%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU375+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 : n020.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 2.19s 0.81s
% Output : CNFRefutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 69 ( 22 unt; 0 def)
% Number of atoms : 348 ( 41 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 496 ( 217 ~; 202 |; 43 &)
% ( 1 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-1 aty)
% Number of variables : 119 ( 0 sgn 31 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d9_yellow_6,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( net_str(B,A)
=> ! [C] :
( subnetstr(C,A,B)
=> ( full_subnetstr(C,A,B)
<=> ( subrelstr(C,B)
& full_subrelstr(C,B) ) ) ) ) ),
file('theBenchmark.p',d9_yellow_6) ).
fof(dt_l1_orders_2,axiom,
! [A] :
( rel_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l1_orders_2) ).
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_0,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( subrelstr(B,A)
=> rel_str(B) ) ),
file('theBenchmark.p',dt_m1_yellow_0) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(the_carrier(A)) ),
file('theBenchmark.p',fc1_struct_0) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t61_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( ( subrelstr(B,A)
& full_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))
=> ( ( in(F,the_carrier(B))
& in(E,the_carrier(B))
& related(A,C,D)
& F = D
& E = C )
=> related(B,E,F) ) ) ) ) ) ) ),
file('theBenchmark.p',t61_yellow_0) ).
fof(t21_yellow_6,conjecture,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( ( net_str(B,A)
& ~ empty_carrier(B) )
=> ! [C] :
( ( subnetstr(C,A,B)
& full_subnetstr(C,A,B)
& ~ empty_carrier(C) )
=> ! [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(B,D,E)
& E = G
& D = F )
=> related(C,F,G) ) ) ) ) ) ) ) ),
file('theBenchmark.p',t21_yellow_6) ).
fof(t21_yellow_6_neg,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> ! [B] :
( ( net_str(B,A)
& ~ empty_carrier(B) )
=> ! [C] :
( ( subnetstr(C,A,B)
& full_subnetstr(C,A,B)
& ~ empty_carrier(C) )
=> ! [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(B,D,E)
& E = G
& D = F )
=> related(C,F,G) ) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t21_yellow_6]) ).
cnf(c_60,plain,
( one_sorted_str(A)
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[dt_l1_orders_2]) ).
cnf(c_62,plain,
( subrelstr(C,B)
| ~ full_subnetstr(C,A,B)
| ~ subnetstr(C,A,B)
| ~ net_str(B,A)
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[d9_yellow_6]) ).
cnf(c_63,plain,
( full_subrelstr(C,B)
| ~ full_subnetstr(C,A,B)
| ~ subnetstr(C,A,B)
| ~ net_str(B,A)
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[d9_yellow_6]) ).
cnf(c_64,plain,
( rel_str(B)
| ~ net_str(B,A)
| ~ one_sorted_str(A) ),
inference(clausify,[status(thm)],[dt_l1_waybel_0]) ).
cnf(c_69,plain,
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[fc1_struct_0]) ).
fof(nnf_40,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( ? [G] :
( ~ related(C,F,G)
& related(B,D,E)
& 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)
& full_subnetstr(C,A,B)
& ~ empty_carrier(C) )
& net_str(B,A)
& ~ empty_carrier(B) )
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[t21_yellow_6_neg]) ).
fof(sk_t21_yellow_6_neg,plain,
( ~ related(sK2,sK5,sK6)
& related(sK1,sK3,sK4)
& 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)
& full_subnetstr(sK2,sK0,sK1)
& ~ empty_carrier(sK2)
& net_str(sK1,sK0)
& ~ empty_carrier(sK1)
& 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_40]) ).
cnf(c_71,negated_conjecture,
one_sorted_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t21_yellow_6_neg]) ).
cnf(c_73,negated_conjecture,
( full_subrelstr(B,A)
| ~ full_subnetstr(B,sK0,A)
| ~ subnetstr(B,sK0,A)
| ~ net_str(A,sK0) ),
inference(resolve,[status(thm)],[c_71,c_63]) ).
cnf(c_80,plain,
( related(B,E,F)
| ~ in(F,the_carrier(B))
| ~ in(E,the_carrier(B))
| ~ related(A,C,D)
| 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)
| ~ full_subrelstr(B,A)
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[t61_yellow_0]) ).
cnf(c_82,plain,
( rel_str(B)
| ~ subrelstr(B,A)
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[dt_m1_yellow_0]) ).
cnf(c_99,negated_conjecture,
( ~ full_subnetstr(B,sK0,A)
| ~ subnetstr(B,sK0,A)
| ~ net_str(A,sK0)
| related(B,E,F)
| ~ in(F,the_carrier(B))
| ~ in(E,the_carrier(B))
| ~ related(A,C,D)
| 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(resolve,[status(thm)],[c_80,c_73]) ).
