%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU267+1 : 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 : n021.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 1.24s 1.71s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 4 unt; 0 def)
% Number of atoms : 52 ( 51 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 62 ( 26 ~; 24 |; 6 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 54 ( 10 sgn 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(c_0_3,plain,
! [X64,X65,X66,X67,X68,X69,X70] :
( ( X67 != pair_second(X64)
| X64 != ordered_pair(X68,X69)
| X67 = X69
| X64 != ordered_pair(X65,X66) )
& ( X64 = ordered_pair(esk8_2(X64,X70),esk9_2(X64,X70))
| X70 = pair_second(X64)
| X64 != ordered_pair(X65,X66) )
& ( X70 != esk9_2(X64,X70)
| X70 = pair_second(X64)
| X64 != ordered_pair(X65,X66) ) ),
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])])])])])]) ).
fof(c_0_4,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_5,plain,
( X1 = X4
| X1 != pair_second(X2)
| X2 != ordered_pair(X3,X4)
| X2 != ordered_pair(X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_6,plain,
! [X55,X56,X57,X58,X59,X60,X61] :
( ( X58 != pair_first(X55)
| X55 != ordered_pair(X59,X60)
| X58 = X59
| X55 != ordered_pair(X56,X57) )
& ( X55 = ordered_pair(esk6_2(X55,X61),esk7_2(X55,X61))
| X61 = pair_first(X55)
| X55 != ordered_pair(X56,X57) )
& ( X61 != esk6_2(X55,X61)
| X61 = pair_first(X55)
| X55 != ordered_pair(X56,X57) ) ),
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_7,negated_conjecture,
( pair_first(ordered_pair(esk4_0,esk5_0)) != esk4_0
| pair_second(ordered_pair(esk4_0,esk5_0)) != esk5_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_8,plain,
( pair_second(ordered_pair(X1,X2)) = X3
| ordered_pair(X1,X2) != ordered_pair(X4,X3) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_5])]) ).
cnf(c_0_9,plain,
( X1 = X3
| X1 != pair_first(X2)
| X2 != ordered_pair(X3,X4)
| X2 != ordered_pair(X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( pair_first(ordered_pair(esk4_0,esk5_0)) != esk4_0
| pair_second(ordered_pair(esk4_0,esk5_0)) != esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
pair_second(ordered_pair(X1,X2)) = X2,
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( pair_first(ordered_pair(X1,X2)) = X3
| ordered_pair(X1,X2) != ordered_pair(X3,X4) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_9])]) ).
cnf(c_0_13,negated_conjecture,
pair_first(ordered_pair(esk4_0,esk5_0)) != esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11])]) ).
cnf(c_0_14,plain,
pair_first(ordered_pair(X1,X2)) = X1,
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU267+1 : 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 : n021.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 02:53:56 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.24/1.71 % Version : CSE_E---1.7
% 1.24/1.71 % Problem : theBenchmark.p
% 1.24/1.71 % SZS status Theorem for theBenchmark.p
% 1.24/1.71 % SZS output start CNFRefutation
% See solution above
% 1.24/1.71 % Total time : 1.370s
%------------------------------------------------------------------------------