TSTP Solution File: SET768+4 by E-SAT---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : SET768+4 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n015.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 21 02:59:28 EDT 2024
% Result : Theorem 129.44s 16.78s
% Output : CNFRefutation 129.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 9 unt; 0 def)
% Number of atoms : 397 ( 0 equ)
% Maximal formula atoms : 207 ( 6 avg)
% Number of connectives : 472 ( 132 ~; 240 |; 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(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))
<=> ( member(X3,X4)
& apply(X7,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',equivalence_class) ).
fof(thIII04,conjecture,
! [X4,X7,X1,X2] :
( ( equivalence(X7,X4)
& member(X1,X4)
& member(X2,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(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(equivalence,axiom,
! [X1,X7] :
( equivalence(X7,X1)
<=> ( ! [X3] :
( member(X3,X1)
=> apply(X7,X3,X3) )
& ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X1) )
=> ( apply(X7,X3,X5)
=> apply(X7,X5,X3) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X1)
& member(X6,X1) )
=> ( ( apply(X7,X3,X5)
& apply(X7,X5,X6) )
=> apply(X7,X3,X6) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',equivalence) ).
fof(c_0_5,plain,
! [X32,X33,X34,X35,X36] :
( ( ~ subset(X32,X33)
| ~ member(X34,X32)
| member(X34,X33) )
& ( member(esk9_2(X35,X36),X35)
| subset(X35,X36) )
& ( ~ member(esk9_2(X35,X36),X36)
| subset(X35,X36) ) ),
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_6,plain,
! [X14,X15,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)
| ~ apply(X14,X16,X17)
| member(X17,equivalence_class(X16,X15,X14)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_class])])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X4,X7,X1,X2] :
( ( equivalence(X7,X4)
& member(X1,X4)
& member(X2,X4) )
=> ( equal_set(equivalence_class(X1,X4,X7),equivalence_class(X2,X4,X7))
<=> apply(X7,X1,X2) ) ),
inference(assume_negation,[status(cth)],[thIII04]) ).
cnf(c_0_8,plain,
( subset(X1,X2)
| ~ member(esk9_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( member(X1,equivalence_class(X4,X2,X3))
| ~ member(X1,X2)
| ~ apply(X3,X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( apply(X1,X2,X3)
| ~ member(X3,equivalence_class(X2,X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( member(esk9_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,plain,
( member(X1,X2)
| ~ member(X1,equivalence_class(X3,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_13,plain,
! [X30,X31] :
( ( subset(X30,X31)
| ~ equal_set(X30,X31) )
& ( subset(X31,X30)
| ~ equal_set(X30,X31) )
& ( ~ subset(X30,X31)
| ~ subset(X31,X30)
| equal_set(X30,X31) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])])]) ).
fof(c_0_14,negated_conjecture,
( equivalence(esk2_0,esk1_0)
& member(esk3_0,esk1_0)
& member(esk4_0,esk1_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))
| apply(esk2_0,esk3_0,esk4_0) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_15,plain,
! [X1,X7] :
( epred1_2(X7,X1)
<=> ( ! [X3] :
( member(X3,X1)
=> apply(X7,X3,X3) )
& ! [X3,X5] :
( ( member(X3,X1)
& member(X5,X1) )
=> ( apply(X7,X3,X5)
=> apply(X7,X5,X3) ) )
& ! [X3,X5,X6] :
( ( member(X3,X1)
& member(X5,X1)
& member(X6,X1) )
=> ( ( apply(X7,X3,X5)
& apply(X7,X5,X6) )
=> apply(X7,X3,X6) ) ) ) ),
introduced(definition) ).
cnf(c_0_16,plain,
( subset(X1,equivalence_class(X2,X3,X4))
| ~ apply(X4,X2,esk9_2(X1,equivalence_class(X2,X3,X4)))
| ~ member(esk9_2(X1,equivalence_class(X2,X3,X4)),X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_17,plain,
( apply(X1,X2,esk9_2(equivalence_class(X2,X3,X1),X4))
| subset(equivalence_class(X2,X3,X1),X4) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_18,plain,
( member(esk9_2(equivalence_class(X1,X2,X3),X4),X2)
| subset(equivalence_class(X1,X2,X3),X4) ),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_19,plain,
( subset(X1,X2)
| ~ equal_set(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( 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) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,axiom,
! [X1,X7] :
( equivalence(X7,X1)
<=> epred1_2(X7,X1) ),
inference(apply_def,[status(thm)],[equivalence,c_0_15]) ).
