TSTP Solution File: SET697+4 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET697+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.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 : Fri May 3 03:01:16 EDT 2024
% Result : Theorem 49.49s 7.73s
% Output : CNFRefutation 49.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 129 ( 10 unt; 0 def)
% Number of atoms : 401 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 450 ( 178 ~; 180 |; 65 &)
% ( 15 <=>; 10 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 259 ( 11 sgn 132 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
fof(f4,axiom,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
fof(f6,axiom,
! [X2] : ~ member(X2,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
fof(f7,axiom,
! [X1,X0,X3] :
( member(X1,difference(X3,X0))
<=> ( ~ member(X1,X0)
& member(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).
fof(f10,axiom,
! [X2,X0] :
( member(X2,sum(X0))
<=> ? [X4] :
( member(X2,X4)
& member(X4,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum) ).
fof(f11,axiom,
! [X2,X0] :
( member(X2,product(X0))
<=> ! [X4] :
( member(X4,X0)
=> member(X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product) ).
fof(f12,conjecture,
! [X0,X1,X3] :
( ( subset(X1,X3)
& subset(X0,X3) )
=> ( subset(X0,X1)
<=> equal_set(intersection(X0,difference(X3,X1)),empty_set) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI31) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X3] :
( ( subset(X1,X3)
& subset(X0,X3) )
=> ( subset(X0,X1)
<=> equal_set(intersection(X0,difference(X3,X1)),empty_set) ) ),
inference(negated_conjecture,[],[f12]) ).
fof(f15,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f17,plain,
! [X0] : ~ member(X0,empty_set),
inference(rectify,[],[f6]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( ~ member(X0,X1)
& member(X0,X2) ) ),
inference(rectify,[],[f7]) ).
fof(f21,plain,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X0,X2)
& member(X2,X1) ) ),
inference(rectify,[],[f10]) ).
fof(f22,plain,
! [X0,X1] :
( member(X0,product(X1))
<=> ! [X2] :
( member(X2,X1)
=> member(X0,X2) ) ),
inference(rectify,[],[f11]) ).
fof(f23,plain,
~ ! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X2) )
=> ( subset(X0,X1)
<=> equal_set(intersection(X0,difference(X2,X1)),empty_set) ) ),
inference(rectify,[],[f13]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f25,plain,
! [X0,X1] :
( member(X0,product(X1))
<=> ! [X2] :
( member(X0,X2)
| ~ member(X2,X1) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f26,plain,
? [X0,X1,X2] :
( ( subset(X0,X1)
<~> equal_set(intersection(X0,difference(X2,X1)),empty_set) )
& subset(X1,X2)
& subset(X0,X2) ),
inference(ennf_transformation,[],[f23]) ).
fof(f27,plain,
? [X0,X1,X2] :
( ( subset(X0,X1)
<~> equal_set(intersection(X0,difference(X2,X1)),empty_set) )
& subset(X1,X2)
& subset(X0,X2) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f29,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f29,f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| ~ equal_set(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f33,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| ~ equal_set(X0,X1) ) ),
inference(flattening,[],[f32]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f35]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) )
& ( ( ~ member(X0,X1)
& member(X0,X2) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f39]) ).
fof(f44,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( member(X0,X2)
& member(X2,X1) )
| ~ member(X0,sum(X1)) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f45,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ? [X3] :
( member(X0,X3)
& member(X3,X1) )
| ~ member(X0,sum(X1)) ) ),
inference(rectify,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ? [X3] :
( member(X0,X3)
& member(X3,X1) )
=> ( member(X0,sK1(X0,X1))
& member(sK1(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ( member(X0,sK1(X0,X1))
& member(sK1(X0,X1),X1) )
| ~ member(X0,sum(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f45,f46]) ).
fof(f48,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ? [X2] :
( ~ member(X0,X2)
& member(X2,X1) ) )
& ( ! [X2] :
( member(X0,X2)
| ~ member(X2,X1) )
| ~ member(X0,product(X1)) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f49,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ? [X2] :
( ~ member(X0,X2)
& member(X2,X1) ) )
& ( ! [X3] :
( member(X0,X3)
| ~ member(X3,X1) )
| ~ member(X0,product(X1)) ) ),
inference(rectify,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X0,X2)
& member(X2,X1) )
=> ( ~ member(X0,sK2(X0,X1))
& member(sK2(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
! [X0,X1] :
( ( member(X0,product(X1))
| ( ~ member(X0,sK2(X0,X1))
& member(sK2(X0,X1),X1) ) )
& ( ! [X3] :
( member(X0,X3)
| ~ member(X3,X1) )
| ~ member(X0,product(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f49,f50]) ).
