%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU368+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 02:51:52 PM UTC 2026
% Result : Theorem 8.31s 6.56s
% Output : Proof 8.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 19 unt; 0 def)
% Number of atoms : 104 ( 52 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 90 ( 35 ~; 28 |; 22 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 74 ( 8 sgn 38 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f33,axiom,
! [A] :
( rel_str(A)
=> ( strict_rel_str(A)
=> A = rel_str_of(the_carrier(A),the_InternalRel(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(f33_nnf,plain,
! [A] :
( A = rel_str_of(the_carrier(A),the_InternalRel(A))
| ~ strict_rel_str(A)
| ~ rel_str(A) ),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [A] :
( A = rel_str_of(the_carrier(A),the_InternalRel(A))
| ~ strict_rel_str(A)
| ~ rel_str(A) ),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c52,plain,
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
fof(f47,axiom,
! [A] :
( rel_str(incl_POSet(A))
& strict_rel_str(incl_POSet(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_yellow_1) ).
fof(f47_nnf,plain,
! [A] :
( rel_str(incl_POSet(A))
& strict_rel_str(incl_POSet(A)) ),
inference(nnf_transformation,[status(thm)],[f47]) ).
fof(f47_sk,plain,
! [A] :
( rel_str(incl_POSet(A))
& strict_rel_str(incl_POSet(A)) ),
inference(skolemisation,[status(esa)],[f47_nnf]) ).
cnf(c78,plain,
rel_str(incl_POSet(X0)),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(p164,plain,
( incl_POSet(X0) = rel_str_of(the_carrier(incl_POSet(X0)),the_InternalRel(incl_POSet(X0)))
| ~ strict_rel_str(incl_POSet(X0)) ),
inference(resolution,[status(thm)],[c52,c78]) ).
cnf(c77,plain,
strict_rel_str(incl_POSet(X0)),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(p354,plain,
incl_POSet(X0) = rel_str_of(the_carrier(incl_POSet(X0)),the_InternalRel(incl_POSet(X0))),
inference(resolution,[status(thm)],[p164,c77]) ).
fof(f45,axiom,
! [A] : inclusion_order(A) = inclusion_relation(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_yellow_1) ).
fof(f45_nnf,plain,
! [A] : inclusion_order(A) = inclusion_relation(A),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
! [A] : inclusion_order(A) = inclusion_relation(A),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c71,plain,
inclusion_order(X0) = inclusion_relation(X0),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
fof(f51,axiom,
! [A] : incl_POSet(A) = rel_str_of(A,inclusion_order(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_yellow_1) ).
fof(f51_nnf,plain,
! [A] : incl_POSet(A) = rel_str_of(A,inclusion_order(A)),
inference(nnf_transformation,[status(thm)],[f51]) ).
fof(f51_sk,plain,
! [A] : incl_POSet(A) = rel_str_of(A,inclusion_order(A)),
inference(skolemisation,[status(esa)],[f51_nnf]) ).
cnf(c85,plain,
incl_POSet(X0) = rel_str_of(X0,inclusion_order(X0)),
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(p124,plain,
incl_POSet(X0) = rel_str_of(X0,inclusion_relation(X0)),
inference(superposition,[status(thm)],[c71,c85]) ).
fof(f32,axiom,
! [A,B] :
( relation_of2(B,A,A)
=> ! [C,D] :
( rel_str_of(A,B) = rel_str_of(C,D)
=> ( B = D
& A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(f32_nnf,plain,
! [A,B] :
( ! [C,D] :
( ( B = D
& A = C )
| rel_str_of(A,B) != rel_str_of(C,D) )
| ~ relation_of2(B,A,A) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [B,A,C,D] :
( ( B = D
& A = C )
| rel_str_of(A,B) != rel_str_of(C,D)
| ~ relation_of2(B,A,A) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c51,plain,
( X1 = X3
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f37,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f37_nnf,plain,
! [A,B,C] :
( ( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [C,A,B] :
( ( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c56,plain,
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
fof(f46,axiom,
! [A] :
( relation_of2_as_subset(inclusion_order(A),A,A)
& v1_partfun1(inclusion_order(A),A,A)
& transitive(inclusion_order(A))
& antisymmetric(inclusion_order(A))
& reflexive(inclusion_order(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_1) ).
