%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET072+1 : TPTP v9.2.1. Bugfixed v5.4.0.
% 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 : n005.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 05:07:09 PM UTC 2026
% Result : Theorem 1.32s 1.72s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 45 ( 20 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 42 ( 14 ~; 14 |; 11 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 21 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(unordered_pair_defn,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( member(X3,universal_class)
& ( X3 = X1
| X3 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(right_cancellation,conjecture,
! [X1,X2,X5] :
( ( member(X1,universal_class)
& member(X2,universal_class)
& unordered_pair(X1,X5) = unordered_pair(X2,X5) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_cancellation) ).
fof(c_0_2,plain,
! [X108,X109,X110] :
( ( member(X108,universal_class)
| ~ member(X108,unordered_pair(X109,X110)) )
& ( X108 = X109
| X108 = X110
| ~ member(X108,unordered_pair(X109,X110)) )
& ( X108 != X109
| ~ member(X108,universal_class)
| member(X108,unordered_pair(X109,X110)) )
& ( X108 != X110
| ~ member(X108,universal_class)
| member(X108,unordered_pair(X109,X110)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair_defn])])]) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X5] :
( ( member(X1,universal_class)
& member(X2,universal_class)
& unordered_pair(X1,X5) = unordered_pair(X2,X5) )
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[right_cancellation]) ).
cnf(c_0_4,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X2
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
fof(c_0_5,negated_conjecture,
( member(esk8_0,universal_class)
& member(esk9_0,universal_class)
& unordered_pair(esk8_0,esk10_0) = unordered_pair(esk9_0,esk10_0)
& esk8_0 != esk9_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
cnf(c_0_6,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(er,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
unordered_pair(esk8_0,esk10_0) = unordered_pair(esk9_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
member(esk9_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_10,negated_conjecture,
member(esk9_0,unordered_pair(esk8_0,esk10_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8])]) ).
cnf(c_0_11,negated_conjecture,
esk8_0 != esk9_0,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
esk10_0 = esk9_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_13,negated_conjecture,
unordered_pair(esk9_0,esk9_0) = unordered_pair(esk8_0,esk9_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_12]),c_0_12]) ).
cnf(c_0_14,negated_conjecture,
( X1 = esk9_0
| ~ member(X1,unordered_pair(esk8_0,esk9_0)) ),
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_15,negated_conjecture,
member(esk8_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_6]),c_0_15])]),c_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET072+1 : TPTP v9.2.1. Bugfixed v5.4.0.
% 0.00/0.11 % 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
% 0.13/0.32 % Computer : n005.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 02:08:45 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.32/1.72 % Version : CSE_E---1.7
% 1.32/1.72 % Problem : theBenchmark.p
% 1.32/1.72 % SZS status Theorem for theBenchmark.p
% 1.32/1.72 % SZS output start CNFRefutation
% See solution above
% 1.32/1.72 % Total time : 1.369s
%------------------------------------------------------------------------------