fof(f52,plain,
? [X0,X1,X2] :
( ( ~ equal_set(intersection(X0,difference(X2,X1)),empty_set)
| ~ subset(X0,X1) )
& ( equal_set(intersection(X0,difference(X2,X1)),empty_set)
| subset(X0,X1) )
& subset(X1,X2)
& subset(X0,X2) ),
inference(nnf_transformation,[],[f27]) ).
fof(f53,plain,
? [X0,X1,X2] :
( ( ~ equal_set(intersection(X0,difference(X2,X1)),empty_set)
| ~ subset(X0,X1) )
& ( equal_set(intersection(X0,difference(X2,X1)),empty_set)
| subset(X0,X1) )
& subset(X1,X2)
& subset(X0,X2) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
( ? [X0,X1,X2] :
( ( ~ equal_set(intersection(X0,difference(X2,X1)),empty_set)
| ~ subset(X0,X1) )
& ( equal_set(intersection(X0,difference(X2,X1)),empty_set)
| subset(X0,X1) )
& subset(X1,X2)
& subset(X0,X2) )
=> ( ( ~ equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
| ~ subset(sK3,sK4) )
& ( equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
| subset(sK3,sK4) )
& subset(sK4,sK5)
& subset(sK3,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
( ( ~ equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
| ~ subset(sK3,sK4) )
& ( equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
| subset(sK3,sK4) )
& subset(sK4,sK5)
& subset(sK3,sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f53,f54]) ).
fof(f56,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f57,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f58,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f59,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f60,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f61,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f64,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f65,plain,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f66,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f70,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f17]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f73,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f79,plain,
! [X0,X1] :
( member(sK1(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f81,plain,
! [X2,X0,X1] :
( member(X0,sum(X1))
| ~ member(X0,X2)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f82,plain,
! [X3,X0,X1] :
( member(X0,X3)
| ~ member(X3,X1)
| ~ member(X0,product(X1)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f83,plain,
! [X0,X1] :
( member(X0,product(X1))
| member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f85,plain,
subset(sK3,sK5),
inference(cnf_transformation,[],[f55]) ).
fof(f87,plain,
( equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
| subset(sK3,sK4) ),
inference(cnf_transformation,[],[f55]) ).
fof(f88,plain,
( ~ equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
| ~ subset(sK3,sK4) ),
inference(cnf_transformation,[],[f55]) ).
cnf(c_49,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f56]) ).
cnf(c_52,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
cnf(c_53,plain,
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f60]) ).
cnf(c_54,plain,
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
cnf(c_57,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f66]) ).
cnf(c_58,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f65]) ).
cnf(c_59,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
cnf(c_63,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[],[f70]) ).
cnf(c_64,plain,
( ~ member(X0,X1)
| member(X0,difference(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f73]) ).
cnf(c_65,plain,
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f72]) ).
cnf(c_72,plain,
( ~ member(X0,X1)
| ~ member(X1,X2)
| member(X0,sum(X2)) ),
inference(cnf_transformation,[],[f81]) ).
cnf(c_74,plain,
( ~ member(X0,sum(X1))
| member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f79]) ).
cnf(c_76,plain,
( member(sK2(X0,X1),X1)
| member(X0,product(X1)) ),
inference(cnf_transformation,[],[f83]) ).
cnf(c_77,plain,
( ~ member(X0,product(X1))
| ~ member(X2,X1)
| member(X0,X2) ),
inference(cnf_transformation,[],[f82]) ).
cnf(c_78,negated_conjecture,
( ~ equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
| ~ subset(sK3,sK4) ),
inference(cnf_transformation,[],[f88]) ).
cnf(c_79,negated_conjecture,
( equal_set(intersection(sK3,difference(sK5,sK4)),empty_set)
| subset(sK3,sK4) ),
inference(cnf_transformation,[],[f87]) ).
cnf(c_81,negated_conjecture,
subset(sK3,sK5),
inference(cnf_transformation,[],[f85]) ).
