
& member(esk4_0,esk1_0)
& member(esk3_0,esk1_0)
& equivalence(esk2_0,esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_10,plain,
! [X1,X7] :
( epred1_2(X7,X1)
<=> ( ! [X3,X5,X6] :
( ( member(X6,X1)
& member(X5,X1)
& member(X3,X1) )
=> ( ( apply(X7,X5,X6)
& apply(X7,X3,X5) )
=> apply(X7,X3,X6) ) )
& ! [X3,X5] :
( ( member(X5,X1)
& member(X3,X1) )
=> ( apply(X7,X3,X5)
=> apply(X7,X5,X3) ) )
& ! [X3] :
( member(X3,X1)
=> apply(X7,X3,X3) ) ) ),
introduced(definition) ).
cnf(c_0_11,plain,
( ~ member(esk5_2(X1,X2),X2)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( ~ apply(X3,X4,X1)
| ~ member(X1,X2)
| member(X1,equivalence_class(X4,X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( ~ member(X3,equivalence_class(X2,X4,X1))
| apply(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( subset(X1,X2)
| member(esk5_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,plain,
( ~ member(X1,equivalence_class(X3,X2,X4))
| member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
( ~ equal_set(X2,X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
( apply(esk2_0,esk3_0,esk4_0)
| equal_set(equivalence_class(esk3_0,esk1_0,esk2_0),equivalence_class(esk4_0,esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_18,axiom,
! [X1,X7] :
( equivalence(X7,X1)
<=> epred1_2(X7,X1) ),
inference(apply_def,[status(thm)],[equivalence,c_0_10]) ).
cnf(c_0_19,plain,
( ~ member(esk5_2(X1,equivalence_class(X2,X3,X4)),X3)
| ~ apply(X4,X2,esk5_2(X1,equivalence_class(X2,X3,X4)))
| subset(X1,equivalence_class(X2,X3,X4)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_20,plain,
( subset(equivalence_class(X2,X3,X1),X4)
| apply(X1,X2,esk5_2(equivalence_class(X2,X3,X1),X4)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_21,plain,
( subset(equivalence_class(X1,X2,X3),X4)
| member(esk5_2(equivalence_class(X1,X2,X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_22,plain,
( ~ member(X3,X1)
| ~ subset(X1,X2)
| member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_23,negated_conjecture,
( subset(equivalence_class(esk4_0,esk1_0,esk2_0),equivalence_class(esk3_0,esk1_0,esk2_0))
| apply(esk2_0,esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_24,plain,
! [X18,X19] :
( ( equivalence(X19,X18)
| ~ epred1_2(X19,X18) )
& ( epred1_2(X19,X18)
| ~ equivalence(X19,X18) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
cnf(c_0_25,plain,
( ~ member(esk5_2(equivalence_class(X1,X2,X3),equivalence_class(X1,X4,X3)),X4)
| subset(equivalence_class(X1,X2,X3),equivalence_class(X1,X4,X3)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
( subset(equivalence_class(X1,equivalence_class(X2,X3,X4),X5),X6)
| member(esk5_2(equivalence_class(X1,equivalence_class(X2,X3,X4),X5),X6),X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
( ~ member(X1,equivalence_class(esk4_0,esk1_0,esk2_0))
| member(X1,equivalence_class(esk3_0,esk1_0,esk2_0))
| apply(esk2_0,esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_28,plain,
! [X26,X27,X28,X29,X30,X31,X32,X33,X34,X35] :
( ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| ~ apply(X35,esk8_2(X34,X35),esk7_2(X34,X35))
| ~ apply(X35,esk9_2(X34,X35),esk11_2(X34,X35)) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| ~ apply(X35,esk8_2(X34,X35),esk7_2(X34,X35))
| apply(X35,esk10_2(X34,X35),esk11_2(X34,X35)) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| ~ apply(X35,esk8_2(X34,X35),esk7_2(X34,X35))
| apply(X35,esk9_2(X34,X35),esk10_2(X34,X35)) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| ~ apply(X35,esk8_2(X34,X35),esk7_2(X34,X35))
| member(esk11_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| ~ apply(X35,esk8_2(X34,X35),esk7_2(X34,X35))
| member(esk10_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| ~ apply(X35,esk8_2(X34,X35),esk7_2(X34,X35))
| member(esk9_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| apply(X35,esk7_2(X34,X35),esk8_2(X34,X35))
