%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU368+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Sun Sep 27 08:46:06 AM UTC 2026
% Result : Theorem 0.24s 0.53s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 20 unt; 0 def)
% Number of atoms : 89 ( 59 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 75 ( 36 ~; 26 |; 8 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 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 : 66 ( 10 sgn 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(free_g1_orders_2,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('theBenchmark.p',free_g1_orders_2) ).
fof(abstractness_v1_orders_2,axiom,
! [A] :
( rel_str(A)
=> ( strict_rel_str(A)
=> A = rel_str_of(the_carrier(A),the_InternalRel(A)) ) ),
file('theBenchmark.p',abstractness_v1_orders_2) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(redefinition_k1_yellow_1,axiom,
! [A] : inclusion_order(A) = inclusion_relation(A),
file('theBenchmark.p',redefinition_k1_yellow_1) ).
fof(dt_k1_yellow_1,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('theBenchmark.p',dt_k1_yellow_1) ).
fof(dt_k2_yellow_1,axiom,
! [A] :
( rel_str(incl_POSet(A))
& strict_rel_str(incl_POSet(A)) ),
file('theBenchmark.p',dt_k2_yellow_1) ).
fof(d1_yellow_1,axiom,
! [A] : incl_POSet(A) = rel_str_of(A,inclusion_order(A)),
file('theBenchmark.p',d1_yellow_1) ).
fof(t1_yellow_1,conjecture,
! [A] :
( the_InternalRel(incl_POSet(A)) = inclusion_order(A)
& the_carrier(incl_POSet(A)) = A ),
file('theBenchmark.p',t1_yellow_1) ).
fof(t1_yellow_1_neg,negated_conjecture,
~ ! [A] :
( the_InternalRel(incl_POSet(A)) = inclusion_order(A)
& the_carrier(incl_POSet(A)) = A ),
inference(assume_negation,[status(cth)],[t1_yellow_1]) ).
cnf(c_59,plain,
rel_str(incl_POSet(A)),
inference(clausify,[status(thm)],[dt_k2_yellow_1]) ).
cnf(c_72,plain,
( rel_str_of(the_carrier(A),the_InternalRel(A)) = A
| ~ strict_rel_str(A)
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[abstractness_v1_orders_2]) ).
cnf(c_88,plain,
relation_of2_as_subset(inclusion_order(A),A,A),
inference(clausify,[status(thm)],[dt_k1_yellow_1]) ).
cnf(c_90,plain,
( relation_of2(A,B,C)
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[redefinition_m2_relset_1]) ).
cnf(c_109,plain,
relation_of2(inclusion_order(A),A,A),
inference(resolve,[status(thm)],[c_90,c_88]) ).
cnf(c_143,plain,
( rel_str_of(the_carrier(incl_POSet(A)),the_InternalRel(incl_POSet(A))) = incl_POSet(A)
| ~ strict_rel_str(incl_POSet(A)) ),
inference(resolve,[status(thm)],[c_72,c_59]) ).
cnf(c_203,plain,
( C = B
| rel_str_of(C,D) != rel_str_of(B,A)
| ~ relation_of2(A,B,B) ),
inference(clausify,[status(thm)],[free_g1_orders_2]) ).
cnf(c_204,plain,
( D = A
| rel_str_of(C,D) != rel_str_of(B,A)
| ~ relation_of2(A,B,B) ),
inference(clausify,[status(thm)],[free_g1_orders_2]) ).
cnf(c_207,plain,
inclusion_order(A) = inclusion_relation(A),
inference(clausify,[status(thm)],[redefinition_k1_yellow_1]) ).
cnf(c_214,plain,
strict_rel_str(incl_POSet(A)),
inference(clausify,[status(thm)],[dt_k2_yellow_1]) ).
cnf(c_218,plain,
rel_str_of(A,inclusion_order(A)) = incl_POSet(A),
inference(clausify,[status(thm)],[d1_yellow_1]) ).