cnf(c_103,negated_conjecture,
( subrelstr(B,A)
| ~ full_subnetstr(B,sK0,A)
| ~ subnetstr(B,sK0,A)
| ~ net_str(A,sK0) ),
inference(resolve,[status(thm)],[c_71,c_62]) ).
cnf(c_113,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_118,negated_conjecture,
net_str(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_t21_yellow_6_neg]) ).
cnf(c_119,negated_conjecture,
~ empty_carrier(sK2),
inference(split_conjunct,[status(thm)],[sk_t21_yellow_6_neg]) ).
cnf(c_120,negated_conjecture,
full_subnetstr(sK2,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t21_yellow_6_neg]) ).
cnf(c_121,negated_conjecture,
subnetstr(sK2,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t21_yellow_6_neg]) ).
cnf(c_122,negated_conjecture,
element(sK3,the_carrier(sK1)),
inference(split_conjunct,[status(thm)],[sk_t21_yellow_6_neg]) ).
cnf(c_123,negated_conjecture,
element(sK4,the_carrier(sK1)),
inference(split_conjunct,[status(thm)],[sk_t21_yellow_6_neg]) ).
cnf(c_124,negated_conjecture,
element(sK5,the_carrier(sK2)),
inference(split_conjunct,[status(thm)],[sk_t21_yellow_6_neg]) ).
cnf(c_125,negated_conjecture,
element(sK6,the_carrier(sK2)),
inference(split_conjunct,[status(thm)],[sk_t21_yellow_6_neg]) ).
cnf(c_126,negated_conjecture,
sK5 = sK3,
inference(split_conjunct,[status(thm)],[sk_t21_yellow_6_neg]) ).
cnf(c_127,negated_conjecture,
sK6 = sK4,
inference(split_conjunct,[status(thm)],[sk_t21_yellow_6_neg]) ).
cnf(c_128,negated_conjecture,
related(sK1,sK3,sK4),
inference(split_conjunct,[status(thm)],[sk_t21_yellow_6_neg]) ).
cnf(c_129,negated_conjecture,
~ related(sK2,sK5,sK6),
inference(split_conjunct,[status(thm)],[sk_t21_yellow_6_neg]) ).
cnf(c_139,plain,
( ~ rel_str(A)
| ~ empty(the_carrier(A))
| empty_carrier(A) ),
inference(resolve,[status(thm)],[c_69,c_60]) ).
cnf(c_150,negated_conjecture,
( rel_str(A)
| ~ net_str(A,sK0) ),
inference(resolve,[status(thm)],[c_71,c_64]) ).
cnf(c_206,negated_conjecture,
( rel_str(B)
| ~ rel_str(A)
| ~ full_subnetstr(B,sK0,A)
| ~ subnetstr(B,sK0,A)
| ~ net_str(A,sK0) ),
inference(resolve,[status(thm)],[c_103,c_82]) ).
cnf(c_213,negated_conjecture,
( ~ full_subnetstr(B,sK0,A)
| ~ subnetstr(B,sK0,A)
| ~ net_str(A,sK0)
| related(B,E,F)
| ~ in(F,the_carrier(B))
| ~ in(E,the_carrier(B))
| ~ related(A,C,D)
| F != D
| E != C
| ~ element(F,the_carrier(B))
| ~ element(E,the_carrier(B))
| ~ element(D,the_carrier(A))
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ full_subnetstr(B,sK0,A)
| ~ subnetstr(B,sK0,A)
| ~ net_str(A,sK0) ),
inference(resolve,[status(thm)],[c_103,c_99]) ).
cnf(c_511,negated_conjecture,
( ~ full_subnetstr(B,sK0,A)
| ~ subnetstr(B,sK0,A)
| related(B,E,F)
| ~ in(F,the_carrier(B))
| ~ in(E,the_carrier(B))
| ~ related(A,C,D)
| F != D
| E != C
| ~ element(F,the_carrier(B))
| ~ element(E,the_carrier(B))
| ~ element(D,the_carrier(A))
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ full_subnetstr(B,sK0,A)
| ~ subnetstr(B,sK0,A)
| ~ net_str(A,sK0) ),
inference(copy,[status(thm)],[c_213]) ).
