%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET604+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 : n031.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 05:08:06 PM UTC 2026
% Result : Theorem 0.25s 1.62s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 34)
% Comments :
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
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_no_difference_with_empty_set,conjecture,
! [X1] : difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_no_difference_with_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(difference_empty_set,axiom,
! [X1,X2] :
( difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_empty_set) ).
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_9,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(i_0_10,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(i_0_11,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(i_0_12,negated_conjecture,
~ ! [X1] : difference(empty_set,X1) = empty_set,
inference(assume_negation,[status(cth)],[prove_no_difference_with_empty_set]) ).
fof(i_0_13,plain,
! [X24,X25,X26] :
( ( member(X26,X24)
| ~ member(X26,difference(X24,X25)) )
& ( ~ member(X26,X25)
| ~ member(X26,difference(X24,X25)) )
& ( ~ member(X26,X24)
| member(X26,X25)
| member(X26,difference(X24,X25)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_9])])]) ).
fof(i_0_14,plain,
! [X29,X30,X31,X32,X33] :
( ( ~ subset(X29,X30)
| ~ member(X31,X29)
| member(X31,X30) )
& ( member(esk1_2(X32,X33),X32)
| subset(X32,X33) )
& ( ~ member(esk1_2(X32,X33),X33)
| subset(X32,X33) ) ),
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_15,plain,
! [X27,X28] :
( ( subset(X27,X28)
| X27 != X28 )
& ( subset(X28,X27)
| X27 != X28 )
& ( ~ subset(X27,X28)
| ~ subset(X28,X27)
| X27 = X28 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
fof(i_0_16,plain,
! [X21,X22] :
( ( difference(X21,X22) != empty_set
| subset(X21,X22) )
& ( ~ subset(X21,X22)
| difference(X21,X22) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[difference_empty_set])]) ).
fof(i_0_17,plain,
! [X36,X37,X38] :
( ( ~ empty(X36)
| ~ member(X37,X36) )
& ( member(esk2_1(X38),X38)
| empty(X38) ) ),
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_10])])])])]) ).
fof(i_0_18,plain,
! [X23] : ~ member(X23,empty_set),
inference(variable_rename,[status(thm)],[i_0_11]) ).
fof(i_0_19,negated_conjecture,
difference(empty_set,esk3_0) != empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_12])])]) ).
fof(i_0_20,plain,
! [X35] : subset(X35,X35),
inference(variable_rename,[status(thm)],[reflexivity_of_subset]) ).
fof(i_0_21,plain,
! [X20] : subset(empty_set,X20),
inference(variable_rename,[status(thm)],[empty_set_subset]) ).
cnf(i_0_22,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_23,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_24,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_25,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_13]),
[final] ).
cnf(i_0_26,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_27,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_14]),
[final] ).
cnf(i_0_28,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_29,plain,
( subset(X1,X2)
| difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_30,plain,
( difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_16]),
[final] ).
cnf(i_0_31,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_32,plain,
( member(esk2_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_17]),
[final] ).
cnf(i_0_33,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_34,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_35,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_15]),
[final] ).
cnf(i_0_36,negated_conjecture,
difference(empty_set,esk3_0) != empty_set,
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_37,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_38,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_39,axiom,
X1 = X1 ).
cnf(i_0_40,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_41,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_42,axiom,
( X1 != X2
| difference(X1,X3) = difference(X2,X3) ) ).
cnf(i_0_43,axiom,
( X1 != X2
| difference(X3,X1) = difference(X3,X2) ) ).
cnf(i_0_44,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_45,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_46,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_47,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_48,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_39_001,axiom,
X1 = X1 ).
cnf(i_0_40_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_41_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_42_004,axiom,
( X1 != X2
| difference(X1,X3) = difference(X2,X3) ) ).
cnf(i_0_43_005,axiom,
( X1 != X2
| difference(X3,X1) = difference(X3,X2) ) ).
cnf(i_0_44_006,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_45_007,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_46_008,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_47_009,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_48_010,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_49,plain,
subset(X1,X1),
inference(equality_inference,[],[34]) ).
cnf(i_0_50,plain,
subset(X1,X1),
inference(equality_inference,[],[35]) ).
cnf(i_0_51,plain,
$false,
inference(scs_inference,[],[i_0_36,i_0_38,i_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET604+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n031.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:31:08 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.25/1.62 % Version : CSE_E---1.7
% 0.25/1.62 % Problem : theBenchmark.p
% 0.25/1.62 % SZS status Theorem for theBenchmark.p
% 0.25/1.62 % SZS output start CNFRefutation
% See solution above
% 0.25/1.63 % Total time : 1.271s
%------------------------------------------------------------------------------