%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET583+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 : n023.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 05:08:02 PM UTC 2026
% Result : Theorem 0.26s 1.62s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 13)
% Comments :
%------------------------------------------------------------------------------
fof(prove_extensionality,conjecture,
! [X1,X2] :
( ( subset(X1,X2)
& subset(X2,X1) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_extensionality) ).
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(i_0_4,negated_conjecture,
~ ! [X1,X2] :
( ( subset(X1,X2)
& subset(X2,X1) )
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[prove_extensionality]) ).
fof(i_0_5,plain,
! [X14,X15,X16,X17,X18] :
( ( ~ subset(X14,X15)
| ~ member(X16,X14)
| member(X16,X15) )
& ( member(esk1_2(X17,X18),X17)
| subset(X17,X18) )
& ( ~ member(esk1_2(X17,X18),X18)
| subset(X17,X18) ) ),
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_6,plain,
! [X12,X13] :
( ( subset(X12,X13)
| X12 != X13 )
& ( subset(X13,X12)
| X12 != X13 )
& ( ~ subset(X12,X13)
| ~ subset(X13,X12)
| X12 = X13 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
fof(i_0_7,plain,
! [X20] : subset(X20,X20),
inference(variable_rename,[status(thm)],[reflexivity_of_subset]) ).
fof(i_0_8,negated_conjecture,
( subset(esk2_0,esk3_0)
& subset(esk3_0,esk2_0)
& esk2_0 != esk3_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_4])])]) ).
cnf(i_0_9,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_5]),
[final] ).
cnf(i_0_10,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_5]),
[final] ).
cnf(i_0_11,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_5]),
[final] ).
cnf(i_0_12,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_13,plain,
( subset(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_14,plain,
( subset(X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_15,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_7]),
[final] ).
cnf(i_0_16,negated_conjecture,
subset(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_17,negated_conjecture,
subset(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_18,negated_conjecture,
esk2_0 != esk3_0,
inference(split_conjunct,[status(thm)],[i_0_8]),
[final] ).
cnf(i_0_19,axiom,
X1 = X1 ).
cnf(i_0_20,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_21,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_22,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_23,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_24,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_25,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_19_001,axiom,
X1 = X1 ).
cnf(i_0_20_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_21_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_22_004,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_23_005,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_24_006,axiom,
( X1 != X2
| ~ member(X1,X3)
| member(X2,X3) ) ).
cnf(i_0_25_007,axiom,
( X1 != X2
| ~ member(X3,X1)
| member(X3,X2) ) ).
cnf(i_0_26,plain,
subset(X1,X1),
inference(equality_inference,[],[13]) ).
cnf(i_0_27,plain,
subset(X1,X1),
inference(equality_inference,[],[14]) ).
cnf(i_0_28,plain,
$false,
inference(scs_inference,[],[i_0_18,i_0_17,i_0_16,i_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET583+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
% 0.14/0.33 % Computer : n023.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:33:23 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % 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 : 1.273s
%------------------------------------------------------------------------------