%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET063+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n026.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 05:07:06 PM UTC 2026
% Result : Theorem 0.17s 1.74s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 24)
% Comments :
%------------------------------------------------------------------------------
fof(empty_defn,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(prove_subset_of_empty_set_is_empty_set,conjecture,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_of_empty_set_is_empty_set) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(reflexivity_of_subset,axiom,
! [X1] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(empty_set_subset,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_subset) ).
fof(i_0_7,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(i_0_8,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(i_0_9,negated_conjecture,
~ ! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
inference(assume_negation,[status(cth)],[prove_subset_of_empty_set_is_empty_set]) ).
fof(i_0_10,plain,
! [X17,X18,X19,X20,X21] :
( ( ~ subset(X17,X18)
| ~ member(X19,X17)
| member(X19,X18) )
& ( member(esk1_2(X20,X21),X20)
| subset(X20,X21) )
& ( ~ member(esk1_2(X20,X21),X21)
| subset(X20,X21) ) ),
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)],[subset_defn])])])])])]) ).
fof(i_0_11,plain,
! [X23,X24] :
( ( subset(X23,X24)
| X23 != X24 )
& ( subset(X24,X23)
| X23 != X24 )
& ( ~ subset(X23,X24)
| ~ subset(X24,X23)
| X23 = X24 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
fof(i_0_12,plain,
! [X26,X27,X28] :
( ( ~ empty(X26)
| ~ member(X27,X26) )
& ( member(esk2_1(X28),X28)
| empty(X28) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_7])])])])]) ).
fof(i_0_13,plain,
! [X16] : ~ member(X16,empty_set),
inference(variable_rename,[status(thm)],[i_0_8]) ).
fof(i_0_14,plain,
! [X25] : subset(X25,X25),
inference(variable_rename,[status(thm)],[reflexivity_of_subset]) ).
fof(i_0_15,plain,
! [X15] : subset(empty_set,X15),
inference(variable_rename,[status(thm)],[empty_set_subset]) ).
fof(i_0_16,negated_conjecture,
( subset(esk3_0,empty_set)
& esk3_0 != empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_9])])]) ).
cnf(i_0_17,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_18,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_19,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_10]),
[final] ).
cnf(i_0_20,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_21,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_22,plain,
( member(esk2_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_12]),
[final] ).
cnf(i_0_23,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_24,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_25,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_11]),
[final] ).
cnf(i_0_26,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_27,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_28,negated_conjecture,
subset(esk3_0,empty_set),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_29,negated_conjecture,
esk3_0 != empty_set,
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_30,axiom,
X1 = X1 ).
cnf(i_0_31,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_32,axiom,
( X1 = X2
| X1 != X3
| 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
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_36,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_37,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_30_001,axiom,
X1 = X1 ).
cnf(i_0_31_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_32_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_33_004,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_34_005,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_35_006,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_36_007,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_37_008,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_38,plain,
subset(X1,X1),
inference(equality_inference,[],[24]) ).
cnf(i_0_39,plain,
subset(X1,X1),
inference(equality_inference,[],[25]) ).
cnf(i_0_40,plain,
$false,
inference(scs_inference,[],[i_0_29,i_0_28,i_0_27,i_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.22 % Problem : SET063+3 : TPTP v9.2.1. Released v2.2.0.
% 0.03/0.22 % 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
% 0.12/0.44 % Computer : n026.cluster.edu
% 0.12/0.44 % Model : x86_64 x86_64
% 0.12/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.44 % Memory : 8042.1875MB
% 0.12/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.44 % CPULimit : 300
% 0.12/0.44 % WCLimit : 300
% 0.12/0.44 % DateTime : Tue May 5 02:08:38 EDT 2026
% 0.15/0.45 % CPUTime :
% 0.15/0.46 % start to proof: theBenchmark
% 0.17/1.74 % Version : CSE_E---1.7
% 0.17/1.74 % Problem : theBenchmark.p
% 0.17/1.74 % SZS status Theorem for theBenchmark.p
% 0.17/1.74 % SZS output start CNFRefutation
% See solution above
% 0.17/1.77 % Total time : 1.283s
%------------------------------------------------------------------------------