%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET813+4 : TPTP v9.2.1. Released v3.2.0.
% 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 : n014.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 05:08:32 PM UTC 2026
% Result : Theorem 1.27s 1.71s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 3 unt; 0 def)
% Number of atoms : 39 ( 4 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 37 ( 14 ~; 13 |; 5 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 1 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thV12,conjecture,
! [X1] :
( member(X1,on)
=> member(X1,suc(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV12) ).
fof(successor,axiom,
! [X1,X3] :
( member(X3,suc(X1))
<=> member(X3,union(X1,singleton(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',successor) ).
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(singleton,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> member(X1,suc(X1)) ),
inference(assume_negation,[status(cth)],[thV12]) ).
fof(c_0_5,plain,
! [X147,X148] :
( ( ~ member(X148,suc(X147))
| member(X148,union(X147,singleton(X147))) )
& ( ~ member(X148,union(X147,singleton(X147)))
| member(X148,suc(X147)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[successor])]) ).
fof(c_0_6,plain,
! [X79,X80,X81] :
( ( ~ member(X79,union(X80,X81))
| member(X79,X80)
| member(X79,X81) )
& ( ~ member(X79,X80)
| member(X79,union(X80,X81)) )
& ( ~ member(X79,X81)
| member(X79,union(X80,X81)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union])])]) ).
fof(c_0_7,plain,
! [X86,X87] :
( ( ~ member(X86,singleton(X87))
| X86 = X87 )
& ( X86 != X87
| member(X86,singleton(X87)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).
fof(c_0_8,negated_conjecture,
( member(esk14_0,on)
& ~ member(esk14_0,suc(esk14_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_9,plain,
( member(X1,suc(X2))
| ~ member(X1,union(X2,singleton(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( member(X1,singleton(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
~ member(esk14_0,suc(esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( member(X1,suc(X2))
| ~ member(X1,singleton(X2)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
member(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET813+4 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.14/0.32 % Computer : n014.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:36:22 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % 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 : 1.368s
%------------------------------------------------------------------------------