%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET903+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 : n012.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 05:08:56 PM UTC 2026
% Result : Theorem 0.14s 1.56s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 23
% Syntax : Number of formulae : 81 ( 38 unt; 0 def)
% Number of atoms : 193 ( 163 equ)
% Maximal formula atoms : 32 ( 2 avg)
% Number of connectives : 191 ( 79 ~; 86 |; 22 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 127 ( 13 sgn 31 !; 3 ?)
% 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(t43_zfmisc_1,axiom,
! [X1,X2,X3] :
~ ( singleton(X1) = set_union2(X2,X3)
& ~ ( X2 = singleton(X1)
& X3 = singleton(X1) )
& ~ ( X2 = empty_set
& X3 = singleton(X1) )
& ~ ( X2 = singleton(X1)
& X3 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_zfmisc_1) ).
fof(t44_zfmisc_1,conjecture,
! [X1,X2,X3] :
~ ( singleton(X1) = set_union2(X2,X3)
& X2 != X3
& X2 != empty_set
& X3 != empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_zfmisc_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
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(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_9,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_10,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_11,plain,
! [X29,X30,X31] :
( ( X30 = singleton(X29)
| X30 = empty_set
| X30 = singleton(X29)
| singleton(X29) != set_union2(X30,X31) )
& ( X31 = empty_set
| X30 = empty_set
| X30 = singleton(X29)
| singleton(X29) != set_union2(X30,X31) )
& ( X30 = singleton(X29)
| X31 = singleton(X29)
| X30 = singleton(X29)
| singleton(X29) != set_union2(X30,X31) )
& ( X31 = empty_set
| X31 = singleton(X29)
| X30 = singleton(X29)
| singleton(X29) != set_union2(X30,X31) )
& ( X30 = singleton(X29)
| X30 = empty_set
| X31 = singleton(X29)
| singleton(X29) != set_union2(X30,X31) )
& ( X31 = empty_set
| X30 = empty_set
| X31 = singleton(X29)
| singleton(X29) != set_union2(X30,X31) )
& ( X30 = singleton(X29)
| X31 = singleton(X29)
| X31 = singleton(X29)
| singleton(X29) != set_union2(X30,X31) )
& ( X31 = empty_set
| X31 = singleton(X29)
| X31 = singleton(X29)
| singleton(X29) != set_union2(X30,X31) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t43_zfmisc_1])])]) ).
fof(i_0_12,negated_conjecture,
~ ! [X1,X2,X3] :
~ ( singleton(X1) = set_union2(X2,X3)
& X2 != X3
& X2 != empty_set
& X3 != empty_set ),
inference(assume_negation,[status(cth)],[t44_zfmisc_1]) ).
fof(i_0_13,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_14,plain,
! [X22,X23] :
( empty(X22)
| ~ empty(set_union2(X22,X23)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_9])]) ).
fof(i_0_15,plain,
! [X24,X25] :
( empty(X24)
| ~ empty(set_union2(X25,X24)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_10])]) ).
cnf(i_0_16,plain,
( X1 = singleton(X2)
| X3 = singleton(X2)
| X1 = singleton(X2)
| singleton(X2) != set_union2(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_11]) ).
cnf(i_0_17,plain,
( X1 = singleton(X2)
| X3 = singleton(X2)
| X3 = singleton(X2)
| singleton(X2) != set_union2(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_11]) ).
cnf(i_0_18,plain,
( X1 = singleton(X2)
| X1 = empty_set
| X1 = singleton(X2)
| singleton(X2) != set_union2(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_11]) ).
cnf(i_0_19,plain,
( X1 = empty_set
| X1 = singleton(X2)
| X1 = singleton(X2)
| singleton(X2) != set_union2(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_11]) ).
fof(i_0_20,plain,
! [X20,X21] : set_union2(X20,X21) = set_union2(X21,X20),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_21,plain,
! [X26] : set_union2(X26,X26) = X26,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_22,negated_conjecture,
( singleton(esk3_0) = set_union2(esk4_0,esk5_0)
& esk4_0 != esk5_0
& esk4_0 != empty_set
& esk5_0 != empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_12])])]) ).
fof(i_0_23,plain,
~ empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_13])]) ).
fof(i_0_24,plain,
empty(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_25,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_26,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_27,plain,
( X1 = singleton(X2)
| X1 = empty_set
| X3 = singleton(X2)
| singleton(X2) != set_union2(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_28,plain,
( X1 = empty_set
| X1 = singleton(X2)
| X3 = singleton(X2)
| singleton(X2) != set_union2(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_29,plain,
( X3 = singleton(X2)
| X1 = singleton(X2)
| singleton(X2) != set_union2(X1,X3) ),
inference(cn,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_30,plain,
( X3 = singleton(X2)
| X1 = singleton(X2)
| singleton(X2) != set_union2(X1,X3) ),
inference(cn,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_31,plain,
( X1 = empty_set
| X2 = empty_set
| X1 = singleton(X3)
| singleton(X3) != set_union2(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_32,plain,
( X1 = empty_set
| X2 = empty_set
| X2 = singleton(X3)
| singleton(X3) != set_union2(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_33,plain,
( X1 = empty_set
| X1 = singleton(X2)
| singleton(X2) != set_union2(X1,X3) ),
inference(cn,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_34,plain,
( X1 = empty_set
| X1 = singleton(X2)
| singleton(X2) != set_union2(X3,X1) ),
inference(cn,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_35,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_36,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_37,negated_conjecture,
singleton(esk3_0) = set_union2(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_38,plain,
~ empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_39,plain,
empty(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_40,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_41,negated_conjecture,
esk4_0 != esk5_0,
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_42,negated_conjecture,
esk5_0 != empty_set,
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_43,negated_conjecture,
esk4_0 != empty_set,
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_44,axiom,
X1 = X1 ).
