%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU148+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n016.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 05:10:47 PM UTC 2026
% Result : Theorem 0.24s 1.61s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 25)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t6_zfmisc_1,conjecture,
! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(l4_zfmisc_1,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(l1_zfmisc_1,axiom,
! [X1] : singleton(X1) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
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] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_10,negated_conjecture,
~ ! [X1,X2] :
( subset(singleton(X1),singleton(X2))
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[t6_zfmisc_1]) ).
fof(i_0_11,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_12,plain,
! [X20,X21,X22,X23,X24,X25] :
( ( ~ in(X22,X21)
| X22 = X20
| X21 != singleton(X20) )
& ( X23 != X20
| in(X23,X21)
| X21 != singleton(X20) )
& ( ~ in(esk1_2(X24,X25),X25)
| esk1_2(X24,X25) != X24
| X25 = singleton(X24) )
& ( in(esk1_2(X24,X25),X25)
| esk1_2(X24,X25) = X24
| X25 = singleton(X24) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tarski])])])])])]) ).
fof(i_0_13,plain,
! [X18,X19] :
( ~ in(X18,X19)
| ~ in(X19,X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_9])]) ).
fof(i_0_14,plain,
! [X28,X29] :
( ( ~ subset(X28,singleton(X29))
| X28 = empty_set
| X28 = singleton(X29) )
& ( X28 != empty_set
| subset(X28,singleton(X29)) )
& ( X28 != singleton(X29)
| subset(X28,singleton(X29)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).
fof(i_0_15,negated_conjecture,
( subset(singleton(esk4_0),singleton(esk5_0))
& esk4_0 != esk5_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_10])])]) ).
fof(i_0_16,plain,
! [X32] : subset(X32,X32),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_17,plain,
! [X27] : singleton(X27) != empty_set,
inference(variable_rename,[status(thm)],[l1_zfmisc_1]) ).
fof(i_0_18,plain,
~ empty(esk3_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_11])]) ).
fof(i_0_19,plain,
empty(esk2_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_20,plain,
( X2 = singleton(X1)
| ~ in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_21,plain,
( in(esk1_2(X1,X2),X2)
| esk1_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_22,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_23,plain,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_24,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_25,plain,
( subset(X1,singleton(X2))
| X1 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_26,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_27,plain,
( subset(X1,singleton(X2))
| X1 != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_28,negated_conjecture,
subset(singleton(esk4_0),singleton(esk5_0)),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_29,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_30,plain,
singleton(X1) != empty_set,
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_31,plain,
~ empty(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_32,plain,
empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_33,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_34,negated_conjecture,
esk4_0 != esk5_0,
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_35,axiom,
X1 = X1 ).
cnf(i_0_36,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_37,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_38,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_39,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_40,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(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_35_001,axiom,
X1 = X1 ).
cnf(i_0_36_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_37_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_38_004,axiom,
( X1 != X2
| singleton(X1) = singleton(X2) ) ).
cnf(i_0_39_005,axiom,
( X1 != X2
| esk1_2(X1,X3) = esk1_2(X2,X3) ) ).
cnf(i_0_40_006,axiom,
( X1 != X2
| esk1_2(X3,X1) = esk1_2(X3,X2) ) ).
cnf(i_0_41_007,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_42_008,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_43_009,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_44_010,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_45_011,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_46,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(equality_inference,[],[24]) ).
cnf(i_0_47,plain,
subset(singleton(X1),singleton(X1)),
inference(equality_inference,[],[25]) ).
cnf(i_0_48,plain,
subset(empty_set,singleton(X1)),
inference(equality_inference,[],[27]) ).
cnf(i_0_49,plain,
singleton(esk4_0) = singleton(esk5_0),
inference(scs_inference,[],[i_0_28,i_0_30,i_0_23]) ).
cnf(i_0_50,plain,
singleton(X1) != empty_set,
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_51,plain,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_52,plain,
~ in(esk4_0,singleton(esk4_0)),
inference(scs_inference,[],[i_0_28,i_0_34,i_0_30,i_0_23,i_0_24]) ).
cnf(i_0_53,plain,
( X1 != singleton(X2)
| X3 = X2
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_24]) ).
cnf(i_0_54,plain,
esk2_0 != esk3_0,
inference(scs_inference,[],[i_0_28,i_0_34,i_0_30,i_0_31,i_0_32,i_0_23,i_0_24,i_0_45]) ).
cnf(i_0_55,plain,
singleton(esk5_0) = singleton(esk4_0),
inference(scs_inference,[],[i_0_28,i_0_34,i_0_30,i_0_31,i_0_32,i_0_23,i_0_24,i_0_45,i_0_36]) ).
cnf(i_0_56,plain,
( in(X1,singleton(esk5_0))
| X1 != esk4_0 ),
inference(scs_inference,[],[i_0_28,i_0_34,i_0_30,i_0_31,i_0_32,i_0_23,i_0_24,i_0_45,i_0_36,i_0_26]) ).
cnf(i_0_57,plain,
( X1 != singleton(X2)
| in(X3,X1)
| X3 != X2 ),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_58,plain,
~ in(singleton(esk5_0),esk4_0),
inference(scs_inference,[],[i_0_28,i_0_34,i_0_30,i_0_31,i_0_32,i_0_23,i_0_24,i_0_45,i_0_36,i_0_26,i_0_42,i_0_46,i_0_22]) ).
cnf(i_0_59,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_60,plain,
( X1 != esk4_0
| ~ in(X1,singleton(esk4_0)) ),
inference(scs_inference,[],[i_0_28,i_0_34,i_0_30,i_0_31,i_0_32,i_0_23,i_0_24,i_0_45,i_0_36,i_0_26,i_0_42,i_0_46,i_0_22,i_0_41]) ).
cnf(i_0_61,plain,
in(esk4_0,singleton(esk5_0)),
inference(equality_inference,[],[56]) ).
cnf(i_0_62,plain,
~ in(esk4_0,singleton(esk4_0)),
inference(equality_inference,[],[60]) ).
cnf(i_0_63,plain,
$false,
inference(scs_inference,[],[i_0_34,i_0_61,i_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU148+1 : TPTP v9.2.1. Released v3.3.0.
% 0.11/0.12 % 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
% 0.15/0.33 % Computer : n016.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:46:21 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.18/0.34 % 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
% 0.24/1.66 % Total time : 1.269s
%------------------------------------------------------------------------------