%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET923+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 : n020.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 05:08:58 PM UTC 2026
% Result : Theorem 0.25s 1.61s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 18)
% Comments :
%------------------------------------------------------------------------------
fof(t66_zfmisc_1,conjecture,
! [X1,X2] :
~ ( set_difference(X1,singleton(X2)) = empty_set
& X1 != empty_set
& X1 != singleton(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t66_zfmisc_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(l4_zfmisc_1,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(t37_xboole_1,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_7,negated_conjecture,
~ ! [X1,X2] :
~ ( set_difference(X1,singleton(X2)) = empty_set
& X1 != empty_set
& X1 != singleton(X2) ),
inference(assume_negation,[status(cth)],[t66_zfmisc_1]) ).
fof(i_0_8,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_9,plain,
! [X13,X14] :
( ( ~ subset(X13,singleton(X14))
| X13 = empty_set
| X13 = singleton(X14) )
& ( X13 != empty_set
| subset(X13,singleton(X14)) )
& ( X13 != singleton(X14)
| subset(X13,singleton(X14)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).
fof(i_0_10,plain,
! [X18,X19] :
( ( set_difference(X18,X19) != empty_set
| subset(X18,X19) )
& ( ~ subset(X18,X19)
| set_difference(X18,X19) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(i_0_11,negated_conjecture,
( set_difference(esk3_0,singleton(esk4_0)) = empty_set
& esk3_0 != empty_set
& esk3_0 != singleton(esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_7])])]) ).
fof(i_0_12,plain,
! [X17] : subset(X17,X17),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_13,plain,
~ empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_8])]) ).
fof(i_0_14,plain,
empty(esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_15,plain,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_16,plain,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_17,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_18,plain,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_19,plain,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_9]),
[final] ).
cnf(i_0_20,negated_conjecture,
set_difference(esk3_0,singleton(esk4_0)) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_21,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_22,plain,
~ empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_23,negated_conjecture,
esk3_0 != singleton(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_24,plain,
empty(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_25,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_26,negated_conjecture,
esk3_0 != empty_set,
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_27,axiom,
X1 = X1 ).
cnf(i_0_28,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_29,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_30,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_31,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_32,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_33,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_34,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_35,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_27_001,axiom,
X1 = X1 ).
cnf(i_0_28_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_29_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_30_004,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_31_005,axiom,
( X1 != X2
| set_difference(X1,X3) = set_difference(X2,X3) ) ).
cnf(i_0_32_006,axiom,
( X1 != X2
| set_difference(X3,X1) = set_difference(X3,X2) ) ).
cnf(i_0_33_007,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_34_008,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_35_009,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_36,plain,
subset(singleton(X1),singleton(X1)),
inference(equality_inference,[],[18]) ).
cnf(i_0_37,plain,
subset(empty_set,singleton(X1)),
inference(equality_inference,[],[19]) ).
cnf(i_0_38,plain,
subset(esk3_0,singleton(esk4_0)),
inference(scs_inference,[],[i_0_20,i_0_16]) ).
cnf(i_0_39,plain,
( set_difference(X1,X2) != empty_set
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_40,plain,
subset(set_difference(esk3_0,singleton(esk4_0)),singleton(X1)),
inference(scs_inference,[],[i_0_20,i_0_16,i_0_19]) ).
cnf(i_0_41,plain,
( X1 != empty_set
| subset(X1,singleton(X2)) ),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_42,plain,
empty_set = set_difference(esk3_0,singleton(esk4_0)),
inference(scs_inference,[],[i_0_20,i_0_16,i_0_19,i_0_28]) ).
cnf(i_0_43,plain,
$false,
inference(scs_inference,[],[i_0_20,i_0_26,i_0_23,i_0_16,i_0_19,i_0_28,i_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET923+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
% 0.15/0.32 % Computer : n020.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:39:20 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % 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 : 1.271s
%------------------------------------------------------------------------------