cnf(c_0_22,plain,
( subset(equivalence_class(X1,X2,X3),equivalence_class(X1,X4,X3))
| ~ member(esk9_2(equivalence_class(X1,X2,X3),equivalence_class(X1,X4,X3)),X4) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( member(esk9_2(equivalence_class(X1,equivalence_class(X2,X3,X4),X5),X6),X3)
| subset(equivalence_class(X1,equivalence_class(X2,X3,X4),X5),X6) ),
inference(spm,[status(thm)],[c_0_12,c_0_18]) ).
cnf(c_0_24,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_25,negated_conjecture,
( apply(esk2_0,esk3_0,esk4_0)
| subset(equivalence_class(esk4_0,esk1_0,esk2_0),equivalence_class(esk3_0,esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_26,plain,
! [X12,X13] :
( ( ~ equivalence(X13,X12)
| epred1_2(X13,X12) )
& ( ~ epred1_2(X13,X12)
| equivalence(X13,X12) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
cnf(c_0_27,plain,
subset(equivalence_class(X1,equivalence_class(X2,X3,X4),X5),equivalence_class(X1,X3,X5)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( apply(esk2_0,esk3_0,esk4_0)
| member(X1,equivalence_class(esk3_0,esk1_0,esk2_0))
| ~ member(X1,equivalence_class(esk4_0,esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_29,plain,
! [X56,X57,X58,X59,X60,X61,X62,X63,X64,X65] :
( ( ~ member(X58,X56)
| apply(X57,X58,X58)
| ~ epred1_2(X57,X56) )
& ( ~ member(X59,X56)
| ~ member(X60,X56)
| ~ apply(X57,X59,X60)
| apply(X57,X60,X59)
| ~ epred1_2(X57,X56) )
& ( ~ member(X61,X56)
| ~ member(X62,X56)
| ~ member(X63,X56)
| ~ apply(X57,X61,X62)
| ~ apply(X57,X62,X63)
| apply(X57,X61,X63)
| ~ epred1_2(X57,X56) )
& ( member(esk19_2(X64,X65),X64)
| member(esk17_2(X64,X65),X64)
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( member(esk20_2(X64,X65),X64)
| member(esk17_2(X64,X65),X64)
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( member(esk21_2(X64,X65),X64)
| member(esk17_2(X64,X65),X64)
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( apply(X65,esk19_2(X64,X65),esk20_2(X64,X65))
| member(esk17_2(X64,X65),X64)
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( apply(X65,esk20_2(X64,X65),esk21_2(X64,X65))
| member(esk17_2(X64,X65),X64)
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( ~ apply(X65,esk19_2(X64,X65),esk21_2(X64,X65))
| member(esk17_2(X64,X65),X64)
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( member(esk19_2(X64,X65),X64)
| member(esk18_2(X64,X65),X64)
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( member(esk20_2(X64,X65),X64)
| member(esk18_2(X64,X65),X64)
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( member(esk21_2(X64,X65),X64)
| member(esk18_2(X64,X65),X64)
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( apply(X65,esk19_2(X64,X65),esk20_2(X64,X65))
| member(esk18_2(X64,X65),X64)
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( apply(X65,esk20_2(X64,X65),esk21_2(X64,X65))
| member(esk18_2(X64,X65),X64)
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( ~ apply(X65,esk19_2(X64,X65),esk21_2(X64,X65))
| member(esk18_2(X64,X65),X64)
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( member(esk19_2(X64,X65),X64)
| apply(X65,esk17_2(X64,X65),esk18_2(X64,X65))
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( member(esk20_2(X64,X65),X64)
| apply(X65,esk17_2(X64,X65),esk18_2(X64,X65))
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( member(esk21_2(X64,X65),X64)
| apply(X65,esk17_2(X64,X65),esk18_2(X64,X65))
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( apply(X65,esk19_2(X64,X65),esk20_2(X64,X65))
| apply(X65,esk17_2(X64,X65),esk18_2(X64,X65))
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( apply(X65,esk20_2(X64,X65),esk21_2(X64,X65))
| apply(X65,esk17_2(X64,X65),esk18_2(X64,X65))
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( ~ apply(X65,esk19_2(X64,X65),esk21_2(X64,X65))
| apply(X65,esk17_2(X64,X65),esk18_2(X64,X65))
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( member(esk19_2(X64,X65),X64)
| ~ apply(X65,esk18_2(X64,X65),esk17_2(X64,X65))
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( member(esk20_2(X64,X65),X64)
