%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU374+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 : n005.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 0.24s 0.66s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 19 unt; 0 def)
% Number of atoms : 196 ( 28 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 245 ( 95 ~; 91 |; 28 &)
% ( 1 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 73 ( 0 sgn 28 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
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(t60_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( subrelstr(B,A)
=> ! [C] :
( element(C,the_carrier(A))
=> ! [D] :
( element(D,the_carrier(A))
=> ! [E] :
( element(E,the_carrier(B))
=> ! [F] :
( element(F,the_carrier(B))
=> ( ( related(B,E,F)
& F = D
& E = C )
=> related(A,C,D) ) ) ) ) ) ) ),
file('theBenchmark.p',t60_yellow_0) ).
fof(t20_yellow_6,conjecture,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( net_str(B,A)
=> ! [C] :
( subnetstr(C,A,B)
=> ! [D] :
( element(D,the_carrier(B))
=> ! [E] :
( element(E,the_carrier(B))
=> ! [F] :
( element(F,the_carrier(C))
=> ! [G] :
( element(G,the_carrier(C))
=> ( ( related(C,F,G)
& E = G
& D = F )
=> related(B,D,E) ) ) ) ) ) ) ) ),
file('theBenchmark.p',t20_yellow_6) ).
fof(t20_yellow_6_neg,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> ! [B] :
( net_str(B,A)
=> ! [C] :
( subnetstr(C,A,B)
=> ! [D] :
( element(D,the_carrier(B))
=> ! [E] :
( element(E,the_carrier(B))
=> ! [F] :
( element(F,the_carrier(C))
=> ! [G] :
( element(G,the_carrier(C))
=> ( ( related(C,F,G)
& E = G
& D = F )
=> related(B,D,E) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t20_yellow_6]) ).
fof(nnf_58,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( ? [G] :
( ~ related(B,D,E)
& related(C,F,G)
& G = E
& F = D
& element(G,the_carrier(C)) )
& element(F,the_carrier(C)) )
& element(E,the_carrier(B)) )
& element(D,the_carrier(B)) )
& subnetstr(C,A,B) )
& net_str(B,A) )
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[t20_yellow_6_neg]) ).
fof(sk_t20_yellow_6_neg,plain,
( ~ related(sK1,sK3,sK4)
& related(sK2,sK5,sK6)
& sK6 = sK4
& sK5 = sK3
& element(sK6,the_carrier(sK2))
& element(sK5,the_carrier(sK2))
& element(sK4,the_carrier(sK1))
& element(sK3,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,sK3,sK4,sK5,sK6]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK3),skolemize(E,sK4),skolemize(F,sK5),skolemize(G,sK6)],[nnf_58]) ).
cnf(c_60,negated_conjecture,
one_sorted_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t20_yellow_6_neg]) ).
cnf(c_66,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]) ).
cnf(c_67,plain,
( rel_str(B)
| ~ net_str(B,A)
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[dt_l1_waybel_0]) ).
cnf(c_71,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_75,negated_conjecture,
( subrelstr(B,A)
| ~ subnetstr(B,sK0,A)
| ~ net_str(B,sK0)
| ~ net_str(A,sK0) ),
inference(resolve,[status(thm)],[c_71,c_60]) ).
cnf(c_80,plain,
( related(A,C,D)
| ~ related(B,E,F)
| F != D
| E != C
| ~ element(F,the_carrier(B))
| ~ element(E,the_carrier(B))
| ~ element(D,the_carrier(A))
| ~ element(C,the_carrier(A))
| ~ subrelstr(B,A)
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[t60_yellow_0]) ).
cnf(c_106,negated_conjecture,
( rel_str(A)
| ~ net_str(A,sK0) ),
inference(resolve,[status(thm)],[c_67,c_60]) ).
cnf(c_108,negated_conjecture,
( net_str(B,sK0)
| ~ subnetstr(B,sK0,A)
| ~ net_str(A,sK0) ),
inference(resolve,[status(thm)],[c_66,c_60]) ).
cnf(c_164,negated_conjecture,
net_str(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t20_yellow_6_neg]) ).
cnf(c_165,negated_conjecture,
subnetstr(sK2,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t20_yellow_6_neg]) ).
cnf(c_166,negated_conjecture,
element(sK3,the_carrier(sK1)),
inference(split_conjunct,[status(thm)],[sk_t20_yellow_6_neg]) ).
cnf(c_167,negated_conjecture,
element(sK4,the_carrier(sK1)),
inference(split_conjunct,[status(thm)],[sk_t20_yellow_6_neg]) ).
cnf(c_168,negated_conjecture,
element(sK5,the_carrier(sK2)),
inference(split_conjunct,[status(thm)],[sk_t20_yellow_6_neg]) ).
cnf(c_169,negated_conjecture,
element(sK6,the_carrier(sK2)),
inference(split_conjunct,[status(thm)],[sk_t20_yellow_6_neg]) ).
cnf(c_170,negated_conjecture,
sK5 = sK3,
inference(split_conjunct,[status(thm)],[sk_t20_yellow_6_neg]) ).
cnf(c_171,negated_conjecture,
sK6 = sK4,
inference(split_conjunct,[status(thm)],[sk_t20_yellow_6_neg]) ).
cnf(c_172,negated_conjecture,
related(sK2,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_t20_yellow_6_neg]) ).
cnf(c_403,negated_conjecture,
related(sK2,sK3,sK6),
inference(paramod,[status(thm)],[c_170,c_172]) ).
cnf(c_173,negated_conjecture,
related(sK2,sK3,sK4),
inference(paramod,[status(thm)],[c_171,c_403]) ).
cnf(c_174,negated_conjecture,
~ related(sK1,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_t20_yellow_6_neg]) ).
