%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET751+4 : TPTP v9.2.1. Bugfixed v2.2.1.
% 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 : n001.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 05:08:25 PM UTC 2026
% Result : Theorem 1.57s 1.80s
% Output : CNFRefutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 57 ( 19 ~; 18 |; 15 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 48 ( 0 sgn 28 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIIa01,conjecture,
! [X6,X1,X2,X3,X5] :
( ( maps(X6,X1,X2)
& subset(X3,X1)
& subset(X5,X1)
& subset(X3,X5) )
=> subset(image2(X6,X3),image2(X6,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIIa01) ).
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(image2,axiom,
! [X6,X1,X5] :
( member(X5,image2(X6,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X6,X3,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',image2) ).
fof(c_0_3,negated_conjecture,
~ ! [X6,X1,X2,X3,X5] :
( ( maps(X6,X1,X2)
& subset(X3,X1)
& subset(X5,X1)
& subset(X3,X5) )
=> subset(image2(X6,X3),image2(X6,X5)) ),
inference(assume_negation,[status(cth)],[thIIa01]) ).
fof(c_0_4,negated_conjecture,
( maps(esk41_0,esk42_0,esk43_0)
& subset(esk44_0,esk42_0)
& subset(esk45_0,esk42_0)
& subset(esk44_0,esk45_0)
& ~ subset(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_5,plain,
! [X155,X156,X157,X158,X159] :
( ( ~ subset(X155,X156)
| ~ member(X157,X155)
| member(X157,X156) )
& ( member(esk1_2(X158,X159),X158)
| subset(X158,X159) )
& ( ~ member(esk1_2(X158,X159),X159)
| subset(X158,X159) ) ),
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)],[subset])])])])])]) ).
fof(c_0_6,plain,
! [X299,X300,X301,X303,X304,X305,X306] :
( ( member(esk25_3(X299,X300,X301),X300)
| ~ member(X301,image2(X299,X300)) )
& ( apply(X299,esk25_3(X299,X300,X301),X301)
| ~ member(X301,image2(X299,X300)) )
& ( ~ member(X306,X304)
| ~ apply(X303,X306,X305)
| member(X305,image2(X303,X304)) ) ),
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)],[image2])])])])])]) ).
cnf(c_0_7,negated_conjecture,
~ subset(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0)),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( apply(X1,esk25_3(X1,X2,X3),X3)
| ~ member(X3,image2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
member(esk1_2(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0)),image2(esk41_0,esk44_0)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
subset(esk44_0,esk45_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,plain,
( member(esk25_3(X1,X2,X3),X2)
| ~ member(X3,image2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( member(X4,image2(X3,X2))
| ~ member(X1,X2)
| ~ apply(X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
apply(esk41_0,esk25_3(esk41_0,esk44_0,esk1_2(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0))),esk1_2(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0))),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( member(X1,esk45_0)
| ~ member(X1,esk44_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
member(esk25_3(esk41_0,esk44_0,esk1_2(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0))),esk44_0),
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_18,negated_conjecture,
( member(esk1_2(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0)),image2(esk41_0,X1))
| ~ member(esk25_3(esk41_0,esk44_0,esk1_2(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0))),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
member(esk25_3(esk41_0,esk44_0,esk1_2(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0))),esk45_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_21,negated_conjecture,
member(esk1_2(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0)),image2(esk41_0,esk45_0)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_7]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET751+4 : TPTP v9.2.1. Bugfixed v2.2.1.
% 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
% 0.15/0.33 % Computer : n001.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:34:33 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.57/1.80 % Version : CSE_E---1.7
% 1.57/1.80 % Problem : theBenchmark.p
% 1.57/1.80 % SZS status Theorem for theBenchmark.p
% 1.57/1.80 % SZS output start CNFRefutation
% See solution above
% 1.57/1.80 % Total time : 1.374s
%------------------------------------------------------------------------------