cnf(c_133,plain,
( member(sK0(sK3,sK4),sK3)
| subset(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_385,plain,
( ~ member(X0,intersection(X1,difference(X2,X3)))
| member(X0,difference(X2,X3)) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_405,plain,
( subset(intersection(sK3,difference(sK5,sK4)),empty_set)
| subset(sK3,sK4) ),
inference(resolution,[status(thm)],[c_54,c_79]) ).
cnf(c_416,plain,
subset(empty_set,X0),
inference(resolution,[status(thm)],[c_63,c_50]) ).
cnf(c_523,plain,
( ~ subset(X0,X1)
| member(sK0(X0,X2),X1)
| subset(X0,X2) ),
inference(resolution,[status(thm)],[c_51,c_50]) ).
cnf(c_554,plain,
( ~ subset(intersection(sK3,difference(sK5,sK4)),empty_set)
| ~ subset(empty_set,intersection(sK3,difference(sK5,sK4)))
| ~ subset(sK3,sK4) ),
inference(resolution,[status(thm)],[c_52,c_78]) ).
cnf(c_558,plain,
( ~ subset(intersection(sK3,difference(sK5,sK4)),empty_set)
| ~ subset(sK3,sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_554,c_416]) ).
cnf(c_605,plain,
( member(sK2(X0,intersection(X1,X2)),X2)
| member(X0,product(intersection(X1,X2))) ),
inference(resolution,[status(thm)],[c_76,c_58]) ).
cnf(c_606,plain,
( member(sK2(X0,intersection(X1,X2)),X1)
| member(X0,product(intersection(X1,X2))) ),
inference(resolution,[status(thm)],[c_76,c_59]) ).
cnf(c_1060,plain,
( ~ member(X0,sum(intersection(X1,X2)))
| member(sK1(X0,intersection(X1,X2)),X2) ),
inference(resolution,[status(thm)],[c_74,c_58]) ).
cnf(c_1061,plain,
( ~ member(X0,sum(intersection(X1,X2)))
| member(sK1(X0,intersection(X1,X2)),X1) ),
inference(resolution,[status(thm)],[c_74,c_59]) ).
cnf(c_1402,plain,
( member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),intersection(sK3,difference(sK5,sK4)))
| subset(intersection(sK3,difference(sK5,sK4)),empty_set) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_1749,plain,
( ~ subset(intersection(X0,X1),X2)
| ~ member(X3,X0)
| ~ member(X3,X1)
| member(X3,X2) ),
inference(resolution,[status(thm)],[c_57,c_51]) ).
cnf(c_1787,plain,
( subset(empty_set,intersection(sK3,difference(sK5,sK4)))
| subset(sK3,sK4) ),
inference(superposition,[status(thm)],[c_79,c_53]) ).
cnf(c_1792,plain,
( ~ subset(intersection(sK3,difference(sK5,sK4)),empty_set)
| equal_set(empty_set,intersection(sK3,difference(sK5,sK4)))
| subset(sK3,sK4) ),
inference(superposition,[status(thm)],[c_1787,c_52]) ).
cnf(c_1793,plain,
( equal_set(empty_set,intersection(sK3,difference(sK5,sK4)))
| subset(sK3,sK4) ),
inference(global_subsumption_just,[status(thm)],[c_1792,c_405,c_1792]) ).
cnf(c_1855,plain,
( subset(intersection(sK3,difference(sK5,sK4)),empty_set)
| subset(sK3,sK4) ),
inference(superposition,[status(thm)],[c_1793,c_53]) ).
cnf(c_2044,plain,
( ~ subset(intersection(X0,X1),X2)
| ~ member(X3,X0)
| ~ member(X3,X1)
| member(X3,X2) ),
inference(superposition,[status(thm)],[c_57,c_51]) ).
cnf(c_2773,plain,
( ~ member(X0,difference(sK5,sK4))
| ~ member(X0,sK3)
| member(X0,empty_set)
| subset(sK3,sK4) ),
inference(superposition,[status(thm)],[c_1855,c_2044]) ).
cnf(c_2775,plain,
( ~ member(X0,sK3)
| ~ member(X0,difference(sK5,sK4))
| subset(sK3,sK4) ),
inference(global_subsumption_just,[status(thm)],[c_2773,c_63,c_2773]) ).
cnf(c_2776,plain,
( ~ member(X0,difference(sK5,sK4))
| ~ member(X0,sK3)
| subset(sK3,sK4) ),
inference(renaming,[status(thm)],[c_2775]) ).
