%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET764+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 : 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 05:08:26 PM UTC 2026
% Result : Theorem 1.35s 1.79s
% Output : CNFRefutation 1.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 9 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 66 ( 26 ~; 23 |; 10 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 54 ( 3 sgn 35 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(power_set,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(thIIa14,conjecture,
! [X6,X1,X2] :
( maps(X6,X1,X2)
=> equal_set(inverse_image2(X6,empty_set),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa14) ).
fof(inverse_image2,axiom,
! [X6,X2,X3] :
( member(X3,inverse_image2(X6,X2))
<=> ? [X5] :
( member(X5,X2)
& apply(X6,X3,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',inverse_image2) ).
fof(c_0_6,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
fof(c_0_7,plain,
! [X161,X162] :
( ( ~ member(X161,power_set(X162))
| subset(X161,X162) )
& ( ~ subset(X161,X162)
| member(X161,power_set(X162)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])]) ).
fof(c_0_8,plain,
! [X153,X154,X155,X156,X157] :
( ( ~ subset(X153,X154)
| ~ member(X155,X153)
| member(X155,X154) )
& ( member(esk1_2(X156,X157),X156)
| subset(X156,X157) )
& ( ~ member(esk1_2(X156,X157),X157)
| subset(X156,X157) ) ),
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_9,plain,
! [X169] : ~ member(X169,empty_set),
inference(variable_rename,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( member(esk1_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_14,plain,
! [X159,X160] :
( ( subset(X159,X160)
| ~ equal_set(X159,X160) )
& ( subset(X160,X159)
| ~ equal_set(X159,X160) )
& ( ~ subset(X159,X160)
| ~ subset(X160,X159)
| equal_set(X159,X160) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).
cnf(c_0_15,plain,
( subset(X1,X2)
| ~ member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
member(empty_set,power_set(X1)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_17,negated_conjecture,
~ ! [X6,X1,X2] :
( maps(X6,X1,X2)
=> equal_set(inverse_image2(X6,empty_set),empty_set) ),
inference(assume_negation,[status(cth)],[thIIa14]) ).
cnf(c_0_18,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_20,negated_conjecture,
( maps(esk41_0,esk42_0,esk43_0)
& ~ equal_set(inverse_image2(esk41_0,empty_set),empty_set) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
cnf(c_0_21,plain,
( equal_set(X1,empty_set)
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_22,plain,
! [X315,X316,X317,X319,X320,X321,X322] :
( ( member(esk27_3(X315,X316,X317),X316)
| ~ member(X317,inverse_image2(X315,X316)) )
& ( apply(X315,X317,esk27_3(X315,X316,X317))
| ~ member(X317,inverse_image2(X315,X316)) )
& ( ~ member(X322,X320)
| ~ apply(X319,X321,X322)
| member(X321,inverse_image2(X319,X320)) ) ),
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)],[inverse_image2])])])])])]) ).
cnf(c_0_23,negated_conjecture,
~ equal_set(inverse_image2(esk41_0,empty_set),empty_set),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
( equal_set(X1,empty_set)
| member(esk1_2(X1,empty_set),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_11]) ).
cnf(c_0_25,plain,
( member(esk27_3(X1,X2,X3),X2)
| ~ member(X3,inverse_image2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
member(esk1_2(inverse_image2(esk41_0,empty_set),empty_set),inverse_image2(esk41_0,empty_set)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET764+4 : TPTP v9.2.1. Bugfixed v2.2.1.
% 0.12/0.13 % 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
% 0.17/0.34 % Computer : n001.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 02:35:18 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.20/0.35 % start to proof: theBenchmark
% 1.35/1.79 % Version : CSE_E---1.7
% 1.35/1.79 % Problem : theBenchmark.p
% 1.35/1.79 % SZS status Theorem for theBenchmark.p
% 1.35/1.79 % SZS output start CNFRefutation
% See solution above
% 1.35/1.79 % Total time : 1.422s
%------------------------------------------------------------------------------