%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET722+4 : TPTP v9.2.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n025.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 05:08:23 PM UTC 2026
% Result : Theorem 45.91s 28.83s
% Output : CNFRefutation 46.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 96 ( 37 ~; 36 |; 17 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-7 aty)
% Number of variables : 70 ( 0 sgn 37 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thII13,conjecture,
! [X6,X10,X1,X2,X11] :
( ( maps(X6,X1,X2)
& maps(X10,X2,X11)
& surjective(compose_function(X10,X6,X1,X2,X11),X1,X11) )
=> surjective(X10,X2,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thII13) ).
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/sandbox/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/sandbox/benchmark/Axioms/SET006+1.ax',compose_function) ).
fof(c_0_3,negated_conjecture,
~ ! [X6,X10,X1,X2,X11] :
( ( maps(X6,X1,X2)
& maps(X10,X2,X11)
& surjective(compose_function(X10,X6,X1,X2,X11),X1,X11) )
=> surjective(X10,X2,X11) ),
inference(assume_negation,[status(cth)],[thII13]) ).
fof(c_0_4,plain,
! [X269,X270,X271,X272,X274,X275,X276,X278] :
( ( member(esk21_4(X269,X270,X271,X272),X270)
| ~ member(X272,X271)
| ~ surjective(X269,X270,X271) )
& ( apply(X269,esk21_4(X269,X270,X271,X272),X272)
| ~ member(X272,X271)
| ~ surjective(X269,X270,X271) )
& ( member(esk22_3(X274,X275,X276),X276)
| surjective(X274,X275,X276) )
& ( ~ member(X278,X275)
| ~ apply(X274,X278,esk22_3(X274,X275,X276))
| surjective(X274,X275,X276) ) ),
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])])])])])]) ).
fof(c_0_5,negated_conjecture,
( maps(esk41_0,esk43_0,esk44_0)
& maps(esk42_0,esk44_0,esk45_0)
& surjective(compose_function(esk42_0,esk41_0,esk43_0,esk44_0,esk45_0),esk43_0,esk45_0)
& ~ surjective(esk42_0,esk44_0,esk45_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
cnf(c_0_6,plain,
( apply(X1,esk21_4(X1,X2,X3,X4),X4)
| ~ member(X4,X3)
| ~ surjective(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
surjective(compose_function(esk42_0,esk41_0,esk43_0,esk44_0,esk45_0),esk43_0,esk45_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
~ surjective(esk42_0,esk44_0,esk45_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( member(esk22_3(X1,X2,X3),X3)
| surjective(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,plain,
( member(esk21_4(X1,X2,X3,X4),X2)
| ~ member(X4,X3)
| ~ surjective(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_11,plain,
! [X228,X229,X230,X231,X232,X233,X234,X236] :
( ( member(esk13_7(X228,X229,X230,X231,X232,X233,X234),X231)
| ~ apply(compose_function(X228,X229,X230,X231,X232),X233,X234)
| ~ member(X233,X230)
| ~ member(X234,X232) )
& ( apply(X229,X233,esk13_7(X228,X229,X230,X231,X232,X233,X234))
| ~ apply(compose_function(X228,X229,X230,X231,X232),X233,X234)
| ~ member(X233,X230)
| ~ member(X234,X232) )
& ( apply(X228,esk13_7(X228,X229,X230,X231,X232,X233,X234),X234)
| ~ apply(compose_function(X228,X229,X230,X231,X232),X233,X234)
| ~ member(X233,X230)
| ~ member(X234,X232) )
& ( ~ member(X236,X231)
| ~ apply(X229,X233,X236)
| ~ apply(X228,X236,X234)
| apply(compose_function(X228,X229,X230,X231,X232),X233,X234)
| ~ member(X233,X230)
| ~ member(X234,X232) ) ),
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_12,negated_conjecture,
( apply(compose_function(esk42_0,esk41_0,esk43_0,esk44_0,esk45_0),esk21_4(compose_function(esk42_0,esk41_0,esk43_0,esk44_0,esk45_0),esk43_0,esk45_0,X1),X1)
| ~ member(X1,esk45_0) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_13,negated_conjecture,
member(esk22_3(esk42_0,esk44_0,esk45_0),esk45_0),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( member(esk21_4(compose_function(esk42_0,esk41_0,esk43_0,esk44_0,esk45_0),esk43_0,esk45_0,X1),esk43_0)
| ~ member(X1,esk45_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
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_11]) ).
cnf(c_0_16,negated_conjecture,
apply(compose_function(esk42_0,esk41_0,esk43_0,esk44_0,esk45_0),esk21_4(compose_function(esk42_0,esk41_0,esk43_0,esk44_0,esk45_0),esk43_0,esk45_0,esk22_3(esk42_0,esk44_0,esk45_0)),esk22_3(esk42_0,esk44_0,esk45_0)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
member(esk21_4(compose_function(esk42_0,esk41_0,esk43_0,esk44_0,esk45_0),esk43_0,esk45_0,esk22_3(esk42_0,esk44_0,esk45_0)),esk43_0),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_18,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_11]) ).
cnf(c_0_19,plain,
( surjective(X3,X2,X4)
| ~ member(X1,X2)
| ~ apply(X3,X1,esk22_3(X3,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_20,negated_conjecture,
apply(esk42_0,esk13_7(esk42_0,esk41_0,esk43_0,esk44_0,esk45_0,esk21_4(compose_function(esk42_0,esk41_0,esk43_0,esk44_0,esk45_0),esk43_0,esk45_0,esk22_3(esk42_0,esk44_0,esk45_0)),esk22_3(esk42_0,esk44_0,esk45_0)),esk22_3(esk42_0,esk44_0,esk45_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_13]),c_0_17])]) ).
cnf(c_0_21,negated_conjecture,
member(esk13_7(esk42_0,esk41_0,esk43_0,esk44_0,esk45_0,esk21_4(compose_function(esk42_0,esk41_0,esk43_0,esk44_0,esk45_0),esk43_0,esk45_0,esk22_3(esk42_0,esk44_0,esk45_0)),esk22_3(esk42_0,esk44_0,esk45_0)),esk44_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_16]),c_0_13]),c_0_17])]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),c_0_8]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.20 % Problem : SET722+4 : TPTP v9.2.1. Bugfixed v2.2.1.
% 0.02/0.20 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.10/0.45 % Computer : n025.cluster.edu
% 0.10/0.45 % Model : x86_64 x86_64
% 0.10/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.45 % Memory : 8042.1875MB
% 0.10/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.45 % CPULimit : 300
% 0.10/0.45 % WCLimit : 300
% 0.10/0.45 % DateTime : Tue May 5 02:33:43 EDT 2026
% 0.10/0.45 % CPUTime :
% 0.10/0.46 % start to proof: theBenchmark
% 45.91/28.83 % Version : CSE_E---1.7
% 45.91/28.83 % Problem : theBenchmark.p
% 45.91/28.83 % SZS status Theorem for theBenchmark.p
% 45.91/28.83 % SZS output start CNFRefutation
% See solution above
% 46.01/29.02 % Total time : 21.430s
%------------------------------------------------------------------------------