%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET603+4 : TPTP v9.2.1. Released v2.2.0.
% 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 : n006.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 05:08:06 PM UTC 2026
% Result : Theorem 1.27s 1.71s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 76 ( 35 ~; 27 |; 9 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 2 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI30,conjecture,
! [X4] : equal_set(difference(X4,empty_set),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI30) ).
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(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(difference,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',difference) ).
fof(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(c_0_5,negated_conjecture,
~ ! [X4] : equal_set(difference(X4,empty_set),X4),
inference(assume_negation,[status(cth)],[thI30]) ).
fof(c_0_6,negated_conjecture,
~ equal_set(difference(esk4_0,empty_set),esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_7,plain,
! [X41,X42] :
( ( subset(X41,X42)
| ~ equal_set(X41,X42) )
& ( subset(X42,X41)
| ~ equal_set(X41,X42) )
& ( ~ subset(X41,X42)
| ~ subset(X42,X41)
| equal_set(X41,X42) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).
cnf(c_0_8,negated_conjecture,
~ equal_set(difference(esk4_0,empty_set),esk4_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X35,X36,X37,X38,X39] :
( ( ~ subset(X35,X36)
| ~ member(X37,X35)
| member(X37,X36) )
& ( member(esk1_2(X38,X39),X38)
| subset(X38,X39) )
& ( ~ member(esk1_2(X38,X39),X39)
| subset(X38,X39) ) ),
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_11,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[difference]) ).
cnf(c_0_12,negated_conjecture,
( ~ subset(esk4_0,difference(esk4_0,empty_set))
| ~ subset(difference(esk4_0,empty_set),esk4_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X52,X53,X54] :
( ( member(X52,X54)
| ~ member(X52,difference(X54,X53)) )
& ( ~ member(X52,X53)
| ~ member(X52,difference(X54,X53)) )
& ( ~ member(X52,X54)
| member(X52,X53)
| member(X52,difference(X54,X53)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
cnf(c_0_16,negated_conjecture,
( member(esk1_2(difference(esk4_0,empty_set),esk4_0),difference(esk4_0,empty_set))
| ~ subset(esk4_0,difference(esk4_0,empty_set)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( ~ member(esk1_2(difference(esk4_0,empty_set),esk4_0),esk4_0)
| ~ subset(esk4_0,difference(esk4_0,empty_set)) ),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_18,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( member(esk1_2(difference(esk4_0,empty_set),esk4_0),difference(esk4_0,empty_set))
| member(esk1_2(esk4_0,difference(esk4_0,empty_set)),esk4_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( member(esk1_2(esk4_0,difference(esk4_0,empty_set)),esk4_0)
| ~ member(esk1_2(difference(esk4_0,empty_set),esk4_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_13]) ).
fof(c_0_21,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
cnf(c_0_22,negated_conjecture,
( member(esk1_2(difference(esk4_0,empty_set),esk4_0),difference(esk4_0,empty_set))
| ~ member(esk1_2(esk4_0,difference(esk4_0,empty_set)),difference(esk4_0,empty_set)) ),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_23,negated_conjecture,
( ~ member(esk1_2(esk4_0,difference(esk4_0,empty_set)),difference(esk4_0,empty_set))
| ~ member(esk1_2(difference(esk4_0,empty_set),esk4_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_24,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,negated_conjecture,
member(esk1_2(esk4_0,difference(esk4_0,empty_set)),esk4_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
fof(c_0_26,plain,
! [X51] : ~ member(X51,empty_set),
inference(variable_rename,[status(thm)],[c_0_21]) ).
cnf(c_0_27,negated_conjecture,
~ member(esk1_2(esk4_0,difference(esk4_0,empty_set)),difference(esk4_0,empty_set)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_22]),c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( member(esk1_2(esk4_0,difference(esk4_0,empty_set)),difference(esk4_0,X1))
| member(esk1_2(esk4_0,difference(esk4_0,empty_set)),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET603+4 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % 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
% 0.15/0.32 % Computer : n006.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:29:01 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.27/1.71 % Version : CSE_E---1.7
% 1.27/1.71 % Problem : theBenchmark.p
% 1.27/1.71 % SZS status Theorem for theBenchmark.p
% 1.27/1.71 % SZS output start CNFRefutation
% See solution above
% 1.27/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------