%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET891+1 : TPTP v9.2.1. Released v3.2.0.
% 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 05:08:55 PM UTC 2026
% Result : Theorem 0.25s 1.61s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_21)
% Comments :
%------------------------------------------------------------------------------
fof(fc2_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(l52_zfmisc_1,axiom,
! [X1,X2] : union(unordered_pair(X1,X2)) = set_union2(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l52_zfmisc_1) ).
fof(t32_zfmisc_1,conjecture,
! [X1,X2] : union(unordered_pair(singleton(X1),singleton(X2))) = unordered_pair(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_zfmisc_1) ).
fof(t41_enumset1,axiom,
! [X1,X2] : unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_enumset1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
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(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(i_0_10,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_11,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_12,plain,
! [X25,X26] :
( empty(X25)
| ~ empty(set_union2(X25,X26)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_10])]) ).
fof(i_0_13,plain,
! [X30,X31] : union(unordered_pair(X30,X31)) = set_union2(X30,X31),
inference(variable_rename,[status(thm)],[l52_zfmisc_1]) ).
fof(i_0_14,plain,
! [X27,X28] :
( empty(X27)
| ~ empty(set_union2(X28,X27)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_11])]) ).
fof(i_0_15,negated_conjecture,
~ ! [X1,X2] : union(unordered_pair(singleton(X1),singleton(X2))) = unordered_pair(X1,X2),
inference(assume_negation,[status(cth)],[t32_zfmisc_1]) ).
fof(i_0_16,plain,
! [X36,X37] : unordered_pair(X36,X37) = set_union2(singleton(X36),singleton(X37)),
inference(variable_rename,[status(thm)],[t41_enumset1]) ).
fof(i_0_17,plain,
! [X23,X24] : set_union2(X23,X24) = set_union2(X24,X23),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_18,plain,
! [X29] : set_union2(X29,X29) = X29,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_19,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
cnf(i_0_20,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_12]) ).
cnf(i_0_21,plain,
union(unordered_pair(X1,X2)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[i_0_13]) ).
cnf(i_0_22,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_14]) ).
fof(i_0_23,negated_conjecture,
union(unordered_pair(singleton(esk3_0),singleton(esk4_0))) != unordered_pair(esk3_0,esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_15])])]) ).
cnf(i_0_24,plain,
unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
inference(split_conjunct,[status(thm)],[i_0_16]) ).
cnf(i_0_25,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_17]) ).
cnf(i_0_26,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_18]) ).
fof(i_0_27,plain,
! [X21,X22] : unordered_pair(X21,X22) = unordered_pair(X22,X21),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(i_0_28,plain,
~ empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_19])]) ).
fof(i_0_29,plain,
empty(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_30,plain,
( empty(X1)
| ~ empty(union(unordered_pair(X1,X2))) ),
inference(rw,[status(thm)],[i_0_20,c_0_21]),
[final] ).
cnf(i_0_31,plain,
( empty(X1)
| ~ empty(union(unordered_pair(X2,X1))) ),
inference(rw,[status(thm)],[i_0_22,c_0_21]),
[final] ).
cnf(i_0_32,negated_conjecture,
union(unordered_pair(singleton(esk3_0),singleton(esk4_0))) != unordered_pair(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_33,plain,
unordered_pair(X1,X2) = union(unordered_pair(singleton(X1),singleton(X2))),
inference(rw,[status(thm)],[i_0_24,c_0_21]),
[final] ).
cnf(i_0_34,plain,
union(unordered_pair(X1,X2)) = union(unordered_pair(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_25,c_0_21]),c_0_21]),
[final] ).
cnf(i_0_35,plain,
union(unordered_pair(X1,X1)) = X1,
inference(rw,[status(thm)],[i_0_26,c_0_21]),
[final] ).
cnf(i_0_36,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_37,plain,
~ empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_38,plain,
empty(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_39,axiom,
X1 = X1 ).
cnf(i_0_40,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_41,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_42,axiom,
( X1 != X2
| union(X1) = union(X2) ) ).
cnf(i_0_43,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_44,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_45,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_39_001,axiom,
X1 = X1 ).
cnf(i_0_40_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_41_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_42_004,axiom,
( X1 != X2
| union(X1) = union(X2) ) ).
cnf(i_0_43_005,axiom,
( X1 != X2
| unordered_pair(X1,X3) = unordered_pair(X2,X3) ) ).
cnf(i_0_44_006,axiom,
( X1 != X2
| unordered_pair(X3,X1) = unordered_pair(X3,X2) ) ).
cnf(i_0_45_007,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_46,plain,
$false,
inference(scs_inference,[],[i_0_32,i_0_33,i_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET891+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.14/0.33 % Computer : n021.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:39:25 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 0.25/1.61 % Version : CSE_E---1.7
% 0.25/1.61 % Problem : theBenchmark.p
% 0.25/1.61 % SZS status Theorem for theBenchmark.p
% 0.25/1.61 % SZS output start CNFRefutation
% See solution above
% 0.25/1.63 % Total time : 1.273s
%------------------------------------------------------------------------------