%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET979+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 05:09:04 PM UTC 2026
% Result : Theorem 0.24s 1.61s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_18)
% Comments :
%------------------------------------------------------------------------------
fof(t132_zfmisc_1,conjecture,
! [X1,X2,X3] :
( cartesian_product2(unordered_pair(X1,X2),X3) = set_union2(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X3))
& cartesian_product2(X3,unordered_pair(X1,X2)) = set_union2(cartesian_product2(X3,singleton(X1)),cartesian_product2(X3,singleton(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t132_zfmisc_1) ).
fof(t41_enumset1,axiom,
! [X1,X2] : unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_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(fc2_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(t120_zfmisc_1,axiom,
! [X1,X2,X3] :
( cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& cartesian_product2(X3,set_union2(X1,X2)) = set_union2(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(i_0_10,negated_conjecture,
~ ! [X1,X2,X3] :
( cartesian_product2(unordered_pair(X1,X2),X3) = set_union2(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X3))
& cartesian_product2(X3,unordered_pair(X1,X2)) = set_union2(cartesian_product2(X3,singleton(X1)),cartesian_product2(X3,singleton(X2))) ),
inference(assume_negation,[status(cth)],[t132_zfmisc_1]) ).
fof(i_0_11,negated_conjecture,
( cartesian_product2(unordered_pair(esk3_0,esk4_0),esk5_0) != set_union2(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk5_0))
| cartesian_product2(esk5_0,unordered_pair(esk3_0,esk4_0)) != set_union2(cartesian_product2(esk5_0,singleton(esk3_0)),cartesian_product2(esk5_0,singleton(esk4_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_10])])]) ).
fof(i_0_12,plain,
! [X41,X42] : unordered_pair(X41,X42) = set_union2(singleton(X41),singleton(X42)),
inference(variable_rename,[status(thm)],[t41_enumset1]) ).
fof(i_0_13,plain,
! [X24,X25] : unordered_pair(X24,X25) = unordered_pair(X25,X24),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_14,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_15,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_16,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
cnf(i_0_17,negated_conjecture,
( cartesian_product2(unordered_pair(esk3_0,esk4_0),esk5_0) != set_union2(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk5_0))
| cartesian_product2(esk5_0,unordered_pair(esk3_0,esk4_0)) != set_union2(cartesian_product2(esk5_0,singleton(esk3_0)),cartesian_product2(esk5_0,singleton(esk4_0))) ),
inference(split_conjunct,[status(thm)],[i_0_11]) ).
cnf(i_0_18,plain,
unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
inference(split_conjunct,[status(thm)],[i_0_12]) ).
fof(i_0_19,plain,
! [X35,X36,X37] :
( cartesian_product2(set_union2(X35,X36),X37) = set_union2(cartesian_product2(X35,X37),cartesian_product2(X36,X37))
& cartesian_product2(X37,set_union2(X35,X36)) = set_union2(cartesian_product2(X37,X35),cartesian_product2(X37,X36)) ),
inference(variable_rename,[status(thm)],[t120_zfmisc_1]) ).
cnf(i_0_20,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_13]) ).
fof(i_0_21,plain,
! [X28,X29] :
( empty(X28)
| ~ empty(set_union2(X28,X29)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_14])]) ).
fof(i_0_22,plain,
! [X30,X31] :
( empty(X30)
| ~ empty(set_union2(X31,X30)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_15])]) ).
fof(i_0_23,plain,
! [X26,X27] : set_union2(X26,X27) = set_union2(X27,X26),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_24,plain,
! [X32] : set_union2(X32,X32) = X32,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_25,plain,
~ empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_16])]) ).
fof(i_0_26,plain,
empty(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_27,negated_conjecture,
( cartesian_product2(esk5_0,set_union2(singleton(esk3_0),singleton(esk4_0))) != set_union2(cartesian_product2(esk5_0,singleton(esk3_0)),cartesian_product2(esk5_0,singleton(esk4_0)))
| cartesian_product2(set_union2(singleton(esk3_0),singleton(esk4_0)),esk5_0) != set_union2(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk5_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_17,c_0_18]),c_0_18]),
[final] ).
cnf(i_0_28,plain,
cartesian_product2(set_union2(X1,X2),X3) = set_union2(cartesian_product2(X1,X3),cartesian_product2(X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_29,plain,
cartesian_product2(X1,set_union2(X2,X3)) = set_union2(cartesian_product2(X1,X2),cartesian_product2(X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_30,plain,
set_union2(singleton(X1),singleton(X2)) = set_union2(singleton(X2),singleton(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_20,c_0_18]),c_0_18]),
[final] ).
cnf(i_0_31,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_32,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_33,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_34,plain,
set_union2(X1,X1) = 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
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_41,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_42,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_43,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(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
| cartesian_product2(X1,X3) = cartesian_product2(X2,X3) ) ).
cnf(i_0_41_005,axiom,
( X1 != X2
| cartesian_product2(X3,X1) = cartesian_product2(X3,X2) ) ).
cnf(i_0_42_006,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_43_007,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_44_008,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_45,plain,
$false,
inference(scs_inference,[],[i_0_29,i_0_28,i_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET979+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.16/0.32 % Computer : n029.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % 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 02:41:29 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.24/1.61 % Version : CSE_E---1.7
% 0.24/1.61 % Problem : theBenchmark.p
% 0.24/1.61 % SZS status Theorem for theBenchmark.p
% 0.24/1.61 % SZS output start CNFRefutation
% See solution above
% 0.24/1.62 % Total time : 1.270s
%------------------------------------------------------------------------------