| ~ apply(X65,esk18_2(X64,X65),esk17_2(X64,X65))
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( member(esk21_2(X64,X65),X64)
| ~ apply(X65,esk18_2(X64,X65),esk17_2(X64,X65))
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( apply(X65,esk19_2(X64,X65),esk20_2(X64,X65))
| ~ apply(X65,esk18_2(X64,X65),esk17_2(X64,X65))
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( apply(X65,esk20_2(X64,X65),esk21_2(X64,X65))
| ~ apply(X65,esk18_2(X64,X65),esk17_2(X64,X65))
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( ~ apply(X65,esk19_2(X64,X65),esk21_2(X64,X65))
| ~ apply(X65,esk18_2(X64,X65),esk17_2(X64,X65))
| member(esk16_2(X64,X65),X64)
| epred1_2(X65,X64) )
& ( member(esk19_2(X64,X65),X64)
| member(esk17_2(X64,X65),X64)
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( member(esk20_2(X64,X65),X64)
| member(esk17_2(X64,X65),X64)
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( member(esk21_2(X64,X65),X64)
| member(esk17_2(X64,X65),X64)
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( apply(X65,esk19_2(X64,X65),esk20_2(X64,X65))
| member(esk17_2(X64,X65),X64)
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( apply(X65,esk20_2(X64,X65),esk21_2(X64,X65))
| member(esk17_2(X64,X65),X64)
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( ~ apply(X65,esk19_2(X64,X65),esk21_2(X64,X65))
| member(esk17_2(X64,X65),X64)
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( member(esk19_2(X64,X65),X64)
| member(esk18_2(X64,X65),X64)
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( member(esk20_2(X64,X65),X64)
| member(esk18_2(X64,X65),X64)
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( member(esk21_2(X64,X65),X64)
| member(esk18_2(X64,X65),X64)
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( apply(X65,esk19_2(X64,X65),esk20_2(X64,X65))
| member(esk18_2(X64,X65),X64)
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( apply(X65,esk20_2(X64,X65),esk21_2(X64,X65))
| member(esk18_2(X64,X65),X64)
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( ~ apply(X65,esk19_2(X64,X65),esk21_2(X64,X65))
| member(esk18_2(X64,X65),X64)
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( member(esk19_2(X64,X65),X64)
| apply(X65,esk17_2(X64,X65),esk18_2(X64,X65))
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( member(esk20_2(X64,X65),X64)
| apply(X65,esk17_2(X64,X65),esk18_2(X64,X65))
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( member(esk21_2(X64,X65),X64)
| apply(X65,esk17_2(X64,X65),esk18_2(X64,X65))
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( apply(X65,esk19_2(X64,X65),esk20_2(X64,X65))
| apply(X65,esk17_2(X64,X65),esk18_2(X64,X65))
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( apply(X65,esk20_2(X64,X65),esk21_2(X64,X65))
| apply(X65,esk17_2(X64,X65),esk18_2(X64,X65))
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( ~ apply(X65,esk19_2(X64,X65),esk21_2(X64,X65))
| apply(X65,esk17_2(X64,X65),esk18_2(X64,X65))
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( member(esk19_2(X64,X65),X64)
| ~ apply(X65,esk18_2(X64,X65),esk17_2(X64,X65))
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( member(esk20_2(X64,X65),X64)
| ~ apply(X65,esk18_2(X64,X65),esk17_2(X64,X65))
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( member(esk21_2(X64,X65),X64)
| ~ apply(X65,esk18_2(X64,X65),esk17_2(X64,X65))
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( apply(X65,esk19_2(X64,X65),esk20_2(X64,X65))
| ~ apply(X65,esk18_2(X64,X65),esk17_2(X64,X65))
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( apply(X65,esk20_2(X64,X65),esk21_2(X64,X65))
| ~ apply(X65,esk18_2(X64,X65),esk17_2(X64,X65))
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) )
& ( ~ apply(X65,esk19_2(X64,X65),esk21_2(X64,X65))
| ~ apply(X65,esk18_2(X64,X65),esk17_2(X64,X65))
| ~ apply(X65,esk16_2(X64,X65),esk16_2(X64,X65))
| epred1_2(X65,X64) ) ),
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_15])])])])])])]) ).
