%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU156+3 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.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 05:10:50 PM UTC 2026
% Result : Theorem 1.30s 1.73s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 19 unt; 0 def)
% Number of atoms : 88 ( 87 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 68 ( 27 ~; 32 |; 5 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 79 ( 9 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t33_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(t69_enumset1,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t10_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
~ ( unordered_pair(X1,X2) = unordered_pair(X3,X4)
& X1 != X3
& X1 != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(t8_zfmisc_1,axiom,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(t9_zfmisc_1,axiom,
! [X1,X2,X3] :
( singleton(X1) = unordered_pair(X2,X3)
=> X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ordered_pair(X1,X2) = ordered_pair(X3,X4)
=> ( X1 = X3
& X2 = X4 ) ),
inference(assume_negation,[status(cth)],[t33_zfmisc_1]) ).
fof(c_0_8,plain,
! [X34,X35] : ordered_pair(X34,X35) = unordered_pair(unordered_pair(X34,X35),singleton(X34)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_9,plain,
! [X49] : unordered_pair(X49,X49) = singleton(X49),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_10,negated_conjecture,
( ordered_pair(esk3_0,esk4_0) = ordered_pair(esk5_0,esk6_0)
& ( esk3_0 != esk5_0
| esk4_0 != esk6_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_11,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
ordered_pair(esk3_0,esk4_0) = ordered_pair(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_15,plain,
! [X32,X33] : unordered_pair(X32,X33) = unordered_pair(X33,X32),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_16,plain,
! [X41,X42,X43,X44] :
( unordered_pair(X41,X42) != unordered_pair(X43,X44)
| X41 = X43
| X41 = X44 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t10_zfmisc_1])]) ).
cnf(c_0_17,negated_conjecture,
unordered_pair(unordered_pair(esk5_0,esk6_0),unordered_pair(esk5_0,esk5_0)) = unordered_pair(unordered_pair(esk3_0,esk4_0),unordered_pair(esk3_0,esk3_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).
cnf(c_0_18,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X52,X53,X54] :
( singleton(X52) != unordered_pair(X53,X54)
| X52 = X53 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_zfmisc_1])]) ).
cnf(c_0_20,plain,
( X1 = X3
| X1 = X4
| unordered_pair(X1,X2) != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
unordered_pair(unordered_pair(esk3_0,esk3_0),unordered_pair(esk3_0,esk4_0)) = unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).
cnf(c_0_22,plain,
( X1 = X2
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( X1 = unordered_pair(esk3_0,esk3_0)
| X1 = unordered_pair(esk3_0,esk4_0)
| unordered_pair(X1,X2) != unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
( X1 = X2
| X1 = X3
| unordered_pair(X4,X1) != unordered_pair(X2,X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_25,plain,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[c_0_22,c_0_12]) ).
cnf(c_0_26,negated_conjecture,
( unordered_pair(esk3_0,esk4_0) = unordered_pair(esk5_0,esk5_0)
| unordered_pair(esk3_0,esk3_0) = unordered_pair(esk5_0,esk5_0) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( X1 = unordered_pair(esk3_0,esk4_0)
| X1 = unordered_pair(esk3_0,esk3_0)
| unordered_pair(X2,X1) != unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_28,negated_conjecture,
( unordered_pair(esk3_0,esk3_0) = unordered_pair(esk5_0,esk5_0)
| X1 = esk3_0
| unordered_pair(X1,X1) != unordered_pair(esk5_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
( X1 = X2
| unordered_pair(X1,X1) != unordered_pair(X3,X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_30,negated_conjecture,
( unordered_pair(esk3_0,esk3_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk3_0,esk4_0) = unordered_pair(esk5_0,esk6_0) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_31,negated_conjecture,
esk3_0 = esk5_0,
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_28]),c_0_29]) ).
fof(c_0_32,plain,
! [X55,X56,X57] :
( singleton(X55) != unordered_pair(X56,X57)
| X56 = X57 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_zfmisc_1])]) ).
cnf(c_0_33,negated_conjecture,
( unordered_pair(esk3_0,esk4_0) = X1
| unordered_pair(esk3_0,esk4_0) = X2
| unordered_pair(unordered_pair(esk5_0,esk5_0),unordered_pair(esk5_0,esk6_0)) != unordered_pair(X2,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_34,negated_conjecture,
( unordered_pair(esk5_0,esk4_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk5_0,esk6_0) = unordered_pair(esk5_0,esk5_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_31]),c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( esk3_0 != esk5_0
| esk4_0 != esk6_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_36,plain,
( X2 = X3
| singleton(X1) != unordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( unordered_pair(esk3_0,esk4_0) = unordered_pair(esk5_0,esk5_0)
| unordered_pair(esk3_0,esk4_0) = unordered_pair(esk5_0,esk6_0) ),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
( unordered_pair(esk5_0,esk6_0) = unordered_pair(esk5_0,esk5_0)
| X1 = esk4_0
| X1 = esk5_0
| unordered_pair(X2,X1) != unordered_pair(esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
esk4_0 != esk6_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_31])]) ).
cnf(c_0_40,plain,
( X2 = X3
| unordered_pair(X1,X1) != unordered_pair(X2,X3) ),
inference(rw,[status(thm)],[c_0_36,c_0_12]) ).
cnf(c_0_41,negated_conjecture,
( unordered_pair(esk5_0,esk4_0) = unordered_pair(esk5_0,esk6_0)
| unordered_pair(esk5_0,esk4_0) = unordered_pair(esk5_0,esk5_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_31]),c_0_31]) ).
cnf(c_0_42,negated_conjecture,
esk6_0 = esk5_0,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_38]),c_0_39]),c_0_29]) ).
cnf(c_0_43,negated_conjecture,
( esk4_0 = esk5_0
| unordered_pair(X1,X1) != unordered_pair(esk5_0,esk6_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_29]) ).
cnf(c_0_44,negated_conjecture,
esk4_0 != esk5_0,
inference(rw,[status(thm)],[c_0_39,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
unordered_pair(X1,X1) != unordered_pair(esk5_0,esk5_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_42]),c_0_44]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU156+3 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n018.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 02:45:32 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.30/1.73 % Version : CSE_E---1.7
% 1.30/1.73 % Problem : theBenchmark.p
% 1.30/1.73 % SZS status Theorem for theBenchmark.p
% 1.30/1.73 % SZS output start CNFRefutation
% See solution above
% 1.30/1.73 % Total time : 1.369s
%------------------------------------------------------------------------------