cnf(c_2828,plain,
( ~ member(X0,sK3)
| ~ member(X0,sK5)
| member(X0,sK4)
| subset(sK3,sK4) ),
inference(superposition,[status(thm)],[c_64,c_2776]) ).
cnf(c_2834,plain,
( ~ member(X0,sK3)
| ~ member(X0,sK5)
| member(X0,sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2828,c_51]) ).
cnf(c_4198,plain,
( ~ subset(X0,empty_set)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[c_523,c_63]) ).
cnf(c_4674,plain,
( subset(intersection(sK3,difference(sK5,sK4)),X0)
| subset(sK3,sK4) ),
inference(resolution,[status(thm)],[c_4198,c_405]) ).
cnf(c_5915,plain,
( ~ member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),intersection(sK3,difference(sK5,sK4)))
| member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),difference(sK5,sK4)) ),
inference(instantiation,[status(thm)],[c_385]) ).
cnf(c_11769,plain,
( ~ member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),difference(sK5,sK4))
| ~ member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),sK4) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_12186,plain,
( ~ member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),intersection(sK3,difference(sK5,sK4)))
| member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),sK3) ),
inference(instantiation,[status(thm)],[c_59]) ).
cnf(c_18170,plain,
( ~ member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),intersection(sK3,difference(sK5,sK4)))
| ~ member(X0,sK0(intersection(sK3,difference(sK5,sK4)),empty_set))
| member(X0,sum(intersection(sK3,difference(sK5,sK4)))) ),
inference(instantiation,[status(thm)],[c_72]) ).
cnf(c_18172,plain,
( ~ member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),intersection(sK3,difference(sK5,sK4)))
| ~ member(X0,product(intersection(sK3,difference(sK5,sK4))))
| member(X0,sK0(intersection(sK3,difference(sK5,sK4)),empty_set)) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_18595,plain,
( ~ member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),sK3)
| ~ subset(sK3,X0)
| member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_21961,plain,
( ~ member(X0,difference(sK5,sK4))
| ~ member(X0,sK3)
| member(X0,X1)
| subset(sK3,sK4) ),
inference(resolution,[status(thm)],[c_1749,c_4674]) ).
cnf(c_24499,plain,
( ~ member(X0,sK3)
| ~ member(X0,difference(sK5,sK4))
| subset(sK3,sK4) ),
inference(global_subsumption_just,[status(thm)],[c_21961,c_2776]) ).
cnf(c_24500,plain,
( ~ member(X0,difference(sK5,sK4))
| ~ member(X0,sK3)
| subset(sK3,sK4) ),
inference(renaming,[status(thm)],[c_24499]) ).
cnf(c_24583,plain,
( ~ member(X0,sK3)
| ~ member(X0,sK5)
| member(X0,sK4)
| subset(sK3,sK4) ),
inference(resolution,[status(thm)],[c_24500,c_64]) ).
cnf(c_24590,plain,
( ~ member(sK2(X0,intersection(X1,difference(sK5,sK4))),sK3)
| member(X0,product(intersection(X1,difference(sK5,sK4))))
| subset(sK3,sK4) ),
inference(resolution,[status(thm)],[c_24500,c_605]) ).
cnf(c_24606,plain,
( ~ member(sK1(X0,intersection(X1,difference(sK5,sK4))),sK3)
| ~ member(X0,sum(intersection(X1,difference(sK5,sK4))))
| subset(sK3,sK4) ),
inference(resolution,[status(thm)],[c_24500,c_1060]) ).
cnf(c_24828,plain,
( member(X0,sK4)
| ~ member(X0,sK5)
| ~ member(X0,sK3) ),
inference(global_subsumption_just,[status(thm)],[c_24583,c_2834]) ).
cnf(c_24829,plain,
( ~ member(X0,sK3)
| ~ member(X0,sK5)
| member(X0,sK4) ),
inference(renaming,[status(thm)],[c_24828]) ).
cnf(c_24856,plain,
( ~ member(sK0(X0,sK4),sK3)
| ~ member(sK0(X0,sK4),sK5)
| subset(X0,sK4) ),
inference(resolution,[status(thm)],[c_24829,c_49]) ).
cnf(c_29896,plain,
( ~ member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),sK3)
| ~ subset(sK3,sK4)
| member(sK0(intersection(sK3,difference(sK5,sK4)),empty_set),sK4) ),
inference(instantiation,[status(thm)],[c_18595]) ).