cnf(c_0_30,plain,
( epred1_2(X1,X2)
| ~ equivalence(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
equivalence(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_32,plain,
( member(X1,equivalence_class(X2,X3,X4))
| ~ member(X1,equivalence_class(X2,equivalence_class(X5,X3,X6),X4)) ),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( apply(esk2_0,esk3_0,esk4_0)
| apply(esk2_0,esk3_0,X1)
| ~ member(X1,equivalence_class(esk4_0,esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_10,c_0_28]) ).
cnf(c_0_34,plain,
( apply(X3,X1,X1)
| ~ member(X1,X2)
| ~ epred1_2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,negated_conjecture,
epred1_2(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
( member(X1,equivalence_class(X2,X3,X4))
| ~ apply(X4,X2,X1)
| ~ member(X1,equivalence_class(X5,X3,X6)) ),
inference(spm,[status(thm)],[c_0_32,c_0_9]) ).
cnf(c_0_37,plain,
( apply(X5,X1,X4)
| ~ member(X1,X2)
| ~ member(X3,X2)
| ~ member(X4,X2)
| ~ apply(X5,X1,X3)
| ~ apply(X5,X3,X4)
| ~ epred1_2(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,negated_conjecture,
( apply(esk2_0,esk3_0,esk4_0)
| apply(esk2_0,esk3_0,X1)
| ~ apply(esk2_0,esk4_0,X1)
| ~ member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_9]) ).
cnf(c_0_39,plain,
( apply(esk2_0,X1,X1)
| ~ member(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
member(esk4_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_41,negated_conjecture,
( ~ 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) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_42,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_43,plain,
( member(esk9_2(equivalence_class(X1,X2,X3),X4),equivalence_class(X5,X2,X6))
| subset(equivalence_class(X1,X2,X3),X4)
| ~ apply(X6,X5,esk9_2(equivalence_class(X1,X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_36,c_0_11]) ).
cnf(c_0_44,plain,
( apply(X1,X2,esk9_2(equivalence_class(X3,X4,X1),X5))
| subset(equivalence_class(X3,X4,X1),X5)
| ~ epred1_2(X1,X6)
| ~ apply(X1,X2,X3)
| ~ member(esk9_2(equivalence_class(X3,X4,X1),X5),X6)
| ~ member(X3,X6)
| ~ member(X2,X6) ),
inference(spm,[status(thm)],[c_0_37,c_0_17]) ).
cnf(c_0_45,plain,
( apply(X4,X3,X1)
| ~ member(X1,X2)
| ~ member(X3,X2)
| ~ apply(X4,X1,X3)
| ~ epred1_2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_46,plain,
apply(esk2_0,esk3_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_47,negated_conjecture,
( ~ apply(esk2_0,esk3_0,esk4_0)
| ~ subset(equivalence_class(esk4_0,esk1_0,esk2_0),equivalence_class(esk3_0,esk1_0,esk2_0))
| ~ subset(equivalence_class(esk3_0,esk1_0,esk2_0),equivalence_class(esk4_0,esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,plain,
( subset(equivalence_class(X1,X2,X3),equivalence_class(X4,X2,X5))
| ~ apply(X5,X4,esk9_2(equivalence_class(X1,X2,X3),equivalence_class(X4,X2,X5))) ),
inference(spm,[status(thm)],[c_0_8,c_0_43]) ).