| ~ apply(X35,esk9_2(X34,X35),esk11_2(X34,X35)) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| apply(X35,esk7_2(X34,X35),esk8_2(X34,X35))
| apply(X35,esk10_2(X34,X35),esk11_2(X34,X35)) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| apply(X35,esk7_2(X34,X35),esk8_2(X34,X35))
| apply(X35,esk9_2(X34,X35),esk10_2(X34,X35)) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| apply(X35,esk7_2(X34,X35),esk8_2(X34,X35))
| member(esk11_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| apply(X35,esk7_2(X34,X35),esk8_2(X34,X35))
| member(esk10_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| apply(X35,esk7_2(X34,X35),esk8_2(X34,X35))
| member(esk9_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| member(esk8_2(X34,X35),X34)
| ~ apply(X35,esk9_2(X34,X35),esk11_2(X34,X35)) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| member(esk8_2(X34,X35),X34)
| apply(X35,esk10_2(X34,X35),esk11_2(X34,X35)) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| member(esk8_2(X34,X35),X34)
| apply(X35,esk9_2(X34,X35),esk10_2(X34,X35)) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| member(esk8_2(X34,X35),X34)
| member(esk11_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| member(esk8_2(X34,X35),X34)
| member(esk10_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| member(esk8_2(X34,X35),X34)
| member(esk9_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| member(esk7_2(X34,X35),X34)
| ~ apply(X35,esk9_2(X34,X35),esk11_2(X34,X35)) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| member(esk7_2(X34,X35),X34)
| apply(X35,esk10_2(X34,X35),esk11_2(X34,X35)) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| member(esk7_2(X34,X35),X34)
| apply(X35,esk9_2(X34,X35),esk10_2(X34,X35)) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| member(esk7_2(X34,X35),X34)
| member(esk11_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| member(esk7_2(X34,X35),X34)
| member(esk10_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| ~ apply(X35,esk6_2(X34,X35),esk6_2(X34,X35))
| member(esk7_2(X34,X35),X34)
| member(esk9_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| ~ apply(X35,esk8_2(X34,X35),esk7_2(X34,X35))
| ~ apply(X35,esk9_2(X34,X35),esk11_2(X34,X35)) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| ~ apply(X35,esk8_2(X34,X35),esk7_2(X34,X35))
| apply(X35,esk10_2(X34,X35),esk11_2(X34,X35)) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| ~ apply(X35,esk8_2(X34,X35),esk7_2(X34,X35))
| apply(X35,esk9_2(X34,X35),esk10_2(X34,X35)) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| ~ apply(X35,esk8_2(X34,X35),esk7_2(X34,X35))
| member(esk11_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| ~ apply(X35,esk8_2(X34,X35),esk7_2(X34,X35))
| member(esk10_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| ~ apply(X35,esk8_2(X34,X35),esk7_2(X34,X35))
| member(esk9_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| apply(X35,esk7_2(X34,X35),esk8_2(X34,X35))
| ~ apply(X35,esk9_2(X34,X35),esk11_2(X34,X35)) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| apply(X35,esk7_2(X34,X35),esk8_2(X34,X35))
| apply(X35,esk10_2(X34,X35),esk11_2(X34,X35)) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| apply(X35,esk7_2(X34,X35),esk8_2(X34,X35))
| apply(X35,esk9_2(X34,X35),esk10_2(X34,X35)) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| apply(X35,esk7_2(X34,X35),esk8_2(X34,X35))
| member(esk11_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| apply(X35,esk7_2(X34,X35),esk8_2(X34,X35))
| member(esk10_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| apply(X35,esk7_2(X34,X35),esk8_2(X34,X35))
| member(esk9_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| member(esk8_2(X34,X35),X34)
| ~ apply(X35,esk9_2(X34,X35),esk11_2(X34,X35)) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| member(esk8_2(X34,X35),X34)
| apply(X35,esk10_2(X34,X35),esk11_2(X34,X35)) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| member(esk8_2(X34,X35),X34)