cnf(c_191,negated_conjecture,
( ~ subnetstr(E,sK0,A)
| ~ net_str(E,sK0)
| ~ net_str(A,sK0)
| related(A,B,C)
| ~ related(E,D,F)
| F != C
| D != B
| ~ element(F,the_carrier(E))
| ~ element(D,the_carrier(E))
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ rel_str(A) ),
inference(resolve,[status(thm)],[c_80,c_75]) ).
cnf(c_198,negated_conjecture,
element(sK3,the_carrier(sK2)),
inference(paramod,[status(thm)],[c_170,c_168]) ).
cnf(c_199,negated_conjecture,
element(sK4,the_carrier(sK2)),
inference(paramod,[status(thm)],[c_171,c_169]) ).
cnf(c_329,plain,
rel_str(sK1),
inference(resolve,[status(thm)],[c_164,c_106]) ).
cnf(c_404,negated_conjecture,
( net_str(sK2,sK0)
| ~ net_str(sK1,sK0) ),
inference(resolve,[status(thm)],[c_165,c_108]) ).
cnf(c_330,negated_conjecture,
net_str(sK2,sK0),
inference(resolve,[status(thm)],[c_164,c_404]) ).
cnf(c_405,negated_conjecture,
( ~ subnetstr(D,sK0,sK1)
| ~ net_str(D,sK0)
| ~ net_str(sK1,sK0)
| related(sK1,A,B)
| ~ related(D,C,E)
| E != B
| C != A
| ~ element(E,the_carrier(D))
| ~ element(C,the_carrier(D))
| ~ element(B,the_carrier(sK1))
| ~ element(A,the_carrier(sK1)) ),
inference(resolve,[status(thm)],[c_191,c_329]) ).
cnf(c_406,negated_conjecture,
( ~ subnetstr(C,sK0,sK1)
| ~ net_str(C,sK0)
| ~ net_str(sK1,sK0)
| related(sK1,sK3,A)
| ~ related(C,B,D)
| D != A
| B != sK3
| ~ element(D,the_carrier(C))
| ~ element(B,the_carrier(C))
| ~ element(A,the_carrier(sK1)) ),
inference(resolve,[status(thm)],[c_405,c_166]) ).
cnf(c_407,negated_conjecture,
( ~ subnetstr(B,sK0,sK1)
| ~ net_str(B,sK0)
| ~ net_str(sK1,sK0)
| related(sK1,sK3,sK4)
| ~ related(B,A,C)
| C != sK4
| A != sK3
| ~ element(C,the_carrier(B))
| ~ element(A,the_carrier(B)) ),
inference(resolve,[status(thm)],[c_406,c_167]) ).
cnf(c_408,negated_conjecture,
( ~ subnetstr(sK2,sK0,sK1)
| ~ net_str(sK2,sK0)
| ~ net_str(sK1,sK0)
| related(sK1,sK3,sK4)
| ~ related(sK2,sK3,A)
| A != sK4
| sK3 != sK3
| ~ element(A,the_carrier(sK2)) ),
inference(resolve,[status(thm)],[c_407,c_198]) ).
cnf(c_409,negated_conjecture,
( ~ subnetstr(sK2,sK0,sK1)
| ~ net_str(sK2,sK0)
| ~ net_str(sK1,sK0)
| related(sK1,sK3,sK4)
| ~ related(sK2,sK3,sK4)
| sK4 != sK4
| sK3 != sK3 ),
inference(resolve,[status(thm)],[c_408,c_199]) ).
cnf(c_410,plain,
( ~ subnetstr(sK2,sK0,sK1)
| ~ net_str(sK2,sK0)
| ~ net_str(sK1,sK0)
| related(sK1,sK3,sK4)
| ~ related(sK2,sK3,sK4)
| sK4 != sK4 ),
inference(xxres,[status(thm)],[c_409]) ).
cnf(c_411,plain,
( ~ subnetstr(sK2,sK0,sK1)
| ~ net_str(sK2,sK0)
| ~ net_str(sK1,sK0)
| related(sK1,sK3,sK4)
| ~ related(sK2,sK3,sK4) ),
inference(xxres,[status(thm)],[c_410]) ).
cnf(c_412,negated_conjecture,
( ~ subnetstr(sK2,sK0,sK1)
| ~ net_str(sK2,sK0)
| ~ net_str(sK1,sK0)
| related(sK1,sK3,sK4) ),
inference(resolve,[status(thm)],[c_411,c_173]) ).
cnf(c_413,negated_conjecture,
( ~ subnetstr(sK2,sK0,sK1)
| ~ net_str(sK2,sK0)
| related(sK1,sK3,sK4) ),
inference(resolve,[status(thm)],[c_412,c_164]) ).
cnf(c_414,negated_conjecture,
( ~ subnetstr(sK2,sK0,sK1)
| related(sK1,sK3,sK4) ),
inference(resolve,[status(thm)],[c_413,c_330]) ).
cnf(c_415,negated_conjecture,
related(sK1,sK3,sK4),
inference(resolve,[status(thm)],[c_414,c_165]) ).
cnf(c_402,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_174,c_415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU374+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n005.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 09:21:31 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 1828959 was started by sandbox2 on n005,
% 0.16/0.44 % Sat Sep 26 09:21:31 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.46
% 0.16/0.46 % From the command line: assign(max_seconds, 300).
% 0.24/0.66
% 0.24/0.66 % SZS status Theorem for theBenchmark
% 0.24/0.66
% 0.24/0.66 % Proof 1 at 0.17 (+ 0.02) seconds.
% 0.24/0.66 % Length of proof is 30.
% 0.24/0.66 % Level of proof is 4.
% 0.24/0.66 % Maximum clause weight is 52.000.
% 0.24/0.66 % Given clauses 185.
% 0.24/0.66
% 0.24/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------