cnf(c_0_49,plain,
( apply(X1,X2,esk9_2(equivalence_class(X3,X4,X1),X5))
| subset(equivalence_class(X3,X4,X1),X5)
| ~ epred1_2(X1,X4)
| ~ apply(X1,X2,X3)
| ~ member(X3,X4)
| ~ member(X2,X4) ),
inference(spm,[status(thm)],[c_0_44,c_0_18]) ).
cnf(c_0_50,plain,
( apply(esk2_0,esk4_0,esk3_0)
| ~ epred1_2(esk2_0,X1)
| ~ member(esk4_0,X1)
| ~ member(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
member(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_52,negated_conjecture,
( ~ subset(equivalence_class(esk4_0,esk1_0,esk2_0),equivalence_class(esk3_0,esk1_0,esk2_0))
| ~ subset(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_47,c_0_46])]) ).
cnf(c_0_53,plain,
( subset(equivalence_class(X1,X2,X3),equivalence_class(X4,X2,X3))
| ~ epred1_2(X3,X2)
| ~ apply(X3,X4,X1)
| ~ member(X1,X2)
| ~ member(X4,X2) ),
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_35]),c_0_40]),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_35]),c_0_54]),c_0_51]),c_0_40])]) ).
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_35]),c_0_46]),c_0_40]),c_0_51])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : SET768+4 : TPTP v8.2.0. Released v2.2.0.
% 0.04/0.09 % Command : run_E %s %d THM
% 0.08/0.29 % Computer : n015.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Mon May 20 11:39:38 EDT 2024
% 0.08/0.29 % CPUTime :
% 0.14/0.42 Running first-order model finding
% 0.14/0.42 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 129.44/16.78 # Version: 3.1.0
% 129.44/16.78 # Preprocessing class: FSMSSMSSSSSNFFN.
% 129.44/16.78 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 129.44/16.78 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 129.44/16.78 # Starting new_bool_3 with 300s (1) cores
% 129.44/16.78 # Starting new_bool_1 with 300s (1) cores
% 129.44/16.78 # Starting sh5l with 300s (1) cores
% 129.44/16.78 # sh5l with pid 27068 completed with status 0
% 129.44/16.78 # Result found by sh5l
% 129.44/16.78 # Preprocessing class: FSMSSMSSSSSNFFN.
% 129.44/16.78 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 129.44/16.78 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 129.44/16.78 # Starting new_bool_3 with 300s (1) cores
% 129.44/16.78 # Starting new_bool_1 with 300s (1) cores
% 129.44/16.78 # Starting sh5l with 300s (1) cores
% 129.44/16.78 # SinE strategy is gf500_gu_R04_F100_L20000
% 129.44/16.78 # Search class: FGHSF-FFLS32-SFFFFFNN
% 129.44/16.78 # partial match(1): FGHSF-FFMS32-SFFFFFNN
% 129.44/16.78 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 129.44/16.78 # Starting G-E--_301_C18_F1_URBAN_S0Y with 181s (1) cores
% 129.44/16.78 # G-E--_301_C18_F1_URBAN_S0Y with pid 27071 completed with status 0
% 129.44/16.78 # Result found by G-E--_301_C18_F1_URBAN_S0Y
% 129.44/16.78 # Preprocessing class: FSMSSMSSSSSNFFN.
% 129.44/16.78 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 129.44/16.78 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 129.44/16.78 # Starting new_bool_3 with 300s (1) cores
% 129.44/16.78 # Starting new_bool_1 with 300s (1) cores
% 129.44/16.78 # Starting sh5l with 300s (1) cores
% 129.44/16.78 # SinE strategy is gf500_gu_R04_F100_L20000
% 129.44/16.78 # Search class: FGHSF-FFLS32-SFFFFFNN
% 129.44/16.78 # partial match(1): FGHSF-FFMS32-SFFFFFNN
% 129.44/16.78 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 129.44/16.78 # Starting G-E--_301_C18_F1_URBAN_S0Y with 181s (1) cores
% 129.44/16.78 # Preprocessing time : 0.005 s
% 129.44/16.78
% 129.44/16.78 # Proof found!