| apply(X35,esk9_2(X34,X35),esk10_2(X34,X35)) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| member(esk8_2(X34,X35),X34)
| member(esk11_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| member(esk8_2(X34,X35),X34)
| member(esk10_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| member(esk8_2(X34,X35),X34)
| member(esk9_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| member(esk7_2(X34,X35),X34)
| ~ apply(X35,esk9_2(X34,X35),esk11_2(X34,X35)) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| member(esk7_2(X34,X35),X34)
| apply(X35,esk10_2(X34,X35),esk11_2(X34,X35)) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| member(esk7_2(X34,X35),X34)
| apply(X35,esk9_2(X34,X35),esk10_2(X34,X35)) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| member(esk7_2(X34,X35),X34)
| member(esk11_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| member(esk7_2(X34,X35),X34)
| member(esk10_2(X34,X35),X34) )
& ( epred1_2(X35,X34)
| member(esk6_2(X34,X35),X34)
| member(esk7_2(X34,X35),X34)
| member(esk9_2(X34,X35),X34) )
& ( ~ epred1_2(X27,X26)
| apply(X27,X31,X33)
| ~ apply(X27,X32,X33)
| ~ apply(X27,X31,X32)
| ~ member(X33,X26)
| ~ member(X32,X26)
| ~ member(X31,X26) )
& ( ~ epred1_2(X27,X26)
| apply(X27,X30,X29)
| ~ apply(X27,X29,X30)
| ~ member(X30,X26)
| ~ member(X29,X26) )
& ( ~ epred1_2(X27,X26)
| apply(X27,X28,X28)
| ~ member(X28,X26) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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)],[c_0_10])])])])])])]) ).
cnf(c_0_29,plain,
( ~ equivalence(X1,X2)
| epred1_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,negated_conjecture,
equivalence(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_31,plain,
subset(equivalence_class(X1,equivalence_class(X2,X3,X4),X5),equivalence_class(X1,X3,X5)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( ~ member(X1,equivalence_class(esk4_0,esk1_0,esk2_0))
| apply(esk2_0,esk3_0,X1)
| apply(esk2_0,esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_27]) ).
cnf(c_0_33,plain,
( ~ epred1_2(X3,X2)
| ~ member(X1,X2)
| apply(X3,X1,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,negated_conjecture,
epred1_2(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( ~ member(X1,equivalence_class(X2,equivalence_class(X5,X3,X6),X4))
| member(X1,equivalence_class(X2,X3,X4)) ),
inference(spm,[status(thm)],[c_0_22,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( ~ member(X1,esk1_0)
| ~ apply(esk2_0,esk4_0,X1)
| apply(esk2_0,esk3_0,X1)
| apply(esk2_0,esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_12]) ).
cnf(c_0_37,negated_conjecture,
( ~ member(X1,esk1_0)
| apply(esk2_0,X1,X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
member(esk4_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_39,plain,
( ~ member(X1,equivalence_class(X5,X3,X6))
| ~ apply(X4,X2,X1)
| member(X1,equivalence_class(X2,X3,X4)) ),
inference(spm,[status(thm)],[c_0_35,c_0_12]) ).
cnf(c_0_40,plain,
( ~ epred1_2(X5,X2)
| ~ apply(X5,X3,X4)
| ~ apply(X5,X1,X3)
| ~ member(X4,X2)
| ~ member(X3,X2)
| ~ member(X1,X2)
| apply(X5,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_41,negated_conjecture,
( ~ apply(esk2_0,esk3_0,esk4_0)
| ~ equal_set(equivalence_class(esk3_0,esk1_0,esk2_0),equivalence_class(esk4_0,esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_42,negated_conjecture,
apply(esk2_0,esk3_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_43,plain,
( ~ apply(X6,X5,esk5_2(equivalence_class(X1,X2,X3),X4))
| subset(equivalence_class(X1,X2,X3),X4)
| member(esk5_2(equivalence_class(X1,X2,X3),X4),equivalence_class(X5,X2,X6)) ),
inference(spm,[status(thm)],[c_0_39,c_0_14]) ).
cnf(c_0_44,plain,
( ~ member(X2,X6)
| ~ member(X3,X6)
| ~ member(esk5_2(equivalence_class(X3,X4,X1),X5),X6)
| ~ apply(X1,X2,X3)
| ~ epred1_2(X1,X6)
| subset(equivalence_class(X3,X4,X1),X5)
| apply(X1,X2,esk5_2(equivalence_class(X3,X4,X1),X5)) ),
inference(spm,[status(thm)],[c_0_40,c_0_20]) ).