cnf(c_507,plain,
rel_str_of(A,inclusion_relation(A)) = incl_POSet(A),
inference(paramod,[status(thm)],[c_207,c_218]) ).
cnf(c_219,plain,
incl_POSet(A) = rel_str_of(A,inclusion_relation(A)),
inference(copy,[status(thm)],[c_507]) ).
fof(nnf_52,plain,
? [A] :
( inclusion_order(A) != the_InternalRel(incl_POSet(A))
| the_carrier(incl_POSet(A)) != A ),
inference(fof_nnf,[status(thm)],[t1_yellow_1_neg]) ).
fof(sk_t1_yellow_1_neg,plain,
( inclusion_order(sK0) != the_InternalRel(incl_POSet(sK0))
| the_carrier(incl_POSet(sK0)) != sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_52]) ).
cnf(c_220,negated_conjecture,
( inclusion_order(sK0) != the_InternalRel(incl_POSet(sK0))
| the_carrier(incl_POSet(sK0)) != sK0 ),
inference(split_conjunct,[status(thm)],[sk_t1_yellow_1_neg]) ).
cnf(c_508,negated_conjecture,
( inclusion_order(sK0) != the_InternalRel(incl_POSet(sK0))
| the_carrier(rel_str_of(sK0,inclusion_relation(sK0))) != sK0 ),
inference(paramod,[status(thm)],[c_219,c_220]) ).
cnf(c_509,negated_conjecture,
( inclusion_relation(sK0) != the_InternalRel(incl_POSet(sK0))
| the_carrier(rel_str_of(sK0,inclusion_relation(sK0))) != sK0 ),
inference(paramod,[status(thm)],[c_207,c_508]) ).
cnf(c_510,negated_conjecture,
( inclusion_relation(sK0) != the_InternalRel(rel_str_of(sK0,inclusion_relation(sK0)))
| the_carrier(rel_str_of(sK0,inclusion_relation(sK0))) != sK0 ),
inference(paramod,[status(thm)],[c_219,c_509]) ).
cnf(c_221,negated_conjecture,
( the_InternalRel(rel_str_of(sK0,inclusion_relation(sK0))) != inclusion_relation(sK0)
| the_carrier(rel_str_of(sK0,inclusion_relation(sK0))) != sK0 ),
inference(copy,[status(thm)],[c_510]) ).
cnf(c_249,plain,
relation_of2(inclusion_relation(A),A,A),
inference(paramod,[status(thm)],[c_207,c_109]) ).
cnf(c_511,plain,
( rel_str_of(the_carrier(incl_POSet(A)),the_InternalRel(incl_POSet(A))) = incl_POSet(A)
| ~ strict_rel_str(rel_str_of(A,inclusion_relation(A))) ),
inference(paramod,[status(thm)],[c_219,c_143]) ).
cnf(c_512,plain,
( rel_str_of(the_carrier(rel_str_of(A,inclusion_relation(A))),the_InternalRel(incl_POSet(A))) = incl_POSet(A)
| ~ strict_rel_str(rel_str_of(A,inclusion_relation(A))) ),
inference(paramod,[status(thm)],[c_219,c_511]) ).
cnf(c_513,plain,
( rel_str_of(the_carrier(rel_str_of(A,inclusion_relation(A))),the_InternalRel(rel_str_of(A,inclusion_relation(A)))) = incl_POSet(A)
| ~ strict_rel_str(rel_str_of(A,inclusion_relation(A))) ),
inference(paramod,[status(thm)],[c_219,c_512]) ).
cnf(c_250,plain,
( rel_str_of(the_carrier(rel_str_of(A,inclusion_relation(A))),the_InternalRel(rel_str_of(A,inclusion_relation(A)))) = rel_str_of(A,inclusion_relation(A))
| ~ strict_rel_str(rel_str_of(A,inclusion_relation(A))) ),
inference(paramod,[status(thm)],[c_219,c_513]) ).
