%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET632+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 : n001.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 05:08:11 PM UTC 2026
% Result : Theorem 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 15 unt; 0 def)
% Number of atoms : 113 ( 10 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 112 ( 46 ~; 39 |; 17 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 6 sgn 41 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_defn,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
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(prove_th114,conjecture,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3)
& disjoint(X2,X3) )
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th114) ).
fof(intersect_defn,axiom,
! [X1,X2] :
( intersect(X1,X2)
<=> ? [X3] :
( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_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(disjoint_defn,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
fof(c_0_7,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(c_0_8,plain,
! [X23,X24,X25,X26,X27] :
( ( ~ subset(X23,X24)
| ~ member(X25,X23)
| member(X25,X24) )
& ( member(esk1_2(X26,X27),X26)
| subset(X26,X27) )
& ( ~ member(esk1_2(X26,X27),X27)
| subset(X26,X27) ) ),
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_9,plain,
! [X43,X44,X45] :
( ( ~ empty(X43)
| ~ member(X44,X43) )
& ( member(esk3_1(X45),X45)
| empty(X45) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X1,X3)
& disjoint(X2,X3) )
=> X1 = empty_set ),
inference(assume_negation,[status(cth)],[prove_th114]) ).
fof(c_0_11,plain,
! [X29,X30,X32,X33,X34] :
( ( member(esk2_2(X29,X30),X29)
| ~ intersect(X29,X30) )
& ( member(esk2_2(X29,X30),X30)
| ~ intersect(X29,X30) )
& ( ~ member(X34,X32)
| ~ member(X34,X33)
| intersect(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)],[intersect_defn])])])])])]) ).
cnf(c_0_12,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( member(esk3_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,negated_conjecture,
( subset(esk4_0,esk5_0)
& subset(esk4_0,esk6_0)
& disjoint(esk5_0,esk6_0)
& esk4_0 != empty_set ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_15,plain,
( intersect(X2,X3)
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( empty(X1)
| member(esk3_1(X1),X2)
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
subset(esk4_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,plain,
( empty(X1)
| intersect(X2,X1)
| ~ member(esk3_1(X1),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_21,negated_conjecture,
( empty(esk4_0)
| member(esk3_1(esk4_0),esk6_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_22,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_23,plain,
! [X38,X39] :
( ( subset(X38,X39)
| X38 != X39 )
& ( subset(X39,X38)
| X38 != X39 )
& ( ~ subset(X38,X39)
| ~ subset(X39,X38)
| X38 = X39 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_24,plain,
( subset(X1,X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( empty(esk4_0)
| intersect(esk6_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_26,plain,
! [X35] : ~ member(X35,empty_set),
inference(variable_rename,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( intersect(esk6_0,esk4_0)
| subset(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
( member(esk2_2(X1,X2),X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_31,negated_conjecture,
( X1 = esk4_0
| intersect(esk6_0,esk4_0)
| ~ subset(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_29,c_0_19]) ).
cnf(c_0_33,negated_conjecture,
esk4_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_34,plain,
( ~ empty(X1)
| ~ intersect(X2,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
intersect(esk6_0,esk4_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
fof(c_0_36,plain,
! [X1,X2] :
( disjoint(X1,X2)
<=> ~ intersect(X1,X2) ),
inference(fof_simplification,[status(thm)],[disjoint_defn]) ).
cnf(c_0_37,negated_conjecture,
~ empty(esk4_0),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_38,plain,
! [X36,X37] :
( ( ~ disjoint(X36,X37)
| ~ intersect(X36,X37) )
& ( intersect(X36,X37)
| disjoint(X36,X37) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])]) ).
cnf(c_0_39,negated_conjecture,
member(esk3_1(esk4_0),esk6_0),
inference(sr,[status(thm)],[c_0_21,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
subset(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_41,plain,
( ~ disjoint(X1,X2)
| ~ intersect(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_42,negated_conjecture,
disjoint(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_43,negated_conjecture,
( intersect(X1,esk6_0)
| ~ member(esk3_1(esk4_0),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
member(esk3_1(esk4_0),esk5_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_40]),c_0_37]) ).
cnf(c_0_45,negated_conjecture,
~ intersect(esk5_0,esk6_0),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET632+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
% 0.15/0.33 % Computer : n001.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 02:31:18 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Theorem for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.368s
%------------------------------------------------------------------------------