%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET904+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 : n019.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 0.26s 1.62s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 30
% Syntax : Number of formulae : 57 ( 21 unt; 0 def)
% Number of atoms : 105 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 105 ( 57 ~; 38 |; 1 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 103 ( 4 sgn 36 !; 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(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t45_zfmisc_1,conjecture,
! [X1,X2] :
( subset(set_union2(singleton(X1),X2),X2)
=> in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_zfmisc_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(l21_zfmisc_1,axiom,
! [X1,X2] :
( subset(set_union2(singleton(X1),X2),X2)
=> in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_zfmisc_1) ).
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(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_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,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_13,negated_conjecture,
~ ! [X1,X2] :
( subset(set_union2(singleton(X1),X2),X2)
=> in(X1,X2) ),
inference(assume_negation,[status(cth)],[t45_zfmisc_1]) ).
fof(i_0_14,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_15,plain,
! [X35,X36] :
( ~ subset(set_union2(singleton(X35),X36),X36)
| in(X35,X36) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l21_zfmisc_1])]) ).
fof(i_0_16,plain,
! [X21,X22] :
( empty(X21)
| ~ empty(set_union2(X21,X22)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_10])]) ).
fof(i_0_17,plain,
! [X23,X24] :
( empty(X23)
| ~ empty(set_union2(X24,X23)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_11])]) ).
fof(i_0_18,plain,
! [X29,X30] :
( ~ in(X29,X30)
| ~ in(X30,X29) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_12])]) ).
fof(i_0_19,negated_conjecture,
( subset(set_union2(singleton(esk3_0),esk4_0),esk4_0)
& ~ in(esk3_0,esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_13])])]) ).
fof(i_0_20,plain,
! [X25,X26] : set_union2(X25,X26) = set_union2(X26,X25),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_21,plain,
! [X27] : set_union2(X27,X27) = X27,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_22,plain,
! [X28] : subset(X28,X28),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_23,plain,
~ empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_14])]) ).
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,
( in(X1,X2)
| ~ subset(set_union2(singleton(X1),X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_26,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_27,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_28,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_29,negated_conjecture,
subset(set_union2(singleton(esk3_0),esk4_0),esk4_0),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_30,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_31,negated_conjecture,
~ in(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_32,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_33,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_34,plain,
~ empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_35,plain,
empty(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_36,axiom,
X1 = X1 ).
cnf(i_0_37,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_38,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_39,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_40,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_41,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_42,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_43,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_44,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_45,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_36_001,axiom,
X1 = X1 ).
cnf(i_0_37_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_38_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_39_004,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_40_005,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_41_006,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_42_007,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_43_008,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_44_009,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_45_010,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_46,plain,
$false,
inference(scs_inference,[],[i_0_31,i_0_29,i_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SET904+1 : TPTP v9.2.1. Released v3.2.0.
% 0.10/0.13 % 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
% 0.16/0.34 % Computer : n019.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 02:40:29 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 0.26/1.62 % Version : CSE_E---1.7
% 0.26/1.62 % Problem : theBenchmark.p
% 0.26/1.62 % SZS status Theorem for theBenchmark.p
% 0.26/1.62 % SZS output start CNFRefutation
% See solution above
% 0.26/1.64 % Total time : 1.271s
%------------------------------------------------------------------------------