%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET008-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:41:26 PM UTC 2026
% Result : Unsatisfiable 4.87s 1.14s
% Output : Proof 4.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 55 ( 24 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 58 ( 7 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f13,axiom,
( ~ difference(A_set,Set1,Set2)
| ~ member(Element,Set2)
| ~ member(Element,Set1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_member_of_difference) ).
fof(f13_nnf,plain,
! [Element,Set1,Set2,A_set] :
( ~ difference(A_set,Set1,Set2)
| ~ member(Element,Set2)
| ~ member(Element,Set1) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [Element,Set1,Set2,A_set] :
( ~ difference(A_set,Set1,Set2)
| ~ member(Element,Set2)
| ~ member(Element,Set1) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( ~ difference(X3,X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(f9,axiom,
( member(h(Set1,Set2,Intersection),Set1)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_axiom1) ).
fof(f9_nnf,plain,
! [Set1,Set2,Intersection] :
( member(h(Set1,Set2,Intersection),Set1)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [Set1,Set2,Intersection] :
( member(h(Set1,Set2,Intersection),Set1)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( member(h(X0,X1,X2),X0)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(f20,negated_conjecture,
~ member(A,aI_bDa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_aI_bDa_is_empty) ).
fof(f20_nnf,plain,
! [A] : ~ member(A,aI_bDa),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A] : ~ member(A,aI_bDa),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
~ member(X0,aI_bDa),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p37,plain,
( member(h(X0,X1,aI_bDa),X0)
| intersection(X0,X1,aI_bDa) ),
inference(resolution,[status(thm)],[c9,c20]) ).
cnf(p72,plain,
( intersection(X0,X1,aI_bDa)
| ~ difference(X3,X0,X2)
| ~ member(h(X0,X1,aI_bDa),X2) ),
inference(resolution,[status(thm)],[c13,p37]) ).
cnf(f10,axiom,
( member(h(Set1,Set2,Intersection),Set2)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_axiom2) ).
fof(f10_nnf,plain,
! [Set1,Set2,Intersection] :
( member(h(Set1,Set2,Intersection),Set2)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Set1,Set2,Intersection] :
( member(h(Set1,Set2,Intersection),Set2)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( member(h(X0,X1,X2),X1)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p50,plain,
( member(h(X0,X1,aI_bDa),X1)
| intersection(X0,X1,aI_bDa) ),
inference(resolution,[status(thm)],[c10,c20]) ).
cnf(p101,plain,
( intersection(X1,X2,aI_bDa)
| intersection(X1,X2,aI_bDa)
| ~ difference(X0,X1,X2) ),
inference(resolution,[status(thm)],[p72,p50]) ).
cnf(p135,plain,
( intersection(X1,X2,aI_bDa)
| ~ difference(X0,X1,X2) ),
inference(factoring,[status(thm)],[p101]) ).
cnf(f18,hypothesis,
difference(b,a,bDa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_minus_a) ).
fof(f18_nnf,plain,
difference(b,a,bDa),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
difference(b,a,bDa),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(p136,plain,
intersection(a,bDa,aI_bDa),
inference(resolution,[status(thm)],[p135,c18]) ).
cnf(f19,negated_conjecture,
~ intersection(a,bDa,aI_bDa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_bDa) ).
fof(f19_nnf,plain,
~ intersection(a,bDa,aI_bDa),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
~ intersection(a,bDa,aI_bDa),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
~ intersection(a,bDa,aI_bDa),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p137,plain,
$false,
inference(resolution,[status(thm)],[p136,c19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 09:07:09 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.87/1.14 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.87/1.14 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------