%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU159+3 : TPTP v9.2.1. Released v3.2.0.
% 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 : n013.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 05:10:51 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 103 ( 33 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 107 ( 38 ~; 52 |; 11 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 69 ( 4 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(t38_zfmisc_1,conjecture,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(c_0_4,plain,
! [X27,X28,X29,X30,X31,X32,X33,X34] :
( ( ~ in(X30,X29)
| X30 = X27
| X30 = X28
| X29 != unordered_pair(X27,X28) )
& ( X31 != X27
| in(X31,X29)
| X29 != unordered_pair(X27,X28) )
& ( X31 != X28
| in(X31,X29)
| X29 != unordered_pair(X27,X28) )
& ( esk1_3(X32,X33,X34) != X32
| ~ in(esk1_3(X32,X33,X34),X34)
| X34 = unordered_pair(X32,X33) )
& ( esk1_3(X32,X33,X34) != X33
| ~ in(esk1_3(X32,X33,X34),X34)
| X34 = unordered_pair(X32,X33) )
& ( in(esk1_3(X32,X33,X34),X34)
| esk1_3(X32,X33,X34) = X32
| esk1_3(X32,X33,X34) = X33
| X34 = unordered_pair(X32,X33) ) ),
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)],[d2_tarski])])])])])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),X3)
<=> ( in(X1,X3)
& in(X2,X3) ) ),
inference(assume_negation,[status(cth)],[t38_zfmisc_1]) ).
cnf(c_0_6,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_7,plain,
! [X36,X37,X38,X39,X40] :
( ( ~ subset(X36,X37)
| ~ in(X38,X36)
| in(X38,X37) )
& ( in(esk2_2(X39,X40),X39)
| subset(X39,X40) )
& ( ~ in(esk2_2(X39,X40),X40)
| subset(X39,X40) ) ),
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)],[d3_tarski])])])])])]) ).
fof(c_0_8,negated_conjecture,
( ( ~ subset(unordered_pair(esk5_0,esk6_0),esk7_0)
| ~ in(esk5_0,esk7_0)
| ~ in(esk6_0,esk7_0) )
& ( in(esk5_0,esk7_0)
| subset(unordered_pair(esk5_0,esk6_0),esk7_0) )
& ( in(esk6_0,esk7_0)
| subset(unordered_pair(esk5_0,esk6_0),esk7_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
cnf(c_0_9,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X3,X2)) ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( in(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( in(esk6_0,esk7_0)
| subset(unordered_pair(esk5_0,esk6_0),esk7_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_14,negated_conjecture,
( in(esk5_0,esk7_0)
| subset(unordered_pair(esk5_0,esk6_0),esk7_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_16,plain,
( subset(X1,X2)
| ~ in(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,plain,
( esk2_2(unordered_pair(X1,X2),X3) = X2
| esk2_2(unordered_pair(X1,X2),X3) = X1
| subset(unordered_pair(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_18,negated_conjecture,
( in(esk6_0,esk7_0)
| in(X1,esk7_0)
| ~ in(X1,unordered_pair(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_19,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_13])]) ).
cnf(c_0_20,negated_conjecture,
( in(esk5_0,esk7_0)
| in(X1,esk7_0)
| ~ in(X1,unordered_pair(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_21,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_15])]) ).
cnf(c_0_22,plain,
( esk2_2(unordered_pair(X1,X2),X3) = X2
| subset(unordered_pair(X1,X2),X3)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
in(esk6_0,esk7_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( ~ subset(unordered_pair(esk5_0,esk6_0),esk7_0)
| ~ in(esk5_0,esk7_0)
| ~ in(esk6_0,esk7_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
in(esk5_0,esk7_0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
( esk2_2(unordered_pair(esk6_0,X1),esk7_0) = X1
| subset(unordered_pair(esk6_0,X1),esk7_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_27,plain,
! [X25,X26] : unordered_pair(X25,X26) = unordered_pair(X26,X25),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_28,negated_conjecture,
( ~ subset(unordered_pair(esk5_0,esk6_0),esk7_0)
| ~ in(esk6_0,esk7_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_29,negated_conjecture,
( subset(unordered_pair(esk6_0,X1),esk7_0)
| ~ in(X1,esk7_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_30,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,negated_conjecture,
~ subset(unordered_pair(esk5_0,esk6_0),esk7_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_23])]) ).
cnf(c_0_32,negated_conjecture,
( subset(unordered_pair(X1,esk6_0),esk7_0)
| ~ in(X1,esk7_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU159+3 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.16/0.33 % Computer : n013.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:46:26 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------