fof(f46_nnf,plain,
! [A] :
( relation_of2_as_subset(inclusion_order(A),A,A)
& v1_partfun1(inclusion_order(A),A,A)
& transitive(inclusion_order(A))
& antisymmetric(inclusion_order(A))
& reflexive(inclusion_order(A)) ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [A] :
( relation_of2_as_subset(inclusion_order(A),A,A)
& v1_partfun1(inclusion_order(A),A,A)
& transitive(inclusion_order(A))
& antisymmetric(inclusion_order(A))
& reflexive(inclusion_order(A)) ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c76,plain,
relation_of2_as_subset(inclusion_order(X0),X0,X0),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(p145,plain,
relation_of2(inclusion_relation(X0),X0,X0),
inference(resolution,[status(thm)],[c56,c76]) ).
cnf(p155,plain,
( inclusion_relation(X0) = X2
| rel_str_of(X0,inclusion_relation(X0)) != rel_str_of(X1,X2) ),
inference(resolution,[status(thm)],[c51,p145]) ).
cnf(p343,plain,
( inclusion_relation(X0) = X2
| incl_POSet(X0) != rel_str_of(X1,X2) ),
inference(superposition,[status(thm)],[p124,p155]) ).
cnf(p367,plain,
inclusion_relation(X0) = the_InternalRel(incl_POSet(X0)),
inference(resolution,[status(thm)],[p354,p343]) ).
cnf(c50,plain,
( X0 = X2
| rel_str_of(X0,X1) != rel_str_of(X2,X3)
| ~ relation_of2(X1,X0,X0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p150,plain,
( X0 = X1
| rel_str_of(X0,inclusion_relation(X0)) != rel_str_of(X1,X2) ),
inference(resolution,[status(thm)],[p145,c50]) ).
cnf(p320,plain,
( X0 = X1
| incl_POSet(X0) != rel_str_of(X1,X2) ),
inference(superposition,[status(thm)],[p124,p150]) ).
cnf(p362,plain,
X0 = the_carrier(incl_POSet(X0)),
inference(resolution,[status(thm)],[p354,p320]) ).
fof(f52,conjecture,
! [A] :
( the_InternalRel(incl_POSet(A)) = inclusion_order(A)
& the_carrier(incl_POSet(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_yellow_1) ).
fof(f52_neg,negated_conjecture,
~ ! [A] :
( the_InternalRel(incl_POSet(A)) = inclusion_order(A)
& the_carrier(incl_POSet(A)) = A ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
? [A] :
( the_InternalRel(incl_POSet(A)) != inclusion_order(A)
| the_carrier(incl_POSet(A)) != A ),
inference(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
( the_InternalRel(incl_POSet(sk13)) != inclusion_order(sk13)
| the_carrier(incl_POSet(sk13)) != sk13 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13])],[f52_nnf]) ).
cnf(c86,plain,
( the_InternalRel(incl_POSet(sk13)) != inclusion_order(sk13)
| the_carrier(incl_POSet(sk13)) != sk13 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(p373,plain,
( the_InternalRel(incl_POSet(sk13)) != inclusion_relation(sk13)
| sk13 != sk13 ),
inference(superposition,[status(thm)],[p362,c86]) ).
cnf(p447,plain,
the_InternalRel(incl_POSet(sk13)) != inclusion_relation(sk13),
inference(equality_resolution,[status(thm)],[p373]) ).
cnf(p448,plain,
inclusion_relation(sk13) != inclusion_relation(sk13),
inference(superposition,[status(thm)],[p367,p447]) ).
cnf(p449,plain,
$false,
inference(equality_resolution,[status(thm)],[p448]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU368+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.36 % Computer : n011.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Thu Sep 24 13:52:17 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.31/6.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.31/6.56 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------