cnf(c_0_45,plain,
( ~ epred1_2(X4,X2)
| ~ apply(X4,X1,X3)
| ~ member(X3,X2)
| ~ member(X1,X2)
| apply(X4,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_46,negated_conjecture,
~ equal_set(equivalence_class(esk3_0,esk1_0,esk2_0),equivalence_class(esk4_0,esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42])]) ).
cnf(c_0_47,plain,
( ~ subset(X2,X1)
| ~ subset(X1,X2)
| equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_48,plain,
( ~ apply(X5,X4,esk5_2(equivalence_class(X1,X2,X3),equivalence_class(X4,X2,X5)))
| subset(equivalence_class(X1,X2,X3),equivalence_class(X4,X2,X5)) ),
inference(spm,[status(thm)],[c_0_11,c_0_43]) ).
cnf(c_0_49,plain,
( ~ member(X2,X4)
| ~ member(X3,X4)
| ~ apply(X1,X2,X3)
| ~ epred1_2(X1,X4)
| subset(equivalence_class(X3,X4,X1),X5)
| apply(X1,X2,esk5_2(equivalence_class(X3,X4,X1),X5)) ),
inference(spm,[status(thm)],[c_0_44,c_0_21]) ).
cnf(c_0_50,negated_conjecture,
( ~ member(esk3_0,X1)
| ~ member(esk4_0,X1)
| ~ epred1_2(esk2_0,X1)
| apply(esk2_0,esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_42]) ).
cnf(c_0_51,negated_conjecture,
member(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_52,negated_conjecture,
( ~ subset(equivalence_class(esk3_0,esk1_0,esk2_0),equivalence_class(esk4_0,esk1_0,esk2_0))
| ~ subset(equivalence_class(esk4_0,esk1_0,esk2_0),equivalence_class(esk3_0,esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,plain,
( ~ member(X4,X2)
| ~ member(X1,X2)
| ~ apply(X3,X4,X1)
| ~ epred1_2(X3,X2)
| subset(equivalence_class(X1,X2,X3),equivalence_class(X4,X2,X3)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,negated_conjecture,
apply(esk2_0,esk4_0,esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_34]),c_0_38]),c_0_51])]) ).
cnf(c_0_55,negated_conjecture,
~ subset(equivalence_class(esk4_0,esk1_0,esk2_0),equivalence_class(esk3_0,esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_34]),c_0_54]),c_0_51]),c_0_38])]) ).
cnf(c_0_56,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_53]),c_0_34]),c_0_42]),c_0_38]),c_0_51])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET768+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n017.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 05:32:11 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 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
% 180.35/26.53 % Version: 3.5.1
% 180.35/26.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 180.35/26.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 180.35/26.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 180.35/26.53 % Starting new_bool_3 with 300s (1) cores
% 180.35/26.53 % Starting new_bool_1 with 300s (1) cores
% 180.35/26.53 % Starting sh5l with 300s (1) cores
% 180.35/26.53 % new_bool_3 with pid 1533628 completed with status 0
% 180.35/26.53 % Result found by new_bool_3
% 180.35/26.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 180.35/26.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 180.35/26.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 180.35/26.53 % Starting new_bool_3 with 300s (1) cores
% 180.35/26.53 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 180.35/26.53 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 180.35/26.53 % Search class: FGHNF-FFMS32-SFFFFFNN
% 180.35/26.53 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 180.35/26.53 % Starting SubtermCWHack with 31s (1) cores
% 180.35/26.53 % SubtermCWHack with pid 1533631 completed with status 0
% 180.35/26.53 % Result found by SubtermCWHack
% 180.35/26.53 % Preprocessing class: FSMSSMSSSSSNFFN.
% 180.35/26.53 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 180.35/26.53 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 180.35/26.53 % Starting new_bool_3 with 300s (1) cores
% 180.35/26.53 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 180.35/26.53 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 180.35/26.53 % Search class: FGHNF-FFMS32-SFFFFFNN
% 180.35/26.53 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 180.35/26.53 % Starting SubtermCWHack with 31s (1) cores
% 180.35/26.53 % Preprocessing time : 0.002 s
% 180.35/26.53
% 180.35/26.53 % Proof found!
