%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET143+3 : TPTP v9.2.1. Released v2.2.0.
% 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 : n027.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 05:07:26 PM UTC 2026
% Result : Theorem 3.81s 3.22s
% Output : CNFRefutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 53 ( 28 unt; 0 def)
% Number of atoms : 100 ( 20 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 79 ( 32 ~; 35 |; 8 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 140 ( 8 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(prove_associativity_of_intersection,conjecture,
! [X1,X2,X3] : intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_intersection) ).
fof(c_0_5,plain,
! [X28,X29,X30,X31,X32] :
( ( ~ subset(X28,X29)
| ~ member(X30,X28)
| member(X30,X29) )
& ( member(esk1_2(X31,X32),X31)
| subset(X31,X32) )
& ( ~ member(esk1_2(X31,X32),X32)
| subset(X31,X32) ) ),
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(c_0_6,plain,
! [X21,X22,X23] :
( ( member(X23,X21)
| ~ member(X23,intersection(X21,X22)) )
& ( member(X23,X22)
| ~ member(X23,intersection(X21,X22)) )
& ( ~ member(X23,X21)
| ~ member(X23,X22)
| member(X23,intersection(X21,X22)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
cnf(c_0_7,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( subset(X1,intersection(X2,X3))
| ~ member(esk1_2(X1,intersection(X2,X3)),X3)
| ~ member(esk1_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_13,plain,
! [X26,X27] : intersection(X26,X27) = intersection(X27,X26),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_14,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_15,plain,
! [X24,X25] :
( ( subset(X24,X25)
| X24 != X25 )
& ( subset(X25,X24)
| X24 != X25 )
& ( ~ subset(X24,X25)
| ~ subset(X25,X24)
| X24 = X25 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_16,plain,
( subset(X1,intersection(X2,X1))
| ~ member(esk1_2(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_17,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_7,c_0_12]) ).
cnf(c_0_18,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_20,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
subset(intersection(X1,X2),intersection(X1,intersection(X1,X2))),
inference(spm,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_22,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( subset(intersection(X1,X2),intersection(X3,X2))
| ~ member(esk1_2(intersection(X1,X2),intersection(X3,X2)),X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_19]) ).
cnf(c_0_24,plain,
( subset(intersection(intersection(X1,X2),X3),X4)
| member(esk1_2(intersection(intersection(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_25,plain,
intersection(X1,intersection(X1,X2)) = intersection(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_26,plain,
( subset(intersection(X1,X2),intersection(X3,X1))
| ~ member(esk1_2(intersection(X1,X2),intersection(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_27,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_28,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X1,X3)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
intersection(X1,intersection(X2,X1)) = intersection(X2,X1),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_30,plain,
subset(intersection(X1,X2),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_31,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,intersection(intersection(X2,X4),X3)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X2,X3)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,intersection(X3,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_30]) ).
cnf(c_0_34,plain,
( subset(intersection(X1,intersection(intersection(X2,X3),X4)),X5)
| member(esk1_2(intersection(X1,intersection(intersection(X2,X3),X4)),X5),intersection(X2,X4)) ),
inference(spm,[status(thm)],[c_0_31,c_0_19]) ).
cnf(c_0_35,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X2,intersection(intersection(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_32,c_0_25]) ).
cnf(c_0_36,plain,
( subset(intersection(X1,X2),intersection(X1,X3))
| ~ member(esk1_2(intersection(X1,X2),intersection(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_37,plain,
( subset(intersection(X1,intersection(X2,X3)),X4)
| member(esk1_2(intersection(X1,intersection(X2,X3)),X4),intersection(X3,X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_19]) ).
cnf(c_0_38,plain,
subset(intersection(X1,intersection(intersection(X2,X3),X4)),intersection(intersection(X2,X4),X1)),
inference(spm,[status(thm)],[c_0_26,c_0_34]) ).
cnf(c_0_39,plain,
intersection(X1,intersection(intersection(X2,X1),X3)) = intersection(intersection(X2,X1),X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_35]),c_0_22])]) ).
fof(c_0_40,negated_conjecture,
~ ! [X1,X2,X3] : intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
inference(assume_negation,[status(cth)],[prove_associativity_of_intersection]) ).
cnf(c_0_41,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X1,intersection(X3,X2))),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
subset(intersection(intersection(X1,X2),X3),intersection(intersection(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
fof(c_0_43,negated_conjecture,
intersection(intersection(esk3_0,esk4_0),esk5_0) != intersection(esk3_0,intersection(esk4_0,esk5_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])]) ).
cnf(c_0_44,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X3,intersection(X2,X1))),
inference(spm,[status(thm)],[c_0_41,c_0_18]) ).
cnf(c_0_45,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(intersection(X3,X2),X1)),
inference(spm,[status(thm)],[c_0_26,c_0_37]) ).
cnf(c_0_46,plain,
intersection(intersection(X1,X2),X3) = intersection(intersection(X1,X3),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_42]),c_0_42])]) ).
cnf(c_0_47,negated_conjecture,
intersection(intersection(esk3_0,esk4_0),esk5_0) != intersection(esk3_0,intersection(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_48,plain,
intersection(X1,intersection(X2,X3)) = intersection(intersection(X3,X2),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_44]),c_0_45])]) ).
cnf(c_0_49,plain,
intersection(intersection(X1,X2),X3) = intersection(X2,intersection(X1,X3)),
inference(spm,[status(thm)],[c_0_18,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
intersection(esk5_0,intersection(esk3_0,esk4_0)) != intersection(esk3_0,intersection(esk4_0,esk5_0)),
inference(rw,[status(thm)],[c_0_47,c_0_18]) ).
cnf(c_0_51,plain,
intersection(X1,intersection(X2,X3)) = intersection(X2,intersection(X3,X1)),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_18]),c_0_51]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET143+3 : TPTP v9.2.1. Released v2.2.0.
% 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
% 0.16/0.33 % Computer : n027.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 02:12:50 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 3.81/3.22 % Version : CSE_E---1.7
% 3.81/3.22 % Problem : theBenchmark.p
% 3.81/3.22 % SZS status Theorem for theBenchmark.p
% 3.81/3.22 % SZS output start CNFRefutation
% See solution above
% 3.81/3.23 % Total time : 2.371s
%------------------------------------------------------------------------------