%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET763+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 : n031.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 1.52s 1.82s
% Output : CNFRefutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 16 unt; 0 def)
% Number of atoms : 161 ( 4 equ)
% Maximal formula atoms : 55 ( 3 avg)
% Number of connectives : 178 ( 60 ~; 72 |; 35 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-4 aty)
% Number of variables : 89 ( 4 sgn 55 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(power_set,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(thIIa13,conjecture,
! [X6,X1,X2,X3] :
( ( maps(X6,X1,X2)
& subset(X3,X1)
& equal_set(image2(X6,X3),empty_set) )
=> equal_set(X3,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIIa13) ).
fof(maps,axiom,
! [X6,X1,X2] :
( maps(X6,X1,X2)
<=> ( ! [X3] :
( member(X3,X1)
=> ? [X5] :
( member(X5,X2)
& apply(X6,X3,X5) ) )
& ! [X3,X7,X8] :
( ( member(X3,X1)
& member(X7,X2)
& member(X8,X2) )
=> ( ( apply(X6,X3,X7)
& apply(X6,X3,X8) )
=> X7 = X8 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+1.ax',maps) ).
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_7,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
fof(c_0_8,plain,
! [X162,X163] :
( ( ~ member(X162,power_set(X163))
| subset(X162,X163) )
& ( ~ subset(X162,X163)
| member(X162,power_set(X163)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])]) ).
fof(c_0_9,plain,
! [X154,X155,X156,X157,X158] :
( ( ~ subset(X154,X155)
| ~ member(X156,X154)
| member(X156,X155) )
& ( member(esk1_2(X157,X158),X157)
| subset(X157,X158) )
& ( ~ member(esk1_2(X157,X158),X158)
| subset(X157,X158) ) ),
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_10,plain,
! [X170] : ~ member(X170,empty_set),
inference(variable_rename,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( member(esk1_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_15,plain,
! [X160,X161] :
( ( subset(X160,X161)
| ~ equal_set(X160,X161) )
& ( subset(X161,X160)
| ~ equal_set(X160,X161) )
& ( ~ subset(X160,X161)
| ~ subset(X161,X160)
| equal_set(X160,X161) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).
cnf(c_0_16,plain,
( subset(X1,X2)
| ~ member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,plain,
member(empty_set,power_set(X1)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_18,negated_conjecture,
~ ! [X6,X1,X2,X3] :
( ( maps(X6,X1,X2)
& subset(X3,X1)
& equal_set(image2(X6,X3),empty_set) )
=> equal_set(X3,empty_set) ),
inference(assume_negation,[status(cth)],[thIIa13]) ).
cnf(c_0_19,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_21,negated_conjecture,
( maps(esk41_0,esk42_0,esk43_0)
& subset(esk44_0,esk42_0)
& equal_set(image2(esk41_0,esk44_0),empty_set)
& ~ equal_set(esk44_0,empty_set) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
cnf(c_0_22,plain,
( equal_set(X1,empty_set)
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_23,plain,
! [X191,X192,X193,X194,X196,X197,X198,X199,X200,X201,X203] :
( ( member(esk4_4(X191,X192,X193,X194),X193)
| ~ member(X194,X192)
| ~ maps(X191,X192,X193) )
& ( apply(X191,X194,esk4_4(X191,X192,X193,X194))
| ~ member(X194,X192)
| ~ maps(X191,X192,X193) )
& ( ~ member(X196,X192)
| ~ member(X197,X193)
| ~ member(X198,X193)
| ~ apply(X191,X196,X197)
| ~ apply(X191,X196,X198)
| X197 = X198
| ~ maps(X191,X192,X193) )
& ( member(esk6_3(X199,X200,X201),X200)
| member(esk5_3(X199,X200,X201),X200)
| maps(X199,X200,X201) )
& ( member(esk7_3(X199,X200,X201),X201)
| member(esk5_3(X199,X200,X201),X200)
| maps(X199,X200,X201) )
& ( member(esk8_3(X199,X200,X201),X201)
| member(esk5_3(X199,X200,X201),X200)
| maps(X199,X200,X201) )
& ( apply(X199,esk6_3(X199,X200,X201),esk7_3(X199,X200,X201))
| member(esk5_3(X199,X200,X201),X200)
| maps(X199,X200,X201) )
& ( apply(X199,esk6_3(X199,X200,X201),esk8_3(X199,X200,X201))
| member(esk5_3(X199,X200,X201),X200)
| maps(X199,X200,X201) )
& ( esk7_3(X199,X200,X201) != esk8_3(X199,X200,X201)
| member(esk5_3(X199,X200,X201),X200)
