%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU149+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : n004.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 05:10:48 PM UTC 2026
% Result : Theorem 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 65 ( 46 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 71 ( 26 ~; 30 |; 9 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 44 ( 2 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t8_zfmisc_1,conjecture,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
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(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[t8_zfmisc_1]) ).
fof(c_0_5,plain,
! [X156,X157,X158,X159,X160,X161] :
( ( ~ in(X158,X157)
| X158 = X156
| X157 != singleton(X156) )
& ( X159 != X156
| in(X159,X157)
| X157 != singleton(X156) )
& ( ~ in(esk1_2(X160,X161),X161)
| esk1_2(X160,X161) != X160
| X161 = singleton(X160) )
& ( in(esk1_2(X160,X161),X161)
| esk1_2(X160,X161) = X160
| X161 = singleton(X160) ) ),
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)],[d1_tarski])])])])])]) ).
fof(c_0_6,lemma,
! [X298] : unordered_pair(X298,X298) = singleton(X298),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_7,plain,
! [X174,X175,X176,X177,X178,X179,X180,X181] :
( ( ~ in(X177,X176)
| X177 = X174
| X177 = X175
| X176 != unordered_pair(X174,X175) )
& ( X178 != X174
| in(X178,X176)
| X176 != unordered_pair(X174,X175) )
& ( X178 != X175
| in(X178,X176)
| X176 != unordered_pair(X174,X175) )
& ( esk4_3(X179,X180,X181) != X179
| ~ in(esk4_3(X179,X180,X181),X181)
| X181 = unordered_pair(X179,X180) )
& ( esk4_3(X179,X180,X181) != X180
| ~ in(esk4_3(X179,X180,X181),X181)
| X181 = unordered_pair(X179,X180) )
& ( in(esk4_3(X179,X180,X181),X181)
| esk4_3(X179,X180,X181) = X179
| esk4_3(X179,X180,X181) = X180
| X181 = unordered_pair(X179,X180) ) ),
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_8,negated_conjecture,
( singleton(esk14_0) = unordered_pair(esk15_0,esk16_0)
& esk14_0 != esk15_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_9,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
singleton(esk14_0) = unordered_pair(esk15_0,esk16_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( X1 = X3
| X2 != unordered_pair(X3,X3)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
in(X1,unordered_pair(X1,X2)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_11])]) ).
cnf(c_0_15,negated_conjecture,
unordered_pair(esk15_0,esk16_0) = unordered_pair(esk14_0,esk14_0),
inference(rw,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_16,plain,
( X1 = X2
| ~ in(X1,unordered_pair(X2,X2)) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
in(esk15_0,unordered_pair(esk14_0,esk14_0)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
esk14_0 != esk15_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU149+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : n004.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 02:45:47 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Theorem for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------