%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET162+4 : TPTP v9.2.1. Released v2.2.0.
% 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 : n028.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 05:07:29 PM UTC 2026
% Result : Theorem 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 72 ( 35 ~; 26 |; 7 &)
% ( 3 <=>; 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 : 36 ( 2 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI18,conjecture,
! [X1] : equal_set(union(X1,empty_set),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI18) ).
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(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(union,axiom,
! [X3,X1,X2] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',union) ).
fof(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] : equal_set(union(X1,empty_set),X1),
inference(assume_negation,[status(cth)],[thI18]) ).
fof(c_0_6,negated_conjecture,
~ equal_set(union(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(union(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])])])])])]) ).
cnf(c_0_11,negated_conjecture,
( ~ subset(esk4_0,union(esk4_0,empty_set))
| ~ subset(union(esk4_0,empty_set),esk4_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( ~ member(esk1_2(union(esk4_0,empty_set),esk4_0),esk4_0)
| ~ subset(esk4_0,union(esk4_0,empty_set)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_14,plain,
! [X48,X49,X50] :
( ( ~ member(X48,union(X49,X50))
| member(X48,X49)
| member(X48,X50) )
& ( ~ member(X48,X49)
| member(X48,union(X49,X50)) )
& ( ~ member(X48,X50)
| member(X48,union(X49,X50)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union])])]) ).
cnf(c_0_15,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
cnf(c_0_17,negated_conjecture,
( ~ member(esk1_2(esk4_0,union(esk4_0,empty_set)),union(esk4_0,empty_set))
| ~ member(esk1_2(union(esk4_0,empty_set),esk4_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_18,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( member(esk1_2(union(esk4_0,empty_set),esk4_0),union(esk4_0,empty_set))
| ~ subset(esk4_0,union(esk4_0,empty_set)) ),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
fof(c_0_20,plain,
! [X51] : ~ member(X51,empty_set),
inference(variable_rename,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( ~ member(esk1_2(union(esk4_0,empty_set),esk4_0),esk4_0)
| ~ member(esk1_2(esk4_0,union(esk4_0,empty_set)),esk4_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,negated_conjecture,
( member(esk1_2(union(esk4_0,empty_set),esk4_0),union(esk4_0,empty_set))
| ~ member(esk1_2(esk4_0,union(esk4_0,empty_set)),union(esk4_0,empty_set)) ),
inference(spm,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_24,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
~ member(esk1_2(union(esk4_0,empty_set),esk4_0),esk4_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_15]),c_0_21]) ).
cnf(c_0_26,negated_conjecture,
~ member(esk1_2(esk4_0,union(esk4_0,empty_set)),union(esk4_0,empty_set)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25]) ).
cnf(c_0_27,negated_conjecture,
~ member(esk1_2(esk4_0,union(esk4_0,empty_set)),esk4_0),
inference(spm,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_28,negated_conjecture,
member(esk1_2(union(esk4_0,empty_set),esk4_0),union(esk4_0,empty_set)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_15]),c_0_27]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_28]),c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET162+4 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % 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 : n028.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
% 0.15/0.34 % DateTime : Tue May 5 02:13:46 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Theorem for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------