% 129.44/16.78 # SZS status Theorem
% 129.44/16.78 # SZS output start CNFRefutation
% See solution above
% 129.44/16.78 # Parsed axioms : 17
% 129.44/16.78 # Removed by relevancy pruning/SinE : 9
% 129.44/16.78 # Initial clauses : 107
% 129.44/16.78 # Removed in clause preprocessing : 0
% 129.44/16.78 # Initial clauses in saturation : 107
% 129.44/16.78 # Processed clauses : 15886
% 129.44/16.78 # ...of these trivial : 687
% 129.44/16.78 # ...subsumed : 9455
% 129.44/16.78 # ...remaining for further processing : 5744
% 129.44/16.78 # Other redundant clauses eliminated : 0
% 129.44/16.78 # Clauses deleted for lack of memory : 0
% 129.44/16.78 # Backward-subsumed : 936
% 129.44/16.78 # Backward-rewritten : 454
% 129.44/16.78 # Generated clauses : 388845
% 129.44/16.78 # ...of the previous two non-redundant : 362978
% 129.44/16.78 # ...aggressively subsumed : 0
% 129.44/16.78 # Contextual simplify-reflections : 122
% 129.44/16.78 # Paramodulations : 388789
% 129.44/16.78 # Factorizations : 56
% 129.44/16.78 # NegExts : 0
% 129.44/16.78 # Equation resolutions : 0
% 129.44/16.78 # Disequality decompositions : 0
% 129.44/16.78 # Total rewrite steps : 24691
% 129.44/16.78 # ...of those cached : 24265
% 129.44/16.78 # Propositional unsat checks : 0
% 129.44/16.78 # Propositional check models : 0
% 129.44/16.78 # Propositional check unsatisfiable : 0
% 129.44/16.78 # Propositional clauses : 0
% 129.44/16.78 # Propositional clauses after purity: 0
% 129.44/16.78 # Propositional unsat core size : 0
% 129.44/16.78 # Propositional preprocessing time : 0.000
% 129.44/16.78 # Propositional encoding time : 0.000
% 129.44/16.78 # Propositional solver time : 0.000
% 129.44/16.78 # Success case prop preproc time : 0.000
% 129.44/16.78 # Success case prop encoding time : 0.000
% 129.44/16.78 # Success case prop solver time : 0.000
% 129.44/16.78 # Current number of processed clauses : 4354
% 129.44/16.78 # Positive orientable unit clauses : 430
% 129.44/16.78 # Positive unorientable unit clauses: 0
% 129.44/16.78 # Negative unit clauses : 3
% 129.44/16.78 # Non-unit-clauses : 3921
% 129.44/16.78 # Current number of unprocessed clauses: 341299
% 129.44/16.78 # ...number of literals in the above : 1899275
% 129.44/16.78 # Current number of archived formulas : 0
% 129.44/16.78 # Current number of archived clauses : 1390
% 129.44/16.78 # Clause-clause subsumption calls (NU) : 2754825
% 129.44/16.78 # Rec. Clause-clause subsumption calls : 485589
% 129.44/16.78 # Non-unit clause-clause subsumptions : 9991
% 129.44/16.78 # Unit Clause-clause subsumption calls : 49990
% 129.44/16.78 # Rewrite failures with RHS unbound : 0
% 129.44/16.78 # BW rewrite match attempts : 22273
% 129.44/16.78 # BW rewrite match successes : 68
% 129.44/16.78 # Condensation attempts : 0
% 129.44/16.78 # Condensation successes : 0
% 129.44/16.78 # Termbank termtop insertions : 15038228
% 129.44/16.78 # Search garbage collected termcells : 1401
% 129.44/16.78
% 129.44/16.78 # -------------------------------------------------
% 129.44/16.78 # User time : 15.837 s
% 129.44/16.78 # System time : 0.324 s
% 129.44/16.78 # Total time : 16.161 s
% 129.44/16.78 # Maximum resident set size: 2044 pages
% 129.44/16.78
% 129.44/16.78 # -------------------------------------------------
% 129.44/16.78 # User time : 15.842 s
% 129.44/16.78 # System time : 0.324 s
% 129.44/16.78 # Total time : 16.166 s
% 129.44/16.78 # Maximum resident set size: 1760 pages
% 129.44/16.78 % E---3.1 exiting
%------------------------------------------------------------------------------