%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET734+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 : n002.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 05:08:24 PM UTC 2026
% Result : Theorem 2.25s 2.09s
% Output : CNFRefutation 2.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 86 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 101 ( 37 ~; 37 |; 19 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-7 aty)
% Number of variables : 70 ( 0 sgn 43 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thII25,conjecture,
! [X6,X10,X1,X2] :
( ( maps(X10,X1,X2)
& maps(X6,X2,X1)
& identity(compose_function(X10,X6,X2,X1,X2),X2) )
=> surjective(X10,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII25) ).
fof(identity,axiom,
! [X6,X1] :
( identity(X6,X1)
<=> ! [X3] :
( member(X3,X1)
=> apply(X6,X3,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',identity) ).
fof(surjective,axiom,
! [X6,X1,X2] :
( surjective(X6,X1,X2)
<=> ! [X5] :
( member(X5,X2)
=> ? [X4] :
( member(X4,X1)
& apply(X6,X4,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',surjective) ).
fof(compose_function,axiom,
! [X10,X6,X1,X2,X11,X3,X12] :
( ( member(X3,X1)
& member(X12,X11) )
=> ( apply(compose_function(X10,X6,X1,X2,X11),X3,X12)
<=> ? [X5] :
( member(X5,X2)
& apply(X6,X3,X5)
& apply(X10,X5,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',compose_function) ).
fof(c_0_4,negated_conjecture,
~ ! [X6,X10,X1,X2] :
( ( maps(X10,X1,X2)
& maps(X6,X2,X1)
& identity(compose_function(X10,X6,X2,X1,X2),X2) )
=> surjective(X10,X1,X2) ),
inference(assume_negation,[status(cth)],[thII25]) ).
fof(c_0_5,plain,
! [X250,X251,X252,X253,X254] :
( ( ~ identity(X250,X251)
| ~ member(X252,X251)
| apply(X250,X252,X252) )
& ( member(esk17_2(X253,X254),X254)
| identity(X253,X254) )
& ( ~ apply(X253,esk17_2(X253,X254),esk17_2(X253,X254))
| identity(X253,X254) ) ),
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)],[identity])])])])])]) ).
fof(c_0_6,negated_conjecture,
( maps(esk42_0,esk43_0,esk44_0)
& maps(esk41_0,esk44_0,esk43_0)
& identity(compose_function(esk42_0,esk41_0,esk44_0,esk43_0,esk44_0),esk44_0)
& ~ surjective(esk42_0,esk43_0,esk44_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X268,X269,X270,X271,X273,X274,X275,X277] :
( ( member(esk21_4(X268,X269,X270,X271),X269)
| ~ member(X271,X270)
| ~ surjective(X268,X269,X270) )
& ( apply(X268,esk21_4(X268,X269,X270,X271),X271)
| ~ member(X271,X270)
| ~ surjective(X268,X269,X270) )
& ( member(esk22_3(X273,X274,X275),X275)
| surjective(X273,X274,X275) )
& ( ~ member(X277,X274)
| ~ apply(X273,X277,esk22_3(X273,X274,X275))
| surjective(X273,X274,X275) ) ),
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)],[surjective])])])])])]) ).
cnf(c_0_8,plain,
( apply(X1,X3,X3)
| ~ identity(X1,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
identity(compose_function(esk42_0,esk41_0,esk44_0,esk43_0,esk44_0),esk44_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
~ surjective(esk42_0,esk43_0,esk44_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( member(esk22_3(X1,X2,X3),X3)
| surjective(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X227,X228,X229,X230,X231,X232,X233,X235] :
( ( member(esk13_7(X227,X228,X229,X230,X231,X232,X233),X230)
| ~ apply(compose_function(X227,X228,X229,X230,X231),X232,X233)
| ~ member(X232,X229)
| ~ member(X233,X231) )
& ( apply(X228,X232,esk13_7(X227,X228,X229,X230,X231,X232,X233))
| ~ apply(compose_function(X227,X228,X229,X230,X231),X232,X233)
| ~ member(X232,X229)
| ~ member(X233,X231) )
& ( apply(X227,esk13_7(X227,X228,X229,X230,X231,X232,X233),X233)
| ~ apply(compose_function(X227,X228,X229,X230,X231),X232,X233)
| ~ member(X232,X229)
| ~ member(X233,X231) )
& ( ~ member(X235,X230)
| ~ apply(X228,X232,X235)
| ~ apply(X227,X235,X233)
| apply(compose_function(X227,X228,X229,X230,X231),X232,X233)
| ~ member(X232,X229)
| ~ member(X233,X231) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[compose_function])])])])]) ).
cnf(c_0_13,negated_conjecture,
( apply(compose_function(esk42_0,esk41_0,esk44_0,esk43_0,esk44_0),X1,X1)
| ~ member(X1,esk44_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,negated_conjecture,
member(esk22_3(esk42_0,esk43_0,esk44_0),esk44_0),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( apply(X1,esk13_7(X1,X2,X3,X4,X5,X6,X7),X7)
| ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
| ~ member(X6,X3)
| ~ member(X7,X5) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
apply(compose_function(esk42_0,esk41_0,esk44_0,esk43_0,esk44_0),esk22_3(esk42_0,esk43_0,esk44_0),esk22_3(esk42_0,esk43_0,esk44_0)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( member(esk13_7(X1,X2,X3,X4,X5,X6,X7),X4)
| ~ apply(compose_function(X1,X2,X3,X4,X5),X6,X7)
| ~ member(X6,X3)
| ~ member(X7,X5) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( surjective(X3,X2,X4)
| ~ member(X1,X2)
| ~ apply(X3,X1,esk22_3(X3,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
apply(esk42_0,esk13_7(esk42_0,esk41_0,esk44_0,esk43_0,esk44_0,esk22_3(esk42_0,esk43_0,esk44_0),esk22_3(esk42_0,esk43_0,esk44_0)),esk22_3(esk42_0,esk43_0,esk44_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_14])]) ).
cnf(c_0_20,negated_conjecture,
member(esk13_7(esk42_0,esk41_0,esk44_0,esk43_0,esk44_0,esk22_3(esk42_0,esk43_0,esk44_0),esk22_3(esk42_0,esk43_0,esk44_0)),esk43_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_16]),c_0_14])]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),c_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET734+4 : TPTP v9.2.1. Bugfixed v2.2.1.
% 0.12/0.13 % 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 : n002.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 02:33:16 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 2.25/2.09 % Version : CSE_E---1.7
% 2.25/2.09 % Problem : theBenchmark.p
% 2.25/2.09 % SZS status Theorem for theBenchmark.p
% 2.25/2.09 % SZS output start CNFRefutation
% See solution above
% 2.25/2.10 % Total time : 1.374s
%------------------------------------------------------------------------------