%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU373+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Sun Sep 27 08:46:07 AM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 9 unt; 0 def)
% Number of atoms : 95 ( 1 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 111 ( 47 ~; 38 |; 9 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 33 ( 0 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d13_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( rel_str(B)
=> ( subrelstr(B,A)
<=> ( subset(the_InternalRel(B),the_InternalRel(A))
& subset(the_carrier(B),the_carrier(A)) ) ) ) ),
file('theBenchmark.p',d13_yellow_0) ).
fof(d8_yellow_6,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( net_str(B,A)
=> ! [C] :
( net_str(C,A)
=> ( subnetstr(C,A,B)
<=> ( the_mapping(A,C) = relation_dom_restr_as_relation_of(the_carrier(B),the_carrier(A),the_mapping(A,B),the_carrier(C))
& subrelstr(C,B) ) ) ) ) ),
file('theBenchmark.p',d8_yellow_6) ).
fof(dt_l1_waybel_0,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( net_str(B,A)
=> rel_str(B) ) ),
file('theBenchmark.p',dt_l1_waybel_0) ).
fof(dt_m1_yellow_6,axiom,
! [A,B] :
( ( net_str(B,A)
& one_sorted_str(A) )
=> ! [C] :
( subnetstr(C,A,B)
=> net_str(C,A) ) ),
file('theBenchmark.p',dt_m1_yellow_6) ).
fof(t19_yellow_6,conjecture,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( net_str(B,A)
=> ! [C] :
( subnetstr(C,A,B)
=> subset(the_carrier(C),the_carrier(B)) ) ) ),
file('theBenchmark.p',t19_yellow_6) ).
fof(t19_yellow_6_neg,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> ! [B] :
( net_str(B,A)
=> ! [C] :
( subnetstr(C,A,B)
=> subset(the_carrier(C),the_carrier(B)) ) ) ),
inference(assume_negation,[status(cth)],[t19_yellow_6]) ).
cnf(c_63,plain,
( subrelstr(C,B)
| ~ subnetstr(C,A,B)
| ~ net_str(C,A)
| ~ net_str(B,A)
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[d8_yellow_6]) ).
cnf(c_66,plain,
( subset(the_carrier(B),the_carrier(A))
| ~ subrelstr(B,A)
| ~ rel_str(B)
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[d13_yellow_0]) ).
cnf(c_74,plain,
( ~ subnetstr(B,C,A)
| ~ net_str(B,C)
| ~ net_str(A,C)
| ~ one_sorted_str(C)
| subset(the_carrier(B),the_carrier(A))
| ~ rel_str(B)
| ~ rel_str(A) ),
inference(resolve,[status(thm)],[c_66,c_63]) ).
cnf(c_91,plain,
( rel_str(B)
| ~ net_str(B,A)
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[dt_l1_waybel_0]) ).
cnf(c_92,plain,
( net_str(C,A)
| ~ subnetstr(C,A,B)
| ~ net_str(B,A)
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[dt_m1_yellow_6]) ).
fof(nnf_59,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ subset(the_carrier(C),the_carrier(B))
& subnetstr(C,A,B) )
& net_str(B,A) )
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[t19_yellow_6_neg]) ).
fof(sk_t19_yellow_6_neg,plain,
( ~ subset(the_carrier(sK2),the_carrier(sK1))
& subnetstr(sK2,sK0,sK1)
& net_str(sK1,sK0)
& one_sorted_str(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_59]) ).
cnf(c_143,negated_conjecture,
one_sorted_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t19_yellow_6_neg]) ).
cnf(c_144,negated_conjecture,
net_str(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t19_yellow_6_neg]) ).
cnf(c_145,negated_conjecture,
subnetstr(sK2,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t19_yellow_6_neg]) ).
cnf(c_146,negated_conjecture,
~ subset(the_carrier(sK2),the_carrier(sK1)),
inference(split_conjunct,[status(thm)],[sk_t19_yellow_6_neg]) ).
cnf(c_245,negated_conjecture,
( rel_str(sK1)
| ~ one_sorted_str(sK0) ),
inference(resolve,[status(thm)],[c_144,c_91]) ).
cnf(c_223,negated_conjecture,
rel_str(sK1),
inference(resolve,[status(thm)],[c_143,c_245]) ).
cnf(c_246,negated_conjecture,
( net_str(sK2,sK0)
| ~ net_str(sK1,sK0)
| ~ one_sorted_str(sK0) ),
inference(resolve,[status(thm)],[c_145,c_92]) ).
cnf(c_247,negated_conjecture,
( net_str(sK2,sK0)
| ~ net_str(sK1,sK0) ),
inference(resolve,[status(thm)],[c_143,c_246]) ).
cnf(c_224,negated_conjecture,
net_str(sK2,sK0),
inference(resolve,[status(thm)],[c_144,c_247]) ).
cnf(c_248,negated_conjecture,
( ~ net_str(sK2,sK0)
| ~ net_str(sK1,sK0)
| ~ one_sorted_str(sK0)
| subset(the_carrier(sK2),the_carrier(sK1))
| ~ rel_str(sK2)
| ~ rel_str(sK1) ),
inference(resolve,[status(thm)],[c_145,c_74]) ).
cnf(c_249,negated_conjecture,
( ~ net_str(sK2,sK0)
| ~ net_str(sK1,sK0)
| ~ one_sorted_str(sK0)
| subset(the_carrier(sK2),the_carrier(sK1))
| ~ rel_str(sK2) ),
inference(resolve,[status(thm)],[c_223,c_248]) ).
cnf(c_250,negated_conjecture,
( ~ net_str(sK2,sK0)
| ~ net_str(sK1,sK0)
| ~ one_sorted_str(sK0)
| ~ rel_str(sK2) ),
inference(resolve,[status(thm)],[c_146,c_249]) ).
cnf(c_251,negated_conjecture,
( ~ net_str(sK2,sK0)
| ~ net_str(sK1,sK0)
| ~ rel_str(sK2) ),
inference(resolve,[status(thm)],[c_143,c_250]) ).
cnf(c_252,negated_conjecture,
( ~ net_str(sK2,sK0)
| ~ rel_str(sK2) ),
inference(resolve,[status(thm)],[c_144,c_251]) ).
cnf(c_228,negated_conjecture,
~ rel_str(sK2),
inference(resolve,[status(thm)],[c_224,c_252]) ).
cnf(c_253,negated_conjecture,
( rel_str(A)
| ~ net_str(A,sK0) ),
inference(resolve,[status(thm)],[c_91,c_143]) ).
cnf(c_254,negated_conjecture,
~ net_str(sK2,sK0),
inference(resolve,[status(thm)],[c_253,c_228]) ).
cnf(c_244,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_224,c_254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU373+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 09:24:25 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 652133 was started by sandbox on n026,
% 0.08/0.36 % Sat Sep 26 09:24:25 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.12/0.40
% 0.12/0.40 % SZS status Theorem for theBenchmark
% 0.12/0.40
% 0.12/0.40 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.12/0.40 % Length of proof is 18.
% 0.12/0.40 % Level of proof is 4.
% 0.12/0.40 % Maximum clause weight is 21.000.
% 0.12/0.40 % Given clauses 83.
% 0.12/0.40
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------