%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET587+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 : n016.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 05:08:03 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 10 unt; 0 def)
% Number of atoms : 98 ( 13 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 101 ( 44 ~; 37 |; 11 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 69 ( 7 sgn 35 !; 0 ?)
% 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(prove_difference_empty_set,conjecture,
! [X1,X2] :
( difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_difference_empty_set) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_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(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(c_0_6,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_7,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
( difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
inference(assume_negation,[status(cth)],[prove_difference_empty_set]) ).
fof(c_0_9,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_10,plain,
! [X27,X28,X29] :
( ( member(X29,X27)
| ~ member(X29,difference(X27,X28)) )
& ( ~ member(X29,X28)
| ~ member(X29,difference(X27,X28)) )
& ( ~ member(X29,X27)
| member(X29,X28)
| member(X29,difference(X27,X28)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_11,plain,
! [X47,X48,X49] :
( ( ~ empty(X47)
| ~ member(X48,X47) )
& ( member(esk4_1(X49),X49)
| empty(X49) ) ),
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_12,negated_conjecture,
( ( difference(esk5_0,esk6_0) != empty_set
| ~ subset(esk5_0,esk6_0) )
& ( difference(esk5_0,esk6_0) = empty_set
| subset(esk5_0,esk6_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_13,plain,
! [X30] : ~ member(X30,empty_set),
inference(variable_rename,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X31,X32,X33,X34,X35] :
( ( ~ subset(X31,X32)
| ~ member(X33,X31)
| member(X33,X32) )
& ( member(esk2_2(X34,X35),X34)
| subset(X34,X35) )
& ( ~ member(esk2_2(X34,X35),X35)
| subset(X34,X35) ) ),
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])])])])])]) ).
cnf(c_0_15,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( member(esk4_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
( difference(esk5_0,esk6_0) = empty_set
| subset(esk5_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( empty(difference(X1,X2))
| ~ member(esk4_1(difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( member(X1,esk6_0)
| ~ member(X1,esk5_0) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]) ).
cnf(c_0_23,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_24,plain,
( subset(X1,X2)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_25,plain,
! [X37,X38] :
( ( subset(X37,X38)
| X37 != X38 )
& ( subset(X38,X37)
| X37 != X38 )
& ( ~ subset(X37,X38)
| ~ subset(X38,X37)
| X37 = X38 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_26,plain,
( member(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_27,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_28,negated_conjecture,
( empty(difference(X1,esk6_0))
| ~ member(esk4_1(difference(X1,esk6_0)),esk5_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
( empty(difference(X1,X2))
| member(esk4_1(difference(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_30,negated_conjecture,
( subset(X1,esk6_0)
| ~ member(esk2_2(X1,esk6_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_31,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_33,plain,
( subset(X1,X2)
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_34,negated_conjecture,
empty(difference(esk5_0,esk6_0)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
( difference(esk5_0,esk6_0) != empty_set
| ~ subset(esk5_0,esk6_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_36,negated_conjecture,
subset(esk5_0,esk6_0),
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_37,plain,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
subset(difference(esk5_0,esk6_0),X1),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
difference(esk5_0,esk6_0) != empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET587+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 : n016.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 02:29:06 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------