cnf(c_512,negated_conjecture,
( ~ full_subnetstr(B,sK0,A)
| related(B,E,F)
| ~ in(F,the_carrier(B))
| ~ in(E,the_carrier(B))
| ~ related(A,C,D)
| F != D
| E != C
| ~ element(F,the_carrier(B))
| ~ element(E,the_carrier(B))
| ~ element(D,the_carrier(A))
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ full_subnetstr(B,sK0,A)
| ~ subnetstr(B,sK0,A)
| ~ net_str(A,sK0) ),
inference(copy,[status(thm)],[c_511]) ).
cnf(c_214,negated_conjecture,
( related(B,E,F)
| ~ in(F,the_carrier(B))
| ~ in(E,the_carrier(B))
| ~ related(A,C,D)
| F != D
| E != C
| ~ element(F,the_carrier(B))
| ~ element(E,the_carrier(B))
| ~ element(D,the_carrier(A))
| ~ element(C,the_carrier(A))
| ~ rel_str(A)
| ~ full_subnetstr(B,sK0,A)
| ~ subnetstr(B,sK0,A)
| ~ net_str(A,sK0) ),
inference(copy,[status(thm)],[c_512]) ).
cnf(c_340,plain,
( in(sK6,the_carrier(sK2))
| empty(the_carrier(sK2)) ),
inference(resolve,[status(thm)],[c_125,c_113]) ).
cnf(c_341,plain,
element(sK3,the_carrier(sK2)),
inference(paramod,[status(thm)],[c_126,c_124]) ).
cnf(c_343,plain,
~ related(sK2,sK3,sK6),
inference(paramod,[status(thm)],[c_126,c_129]) ).
cnf(c_359,plain,
rel_str(sK1),
inference(resolve,[status(thm)],[c_150,c_118]) ).
cnf(c_513,negated_conjecture,
( rel_str(sK2)
| ~ rel_str(sK1)
| ~ subnetstr(sK2,sK0,sK1)
| ~ net_str(sK1,sK0) ),
inference(resolve,[status(thm)],[c_206,c_120]) ).
cnf(c_514,negated_conjecture,
( rel_str(sK2)
| ~ rel_str(sK1)
| ~ subnetstr(sK2,sK0,sK1) ),
inference(resolve,[status(thm)],[c_118,c_513]) ).
cnf(c_515,negated_conjecture,
( rel_str(sK2)
| ~ rel_str(sK1) ),
inference(resolve,[status(thm)],[c_121,c_514]) ).
cnf(c_366,negated_conjecture,
rel_str(sK2),
inference(resolve,[status(thm)],[c_359,c_515]) ).
cnf(c_516,negated_conjecture,
( ~ rel_str(sK2)
| ~ empty(the_carrier(sK2)) ),
inference(resolve,[status(thm)],[c_139,c_119]) ).
cnf(c_464,negated_conjecture,
~ empty(the_carrier(sK2)),
inference(resolve,[status(thm)],[c_516,c_366]) ).
cnf(c_465,plain,
in(sK6,the_carrier(sK2)),
inference(resolve,[status(thm)],[c_464,c_340]) ).
cnf(c_517,plain,
( in(sK3,the_carrier(sK2))
| empty(the_carrier(sK2)) ),
inference(resolve,[status(thm)],[c_341,c_113]) ).
cnf(c_472,plain,
in(sK3,the_carrier(sK2)),
inference(resolve,[status(thm)],[c_464,c_517]) ).
cnf(c_518,negated_conjecture,
( related(A,D,E)
| ~ in(E,the_carrier(A))
| ~ in(D,the_carrier(A))
| ~ related(sK1,B,C)
| E != C
| D != B
| ~ element(E,the_carrier(A))
| ~ element(D,the_carrier(A))
| ~ element(C,the_carrier(sK1))
| ~ element(B,the_carrier(sK1))
| ~ rel_str(sK1)
| ~ full_subnetstr(A,sK0,sK1)
| ~ subnetstr(A,sK0,sK1) ),
inference(resolve,[status(thm)],[c_214,c_118]) ).
cnf(c_519,negated_conjecture,
( related(sK2,C,D)
| ~ in(D,the_carrier(sK2))
| ~ in(C,the_carrier(sK2))
| ~ related(sK1,A,B)
| D != B
| C != A
| ~ element(D,the_carrier(sK2))
| ~ element(C,the_carrier(sK2))
| ~ element(B,the_carrier(sK1))
| ~ element(A,the_carrier(sK1))
| ~ rel_str(sK1)
| ~ full_subnetstr(sK2,sK0,sK1) ),
inference(resolve,[status(thm)],[c_518,c_121]) ).
