%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU267+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 : n015.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 05:11:18 PM UTC 2026
% Result : Theorem 34.53s 22.75s
% Output : CNFRefutation 34.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 16 unt; 0 def)
% Number of atoms : 76 ( 75 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 80 ( 36 ~; 32 |; 6 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 87 ( 12 sgn 36 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(d2_mcart_1,axiom,
! [X1] :
( ? [X2,X3] : X1 = ordered_pair(X2,X3)
=> ! [X2] :
( X2 = pair_second(X1)
<=> ! [X3,X4] :
( X1 = ordered_pair(X3,X4)
=> X2 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_mcart_1) ).
fof(t7_mcart_1,conjecture,
! [X1,X2] :
( pair_first(ordered_pair(X1,X2)) = X1
& pair_second(ordered_pair(X1,X2)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_mcart_1) ).
fof(d1_mcart_1,axiom,
! [X1] :
( ? [X2,X3] : X1 = ordered_pair(X2,X3)
=> ! [X2] :
( X2 = pair_first(X1)
<=> ! [X3,X4] :
( X1 = ordered_pair(X3,X4)
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_mcart_1) ).
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_6,plain,
! [X1093,X1094] : ordered_pair(X1093,X1094) = unordered_pair(unordered_pair(X1093,X1094),singleton(X1093)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_7,lemma,
! [X1651] : unordered_pair(X1651,X1651) = singleton(X1651),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_8,plain,
! [X931,X932,X933,X934,X935,X936,X937] :
( ( X934 != pair_second(X931)
| X931 != ordered_pair(X935,X936)
| X934 = X936
| X931 != ordered_pair(X932,X933) )
& ( X931 = ordered_pair(esk31_2(X931,X937),esk32_2(X931,X937))
| X937 = pair_second(X931)
| X931 != ordered_pair(X932,X933) )
& ( X937 != esk32_2(X931,X937)
| X937 = pair_second(X931)
| X931 != ordered_pair(X932,X933) ) ),
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_mcart_1])])])])])]) ).
cnf(c_0_9,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1,X2] :
( pair_first(ordered_pair(X1,X2)) = X1
& pair_second(ordered_pair(X1,X2)) = X2 ),
inference(assume_negation,[status(cth)],[t7_mcart_1]) ).
cnf(c_0_12,plain,
( X1 = X4
| X1 != pair_second(X2)
| X2 != ordered_pair(X3,X4)
| X2 != ordered_pair(X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_14,plain,
! [X866,X867,X868,X869,X870,X871,X872] :
( ( X869 != pair_first(X866)
| X866 != ordered_pair(X870,X871)
| X869 = X870
| X866 != ordered_pair(X867,X868) )
& ( X866 = ordered_pair(esk18_2(X866,X872),esk19_2(X866,X872))
| X872 = pair_first(X866)
| X866 != ordered_pair(X867,X868) )
& ( X872 != esk18_2(X866,X872)
| X872 = pair_first(X866)
| X866 != ordered_pair(X867,X868) ) ),
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_mcart_1])])])])])]) ).
fof(c_0_15,negated_conjecture,
( pair_first(ordered_pair(esk132_0,esk133_0)) != esk132_0
| pair_second(ordered_pair(esk132_0,esk133_0)) != esk133_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
cnf(c_0_16,plain,
( X1 = X4
| X1 != pair_second(X2)
| X2 != unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5))
| X2 != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).
cnf(c_0_17,plain,
( X1 = X3
| X1 != pair_first(X2)
| X2 != ordered_pair(X3,X4)
| X2 != ordered_pair(X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( pair_first(ordered_pair(esk132_0,esk133_0)) != esk132_0
| pair_second(ordered_pair(esk132_0,esk133_0)) != esk133_0 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X772,X773] : unordered_pair(X772,X773) = unordered_pair(X773,X772),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_20,plain,
( pair_second(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1))) = X3
| unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)) != unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_16])]) ).
cnf(c_0_21,plain,
( X1 = X3
| X1 != pair_first(X2)
| X2 != unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5))
| X2 != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_13]),c_0_13]) ).
cnf(c_0_22,negated_conjecture,
( pair_first(unordered_pair(unordered_pair(esk132_0,esk133_0),unordered_pair(esk132_0,esk132_0))) != esk132_0
| pair_second(unordered_pair(unordered_pair(esk132_0,esk133_0),unordered_pair(esk132_0,esk132_0))) != esk133_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_13]),c_0_13]) ).
cnf(c_0_23,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
pair_second(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1))) = X2,
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
( pair_first(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1))) = X3
| unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)) != unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_21])]) ).
cnf(c_0_26,negated_conjecture,
( pair_first(unordered_pair(unordered_pair(esk132_0,esk132_0),unordered_pair(esk132_0,esk133_0))) != esk132_0
| pair_second(unordered_pair(unordered_pair(esk132_0,esk132_0),unordered_pair(esk132_0,esk133_0))) != esk133_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]) ).
cnf(c_0_27,plain,
pair_second(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X2))) = X2,
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_28,plain,
pair_first(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1))) = X1,
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
pair_first(unordered_pair(unordered_pair(esk132_0,esk132_0),unordered_pair(esk132_0,esk133_0))) != esk132_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]) ).
cnf(c_0_30,plain,
pair_first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X2))) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_23]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU267+2 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.14/0.32 % Computer : n015.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 02:53:02 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 34.53/22.75 % Version : CSE_E---1.7
% 34.53/22.75 % Problem : theBenchmark.p
% 34.53/22.75 % SZS status Theorem for theBenchmark.p
% 34.53/22.75 % SZS output start CNFRefutation
% See solution above
% 34.63/22.85 % Total time : 18.483s
%------------------------------------------------------------------------------