%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET787-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 02:43:56 PM UTC 2026
% Result : Unsatisfiable 7.35s 1.75s
% Output : Proof 7.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 17 unt; 0 def)
% Number of atoms : 72 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 28 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 59 ( 9 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,axiom,
( member(U,W)
| U = V
| ~ member(U,cons(V,W)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).
fof(f4_nnf,plain,
! [U,V,W] :
( member(U,W)
| U = V
| ~ member(U,cons(V,W)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [U,V,W] :
( member(U,W)
| U = V
| ~ member(U,cons(V,W)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( member(X0,X2)
| X0 = X1
| ~ member(X0,cons(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(f1,axiom,
( member(unionE_sk1(U,V),V)
| ~ member(U,union(V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
fof(f1_nnf,plain,
! [U,V] :
( member(unionE_sk1(U,V),V)
| ~ member(U,union(V)) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [U,V] :
( member(unionE_sk1(U,V),V)
| ~ member(U,union(V)) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( member(unionE_sk1(X0,X1),X1)
| ~ member(X0,union(X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(f12,negated_conjecture,
member(sk2,union(cons(a,cons(b,eptset)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',un_eq_Union_2_c1) ).
fof(f12_nnf,plain,
member(sk2,union(cons(a,cons(b,eptset)))),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
member(sk2,union(cons(a,cons(b,eptset)))),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(p19,plain,
member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))),
inference(resolution,[status(thm)],[c1,c12]) ).
cnf(p27,plain,
( member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = a ),
inference(resolution,[status(thm)],[c4,p19]) ).
cnf(p141,plain,
( member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = b
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = a ),
inference(resolution,[status(thm)],[p27,c4]) ).
cnf(f7,axiom,
~ member(X,eptset),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause158) ).
fof(f7_nnf,plain,
! [X] : ~ member(X,eptset),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X] : ~ member(X,eptset),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
~ member(X0,eptset),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p541,plain,
( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = a ),
inference(resolution,[status(thm)],[p141,c7]) ).
cnf(f0,axiom,
( member(U,unionE_sk1(U,V))
| ~ member(U,union(V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
fof(f0_nnf,plain,
! [U,V] :
( member(U,unionE_sk1(U,V))
| ~ member(U,union(V)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [U,V] :
( member(U,unionE_sk1(U,V))
| ~ member(U,union(V)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( member(X0,unionE_sk1(X0,X1))
| ~ member(X0,union(X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p15,plain,
member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))),
inference(resolution,[status(thm)],[c0,c12]) ).
cnf(p544,plain,
( member(sk2,b)
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = a ),
inference(superposition,[status(thm)],[p541,p15]) ).
cnf(f5,axiom,
( member(C,un(A,B))
| ~ member(C,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unI1) ).
fof(f5_nnf,plain,
! [C,A,B] :
( member(C,un(A,B))
| ~ member(C,A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [C,A,B] :
( member(C,un(A,B))
| ~ member(C,A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( member(X0,un(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p23,plain,
member(sk2,un(unionE_sk1(sk2,cons(a,cons(b,eptset))),X0)),
inference(resolution,[status(thm)],[c5,p15]) ).
cnf(p626,plain,
( member(sk2,un(a,X0))
| member(sk2,b) ),
inference(superposition,[status(thm)],[p544,p23]) ).
cnf(f13,negated_conjecture,
~ member(sk2,un(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',un_eq_Union_2_c2) ).
fof(f13_nnf,plain,
~ member(sk2,un(a,b)),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
~ member(sk2,un(a,b)),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
~ member(sk2,un(a,b)),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p707,plain,
member(sk2,b),
inference(resolution,[status(thm)],[p626,c13]) ).
cnf(f6,axiom,
( member(C,un(A,B))
| ~ member(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unI2) ).
fof(f6_nnf,plain,
! [C,B,A] :
( member(C,un(A,B))
| ~ member(C,B) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [C,B,A] :
( member(C,un(A,B))
| ~ member(C,B) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( member(X0,un(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p709,plain,
member(sk2,un(X0,b)),
inference(resolution,[status(thm)],[p707,c6]) ).
cnf(p713,plain,
$false,
inference(resolution,[status(thm)],[p709,c13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET787-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n008.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 11:58:08 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.35/1.75 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.35/1.75 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------