cnf(c_31171,plain,
( member(X0,product(intersection(X1,difference(sK5,sK4))))
| ~ member(sK2(X0,intersection(X1,difference(sK5,sK4))),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_24590,c_558,c_1402,c_5915,c_11769,c_12186,c_24590,c_29896]) ).
cnf(c_31172,plain,
( ~ member(sK2(X0,intersection(X1,difference(sK5,sK4))),sK3)
| member(X0,product(intersection(X1,difference(sK5,sK4)))) ),
inference(renaming,[status(thm)],[c_31171]) ).
cnf(c_31221,plain,
member(X0,product(intersection(sK3,difference(sK5,sK4)))),
inference(resolution,[status(thm)],[c_31172,c_606]) ).
cnf(c_32042,plain,
( ~ member(X0,sum(intersection(X1,difference(sK5,sK4))))
| ~ member(sK1(X0,intersection(X1,difference(sK5,sK4))),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_24606,c_558,c_1402,c_5915,c_11769,c_12186,c_24606,c_29896]) ).
cnf(c_32043,plain,
( ~ member(sK1(X0,intersection(X1,difference(sK5,sK4))),sK3)
| ~ member(X0,sum(intersection(X1,difference(sK5,sK4)))) ),
inference(renaming,[status(thm)],[c_32042]) ).
cnf(c_32055,plain,
~ member(X0,sum(intersection(sK3,difference(sK5,sK4)))),
inference(resolution,[status(thm)],[c_32043,c_1061]) ).
cnf(c_47022,plain,
( ~ member(sK0(X0,sK4),sK3)
| ~ subset(X0,sK5)
| subset(X0,sK4) ),
inference(resolution,[status(thm)],[c_24856,c_523]) ).
cnf(c_47023,plain,
( ~ member(sK0(sK3,sK4),sK3)
| ~ subset(sK3,sK5)
| subset(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_47022]) ).
cnf(c_47024,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_47023,c_32055,c_31221,c_18172,c_18170,c_1402,c_558,c_133,c_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET697+4 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 2 20:55:51 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 49.49/7.73 % SZS status Started for theBenchmark.p
% 49.49/7.73 % SZS status Theorem for theBenchmark.p
% 49.49/7.73
% 49.49/7.73 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 49.49/7.73
% 49.49/7.73 ------ iProver source info
% 49.49/7.73
% 49.49/7.73 git: date: 2024-05-02 19:28:25 +0000
% 49.49/7.73 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 49.49/7.73 git: non_committed_changes: false
% 49.49/7.73
% 49.49/7.73 ------ Parsing...
% 49.49/7.73 ------ Clausification by vclausify_rel & Parsing by iProver...
% 49.49/7.73
% 49.49/7.73 ------ Preprocessing... sf_s rm: 1 0s sf_e
% 49.49/7.73
% 49.49/7.73 ------ Preprocessing...
% 49.49/7.73
% 49.49/7.73 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 49.49/7.73 ------ Proving...
% 49.49/7.73 ------ Problem Properties
% 49.49/7.73
% 49.49/7.73
% 49.49/7.73 clauses 33
% 49.49/7.73 conjectures 4
% 49.49/7.73 EPR 7
% 49.49/7.73 Horn 27
% 49.49/7.73 unary 6
% 49.49/7.73 binary 19
% 49.49/7.73 lits 68
% 49.49/7.73 lits eq 3
% 49.49/7.73 fd_pure 0
% 49.49/7.73 fd_pseudo 0
% 49.49/7.73 fd_cond 0
% 49.49/7.73 fd_pseudo_cond 2
% 49.49/7.73 AC symbols 0
% 49.49/7.73
% 49.49/7.73 ------ Input Options Time Limit: Unbounded
% 49.49/7.73
% 49.49/7.73
% 49.49/7.73 ------
% 49.49/7.73 Current options:
% 49.49/7.73 ------
% 49.49/7.73
% 49.49/7.73
% 49.49/7.73
% 49.49/7.73
% 49.49/7.73 ------ Proving...
% 49.49/7.73
% 49.49/7.73
% 49.49/7.73 % SZS status Theorem for theBenchmark.p
% 49.49/7.73
% 49.49/7.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 49.49/7.74
% 49.49/7.74
%------------------------------------------------------------------------------