| maps(X199,X200,X201) )
& ( member(esk6_3(X199,X200,X201),X200)
| ~ member(X203,X201)
| ~ apply(X199,esk5_3(X199,X200,X201),X203)
| maps(X199,X200,X201) )
& ( member(esk7_3(X199,X200,X201),X201)
| ~ member(X203,X201)
| ~ apply(X199,esk5_3(X199,X200,X201),X203)
| maps(X199,X200,X201) )
& ( member(esk8_3(X199,X200,X201),X201)
| ~ member(X203,X201)
| ~ apply(X199,esk5_3(X199,X200,X201),X203)
| maps(X199,X200,X201) )
& ( apply(X199,esk6_3(X199,X200,X201),esk7_3(X199,X200,X201))
| ~ member(X203,X201)
| ~ apply(X199,esk5_3(X199,X200,X201),X203)
| maps(X199,X200,X201) )
& ( apply(X199,esk6_3(X199,X200,X201),esk8_3(X199,X200,X201))
| ~ member(X203,X201)
| ~ apply(X199,esk5_3(X199,X200,X201),X203)
| maps(X199,X200,X201) )
& ( esk7_3(X199,X200,X201) != esk8_3(X199,X200,X201)
| ~ member(X203,X201)
| ~ apply(X199,esk5_3(X199,X200,X201),X203)
| maps(X199,X200,X201) ) ),
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)],[maps])])])])])]) ).
cnf(c_0_24,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,negated_conjecture,
subset(esk44_0,esk42_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,negated_conjecture,
~ equal_set(esk44_0,empty_set),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
( equal_set(X1,empty_set)
| member(esk1_2(X1,empty_set),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_12]) ).
cnf(c_0_28,plain,
( apply(X1,X2,esk4_4(X1,X3,X4,X2))
| ~ member(X2,X3)
| ~ maps(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,negated_conjecture,
maps(esk41_0,esk42_0,esk43_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,negated_conjecture,
( member(X1,esk42_0)
| ~ member(X1,esk44_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
member(esk1_2(esk44_0,empty_set),esk44_0),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_32,plain,
! [X298,X299,X300,X302,X303,X304,X305] :
( ( member(esk25_3(X298,X299,X300),X299)
| ~ member(X300,image2(X298,X299)) )
& ( apply(X298,esk25_3(X298,X299,X300),X300)
| ~ member(X300,image2(X298,X299)) )
& ( ~ member(X305,X303)
| ~ apply(X302,X305,X304)
| member(X304,image2(X302,X303)) ) ),
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_33,negated_conjecture,
( apply(esk41_0,X1,esk4_4(esk41_0,esk42_0,esk43_0,X1))
| ~ member(X1,esk42_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
member(esk1_2(esk44_0,empty_set),esk42_0),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
( subset(X1,X2)
| ~ equal_set(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_36,negated_conjecture,
equal_set(image2(esk41_0,esk44_0),empty_set),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_37,plain,
( member(X4,image2(X3,X2))
| ~ member(X1,X2)
| ~ apply(X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,negated_conjecture,
apply(esk41_0,esk1_2(esk44_0,empty_set),esk4_4(esk41_0,esk42_0,esk43_0,esk1_2(esk44_0,empty_set))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
subset(image2(esk41_0,esk44_0),empty_set),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( member(esk4_4(esk41_0,esk42_0,esk43_0,esk1_2(esk44_0,empty_set)),image2(esk41_0,X1))
| ~ member(esk1_2(esk44_0,empty_set),X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,negated_conjecture,
~ member(X1,image2(esk41_0,esk44_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_39]),c_0_13]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_31]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET763+4 : TPTP v9.2.1. Bugfixed v2.2.1.
% 0.00/0.11 % 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
% 0.12/0.32 % Computer : n031.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue May 5 02:37:09 EDT 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.33 % start to proof: theBenchmark
% 1.52/1.82 % Version : CSE_E---1.7
% 1.52/1.82 % Problem : theBenchmark.p
% 1.52/1.82 % SZS status Theorem for theBenchmark.p
% 1.52/1.82 % SZS output start CNFRefutation
% See solution above
% 1.52/1.83 % Total time : 1.373s
%------------------------------------------------------------------------------