% 180.35/26.53 % SZS status Theorem
% 180.35/26.53 % SZS output start CNFRefutation
% See solution above
% 180.35/26.53 % Parsed axioms : 17
% 180.35/26.53 % Removed by relevancy pruning/SinE : 12
% 180.35/26.53 % Initial clauses : 67
% 180.35/26.53 % Removed in clause preprocessing : 0
% 180.35/26.53 % Initial clauses in saturation : 67
% 180.35/26.53 % Processed clauses : 67879
% 180.35/26.53 % ...of these trivial : 1521
% 180.35/26.53 % ...subsumed : 59851
% 180.35/26.53 % ...remaining for further processing : 6507
% 180.35/26.53 % Other redundant clauses eliminated : 0
% 180.35/26.53 % Clauses deleted for lack of memory : 0
% 180.35/26.53 % Backward-subsumed : 56
% 180.35/26.53 % Backward-rewritten : 37
% 180.35/26.53 % Generated clauses : 1020687
% 180.35/26.53 % ...of the previous two non-redundant : 971484
% 180.35/26.53 % ...aggressively subsumed : 0
% 180.35/26.53 % Contextual simplify-reflections : 28
% 180.35/26.53 % Paramodulations : 1020667
% 180.35/26.53 % Factorizations : 20
% 180.35/26.53 % NegExts : 0
% 180.35/26.53 % Equation resolutions : 0
% 180.35/26.53 % Disequality decompositions : 0
% 180.35/26.53 % Total rewrite steps : 33078
% 180.35/26.53 % ...of those cached : 32563
% 180.35/26.53 % Propositional unsat checks : 0
% 180.35/26.53 % Propositional check models : 0
% 180.35/26.53 % Propositional check unsatisfiable : 0
% 180.35/26.53 % Propositional clauses : 0
% 180.35/26.53 % Propositional clauses after purity: 0
% 180.35/26.53 % Propositional unsat core size : 0
% 180.35/26.53 % Propositional preprocessing time : 0.000
% 180.35/26.53 % Propositional encoding time : 0.000
% 180.35/26.53 % Propositional solver time : 0.000
% 180.35/26.53 % Success case prop preproc time : 0.000
% 180.35/26.53 % Success case prop encoding time : 0.000
% 180.35/26.53 % Success case prop solver time : 0.000
% 180.35/26.53 % Current number of processed clauses : 6414
% 180.35/26.53 % Positive orientable unit clauses : 511
% 180.35/26.53 % Positive unorientable unit clauses: 0
% 180.35/26.53 % Negative unit clauses : 2
% 180.35/26.53 % Non-unit-clauses : 5901
% 180.35/26.53 % Current number of unprocessed clauses: 901344
% 180.35/26.53 % ...number of literals in the above : 4993043
% 180.35/26.53 % Current number of archived formulas : 0
% 180.35/26.53 % Current number of archived clauses : 93
% 180.35/26.53 % Clause-clause subsumption calls (NU) : 8896286
% 180.35/26.53 % Rec. Clause-clause subsumption calls : 3632287
% 180.35/26.53 % Non-unit clause-clause subsumptions : 59894
% 180.35/26.53 % Unit Clause-clause subsumption calls : 185862
% 180.35/26.53 % Rewrite failures with RHS unbound : 0
% 180.35/26.53 % BW rewrite match attempts : 46657
% 180.35/26.53 % BW rewrite match successes : 29
% 180.35/26.53 % Condensation attempts : 0
% 180.35/26.53 % Condensation successes : 0
% 180.35/26.53 % Termbank termtop insertions : 42114632
% 180.35/26.53 % Search garbage collected termcells : 854
% 180.35/26.53
% 180.35/26.53 % -------------------------------------------------
% 180.35/26.53 % User time : 25.020 s
% 180.35/26.53 % System time : 0.555 s
% 180.35/26.53 % Total time : 25.576 s
% 180.35/26.53 % Maximum resident set size: 3664 pages
% 180.35/26.53
% 180.35/26.53 % -------------------------------------------------
% 180.35/26.53 % User time : 25.022 s
% 180.35/26.53 % System time : 0.566 s
% 180.35/26.53 % Total time : 25.588 s
% 180.35/26.53 % Maximum resident set size: 4864 pages
% 180.35/26.53 % E exiting
%------------------------------------------------------------------------------