cnf(i_0_45,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_46,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_47,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_48,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_49,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_50,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_44_001,axiom,
X1 = X1 ).
cnf(i_0_45_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_46_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_47_004,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_48_005,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_49_006,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_50_007,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_51,plain,
set_union2(esk4_0,esk5_0) = singleton(esk3_0),
inference(scs_inference,[],[i_0_37,i_0_45]) ).
cnf(i_0_52,plain,
esk1_0 != esk2_0,
inference(scs_inference,[],[i_0_37,i_0_38,i_0_39,i_0_45,i_0_50]) ).
cnf(i_0_53,plain,
esk4_0 = singleton(esk3_0),
inference(scs_inference,[],[i_0_37,i_0_43,i_0_38,i_0_39,i_0_45,i_0_50,i_0_33]) ).
cnf(i_0_54,plain,
( X1 = empty_set
| X1 = singleton(X2)
| singleton(X2) != set_union2(X1,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_55,plain,
esk5_0 = singleton(esk3_0),
inference(scs_inference,[],[i_0_37,i_0_42,i_0_43,i_0_38,i_0_39,i_0_45,i_0_50,i_0_33,i_0_34]) ).
cnf(i_0_56,plain,
( X1 = empty_set
| X1 = singleton(X2)
| singleton(X2) != set_union2(X3,X1) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_57,plain,
set_union2(singleton(esk3_0),singleton(esk3_0)) = set_union2(esk4_0,esk5_0),
inference(scs_inference,[],[i_0_37,i_0_42,i_0_43,i_0_36,i_0_38,i_0_39,i_0_45,i_0_50,i_0_33,i_0_34,i_0_46]) ).
cnf(i_0_58,plain,
set_union2(X1,X1) = X1,
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_59,plain,
singleton(esk3_0) = esk4_0,
inference(scs_inference,[],[i_0_53,i_0_45]) ).
cnf(i_0_60,plain,
empty_set != esk2_0,
inference(scs_inference,[],[i_0_53,i_0_40,i_0_38,i_0_45,i_0_50]) ).
cnf(i_0_61,plain,
esk4_0 = set_union2(esk4_0,esk5_0),
inference(scs_inference,[],[i_0_37,i_0_53,i_0_40,i_0_38,i_0_45,i_0_50,i_0_46]) ).
cnf(i_0_62,plain,
( esk5_0 = singleton(X1)
| singleton(X1) != set_union2(esk5_0,X2) ),
inference(scs_inference,[],[i_0_37,i_0_42,i_0_53,i_0_40,i_0_38,i_0_45,i_0_50,i_0_46,i_0_33]) ).
cnf(i_0_63,plain,
( X1 = empty_set
| X1 = singleton(X2)
| singleton(X2) != set_union2(X1,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_64,plain,
( esk4_0 = singleton(X1)
| singleton(X1) != set_union2(X2,esk4_0) ),
inference(scs_inference,[],[i_0_37,i_0_42,i_0_43,i_0_53,i_0_40,i_0_38,i_0_45,i_0_50,i_0_46,i_0_33,i_0_34]) ).
cnf(i_0_65,plain,
( X1 = empty_set
| X1 = singleton(X2)
| singleton(X2) != set_union2(X3,X1) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_66,plain,
singleton(esk3_0) = esk5_0,
inference(scs_inference,[],[i_0_55,i_0_45]) ).
cnf(i_0_67,plain,
esk5_0 = set_union2(esk4_0,esk5_0),
inference(scs_inference,[],[i_0_37,i_0_55,i_0_45,i_0_46]) ).
cnf(i_0_68,plain,
set_union2(esk4_0,esk5_0) = set_union2(singleton(esk3_0),singleton(esk3_0)),
inference(scs_inference,[],[i_0_57,i_0_45]) ).
cnf(i_0_69,plain,
set_union2(esk4_0,esk5_0) = esk4_0,
inference(scs_inference,[],[i_0_51,i_0_57,i_0_59,i_0_45,i_0_46]) ).
cnf(i_0_70,plain,
set_union2(esk4_0,esk5_0) = esk5_0,
inference(scs_inference,[],[i_0_67,i_0_45]) ).
cnf(i_0_71,plain,
singleton(esk3_0) = set_union2(singleton(esk3_0),singleton(esk3_0)),
inference(scs_inference,[],[i_0_37,i_0_68,i_0_67,i_0_45,i_0_46]) ).
cnf(i_0_72,plain,
X1 = set_union2(X1,X1),
inference(scs_inference,[],[i_0_36,i_0_45]) ).
cnf(i_0_73,plain,
$false,
inference(scs_inference,[],[i_0_41,i_0_66,i_0_36,i_0_53,i_0_45,i_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET903+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.10 % 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
% 0.07/0.29 % Computer : n012.cluster.edu
% 0.07/0.29 % Model : x86_64 x86_64
% 0.07/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.29 % Memory : 8042.1875MB
% 0.07/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.29 % CPULimit : 300
% 0.07/0.29 % WCLimit : 300
% 0.07/0.29 % DateTime : Tue May 5 02:40:16 EDT 2026
% 0.07/0.29 % CPUTime :
% 0.07/0.30 % start to proof: theBenchmark
% 0.14/1.56 % Version : CSE_E---1.7
% 0.14/1.56 % Problem : theBenchmark.p
% 0.14/1.56 % SZS status Theorem for theBenchmark.p
% 0.14/1.56 % SZS output start CNFRefutation
% See solution above
% 0.14/1.59 % Total time : 1.261s
%------------------------------------------------------------------------------