cnf(c_520,negated_conjecture,
( related(sK2,C,D)
| ~ in(D,the_carrier(sK2))
| ~ in(C,the_carrier(sK2))
| ~ related(sK1,A,B)
| D != B
| C != A
| ~ element(D,the_carrier(sK2))
| ~ element(C,the_carrier(sK2))
| ~ element(B,the_carrier(sK1))
| ~ element(A,the_carrier(sK1))
| ~ rel_str(sK1) ),
inference(resolve,[status(thm)],[c_519,c_120]) ).
cnf(c_521,negated_conjecture,
( related(sK2,C,D)
| ~ in(D,the_carrier(sK2))
| ~ in(C,the_carrier(sK2))
| ~ related(sK1,A,B)
| D != B
| C != A
| ~ element(D,the_carrier(sK2))
| ~ element(C,the_carrier(sK2))
| ~ element(B,the_carrier(sK1))
| ~ element(A,the_carrier(sK1)) ),
inference(resolve,[status(thm)],[c_520,c_359]) ).
cnf(c_522,negated_conjecture,
( related(sK2,B,C)
| ~ in(C,the_carrier(sK2))
| ~ in(B,the_carrier(sK2))
| ~ related(sK1,sK3,A)
| C != A
| B != sK3
| ~ element(C,the_carrier(sK2))
| ~ element(B,the_carrier(sK2))
| ~ element(A,the_carrier(sK1)) ),
inference(resolve,[status(thm)],[c_521,c_122]) ).
cnf(c_523,negated_conjecture,
( related(sK2,A,B)
| ~ in(B,the_carrier(sK2))
| ~ in(A,the_carrier(sK2))
| ~ related(sK1,sK3,sK4)
| B != sK4
| A != sK3
| ~ element(B,the_carrier(sK2))
| ~ element(A,the_carrier(sK2)) ),
inference(resolve,[status(thm)],[c_522,c_123]) ).
cnf(c_524,negated_conjecture,
( related(sK2,sK3,A)
| ~ in(A,the_carrier(sK2))
| ~ in(sK3,the_carrier(sK2))
| ~ related(sK1,sK3,sK4)
| A != sK4
| sK3 != sK3
| ~ element(A,the_carrier(sK2)) ),
inference(resolve,[status(thm)],[c_523,c_341]) ).
cnf(c_525,negated_conjecture,
( related(sK2,sK3,sK6)
| ~ in(sK6,the_carrier(sK2))
| ~ in(sK3,the_carrier(sK2))
| ~ related(sK1,sK3,sK4)
| sK6 != sK4
| sK3 != sK3 ),
inference(resolve,[status(thm)],[c_524,c_125]) ).
cnf(c_526,plain,
( related(sK2,sK3,sK6)
| ~ in(sK6,the_carrier(sK2))
| ~ in(sK3,the_carrier(sK2))
| ~ related(sK1,sK3,sK4)
| sK6 != sK4 ),
inference(xxres,[status(thm)],[c_525]) ).
cnf(c_527,negated_conjecture,
( related(sK2,sK3,sK6)
| ~ in(sK6,the_carrier(sK2))
| ~ in(sK3,the_carrier(sK2))
| ~ related(sK1,sK3,sK4) ),
inference(resolve,[status(thm)],[c_526,c_127]) ).
cnf(c_528,negated_conjecture,
( related(sK2,sK3,sK6)
| ~ in(sK6,the_carrier(sK2))
| ~ in(sK3,the_carrier(sK2)) ),
inference(resolve,[status(thm)],[c_527,c_128]) ).
cnf(c_529,negated_conjecture,
( related(sK2,sK3,sK6)
| ~ in(sK3,the_carrier(sK2)) ),
inference(resolve,[status(thm)],[c_528,c_465]) ).
cnf(c_530,negated_conjecture,
~ in(sK3,the_carrier(sK2)),
inference(resolve,[status(thm)],[c_529,c_343]) ).
cnf(c_510,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_472,c_530]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU375+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n020.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sat Sep 26 09:22:50 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 1205012 was started by sandbox on n020,
% 0.17/0.45 % Sat Sep 26 09:22:50 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.47
% 0.17/0.47 % From the command line: assign(max_seconds, 300).
% 2.19/0.81
% 2.19/0.81 % SZS status Theorem for theBenchmark
% 2.19/0.81
% 2.19/0.81 % Proof 1 at 0.28 (+ 0.01) seconds.
% 2.19/0.81 % Length of proof is 46.
% 2.19/0.81 % Level of proof is 7.
% 2.19/0.81 % Maximum clause weight is 61.000.
% 2.19/0.81 % Given clauses 178.
% 2.19/0.81
% 2.19/0.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
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