cnf(c_260,plain,
strict_rel_str(rel_str_of(A,inclusion_relation(A))),
inference(paramod,[status(thm)],[c_219,c_214]) ).
cnf(c_273,plain,
rel_str_of(the_carrier(rel_str_of(A,inclusion_relation(A))),the_InternalRel(rel_str_of(A,inclusion_relation(A)))) = rel_str_of(A,inclusion_relation(A)),
inference(resolve,[status(thm)],[c_260,c_250]) ).
cnf(c_514,plain,
( B = inclusion_relation(C)
| rel_str_of(A,B) != rel_str_of(C,inclusion_relation(C)) ),
inference(resolve,[status(thm)],[c_249,c_204]) ).
cnf(c_515,plain,
( B = inclusion_relation(C)
| rel_str_of(C,inclusion_relation(C)) != rel_str_of(A,B) ),
inference(copy,[status(thm)],[c_514]) ).
cnf(c_343,plain,
( inclusion_relation(A) = C
| rel_str_of(A,inclusion_relation(A)) != rel_str_of(B,C) ),
inference(copy,[status(thm)],[c_515]) ).
cnf(c_516,plain,
( A = C
| rel_str_of(A,B) != rel_str_of(C,inclusion_relation(C)) ),
inference(resolve,[status(thm)],[c_249,c_203]) ).
cnf(c_344,plain,
( B = A
| rel_str_of(A,inclusion_relation(A)) != rel_str_of(B,C) ),
inference(copy,[status(thm)],[c_516]) ).
cnf(c_517,plain,
rel_str_of(A,inclusion_relation(A)) = rel_str_of(the_carrier(rel_str_of(A,inclusion_relation(A))),the_InternalRel(rel_str_of(A,inclusion_relation(A)))),
inference(copy,[status(thm)],[c_273]) ).
cnf(c_449,plain,
the_carrier(rel_str_of(A,inclusion_relation(A))) = A,
inference(resolve,[status(thm)],[c_344,c_517]) ).
cnf(c_456,plain,
rel_str_of(A,the_InternalRel(rel_str_of(A,inclusion_relation(A)))) = rel_str_of(A,inclusion_relation(A)),
inference(paramod,[status(thm)],[c_449,c_273]) ).
cnf(c_518,negated_conjecture,
( the_InternalRel(rel_str_of(sK0,inclusion_relation(sK0))) != inclusion_relation(sK0)
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_449,c_221]) ).
cnf(c_462,negated_conjecture,
the_InternalRel(rel_str_of(sK0,inclusion_relation(sK0))) != inclusion_relation(sK0),
inference(copy,[status(thm)],[c_518]) ).
cnf(c_519,plain,
( inclusion_relation(A) = C
| rel_str_of(B,C) != rel_str_of(A,inclusion_relation(A)) ),
inference(copy,[status(thm)],[c_343]) ).
cnf(c_520,plain,
inclusion_relation(A) = the_InternalRel(rel_str_of(A,inclusion_relation(A))),
inference(resolve,[status(thm)],[c_456,c_519]) ).
cnf(c_505,plain,
the_InternalRel(rel_str_of(A,inclusion_relation(A))) = inclusion_relation(A),
inference(copy,[status(thm)],[c_520]) ).
cnf(c_506,plain,
$false,
inference(resolve,[status(thm)],[c_505,c_462]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU368+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n008.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 09:21:13 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 3293118 was started by sandbox2 on n008,
% 0.18/0.45 % Sat Sep 26 09:21:13 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 0.24/0.53
% 0.24/0.53 % SZS status Theorem for theBenchmark
% 0.24/0.53
% 0.24/0.53 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.24/0.53 % Length of proof is 33.
% 0.24/0.53 % Level of proof is 8.
% 0.24/0.53 % Maximum clause weight is 21.000.
% 0.24/0.53 % Given clauses 263.
% 0.24/0.53
% 0.24/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------