%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET954+1 : 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 : n029.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 05:09:02 PM UTC 2026
% Result : Theorem 0.27s 1.62s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_17)
% Comments :
%------------------------------------------------------------------------------
fof(t107_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
=> in(ordered_pair(X2,X1),cartesian_product2(X4,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_zfmisc_1) ).
fof(fc1_zfmisc_1,axiom,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(l55_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_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(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
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(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(i_0_8,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
=> in(ordered_pair(X2,X1),cartesian_product2(X4,X3)) ),
inference(assume_negation,[status(cth)],[t107_zfmisc_1]) ).
fof(i_0_9,plain,
! [X1,X2] : ~ empty(ordered_pair(X1,X2)),
inference(fof_simplification,[status(thm)],[fc1_zfmisc_1]) ).
fof(i_0_10,plain,
! [X31,X32,X33,X34] :
( ( in(X31,X33)
| ~ in(ordered_pair(X31,X32),cartesian_product2(X33,X34)) )
& ( in(X32,X34)
| ~ in(ordered_pair(X31,X32),cartesian_product2(X33,X34)) )
& ( ~ in(X31,X33)
| ~ in(X32,X34)
| in(ordered_pair(X31,X32),cartesian_product2(X33,X34)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
fof(i_0_11,plain,
! [X27,X28] : ordered_pair(X27,X28) = unordered_pair(unordered_pair(X27,X28),singleton(X27)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(i_0_12,negated_conjecture,
( in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
& ~ in(ordered_pair(esk4_0,esk3_0),cartesian_product2(esk6_0,esk5_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_8])])]) ).
fof(i_0_13,plain,
! [X29,X30] : ~ empty(ordered_pair(X29,X30)),
inference(variable_rename,[status(thm)],[i_0_9]) ).
fof(i_0_14,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_15,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
cnf(i_0_16,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_10]) ).
cnf(i_0_17,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[i_0_11]) ).
cnf(i_0_18,plain,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_10]) ).
cnf(i_0_19,plain,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_10]) ).
cnf(i_0_20,negated_conjecture,
~ in(ordered_pair(esk4_0,esk3_0),cartesian_product2(esk6_0,esk5_0)),
inference(split_conjunct,[status(thm)],[i_0_12]) ).
cnf(i_0_21,plain,
~ empty(ordered_pair(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_13]) ).
cnf(i_0_22,negated_conjecture,
in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[i_0_12]) ).
fof(i_0_23,plain,
! [X23,X24] :
( ~ in(X23,X24)
| ~ in(X24,X23) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_14])]) ).
fof(i_0_24,plain,
! [X25,X26] : unordered_pair(X25,X26) = unordered_pair(X26,X25),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_25,plain,
~ empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_15])]) ).
fof(i_0_26,plain,
empty(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_27,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[i_0_16,c_0_17]),
[final] ).
cnf(i_0_28,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[i_0_18,c_0_17]),
[final] ).
cnf(i_0_29,plain,
( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[i_0_19,c_0_17]),
[final] ).
cnf(i_0_30,negated_conjecture,
~ in(unordered_pair(unordered_pair(esk4_0,esk3_0),singleton(esk4_0)),cartesian_product2(esk6_0,esk5_0)),
inference(rw,[status(thm)],[i_0_20,c_0_17]),
[final] ).
cnf(i_0_31,plain,
~ empty(unordered_pair(unordered_pair(X1,X2),singleton(X1))),
inference(rw,[status(thm)],[i_0_21,c_0_17]),
[final] ).
cnf(i_0_32,negated_conjecture,
in(unordered_pair(unordered_pair(esk3_0,esk4_0),singleton(esk3_0)),cartesian_product2(esk5_0,esk6_0)),
inference(rw,[status(thm)],[i_0_22,c_0_17]),
[final] ).
cnf(i_0_33,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_34,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_35,plain,
~ empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_36,plain,
empty(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_37,axiom,
X1 = X1 ).
cnf(i_0_38,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_39,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_40,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_41,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_42,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_43,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_44,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_37_001,axiom,
X1 = X1 ).
cnf(i_0_38_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_39_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_40_004,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_41_005,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_42_006,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_43_007,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_44_008,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_45,plain,
in(esk3_0,esk5_0),
inference(scs_inference,[],[i_0_32,i_0_27]) ).
cnf(i_0_46,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| in(X1,X3) ),
inference(rename_variables,[],[i_0_27]) ).
cnf(i_0_47,plain,
in(esk4_0,esk6_0),
inference(scs_inference,[],[i_0_32,i_0_27,i_0_28]) ).
cnf(i_0_48,plain,
( ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
| in(X2,X4) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_49,plain,
~ in(cartesian_product2(esk5_0,esk6_0),unordered_pair(unordered_pair(esk3_0,esk4_0),singleton(esk3_0))),
inference(scs_inference,[],[i_0_32,i_0_27,i_0_28,i_0_33]) ).
cnf(i_0_50,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_51,plain,
$false,
inference(scs_inference,[],[i_0_30,i_0_32,i_0_27,i_0_28,i_0_33,i_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET954+1 : 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
% 0.15/0.33 % Computer : n029.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:39:59 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.27/1.62 % Version : CSE_E---1.7
% 0.27/1.62 % Problem : theBenchmark.p
% 0.27/1.62 % SZS status Theorem for theBenchmark.p
% 0.27/1.62 % SZS output start CNFRefutation
% See solution above
% 0.27/1.64 % Total time : 1.272s
%------------------------------------------------------------------------------