%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU362+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 : n013.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 08:46:05 AM UTC 2026
% Result : Theorem 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 22 unt; 0 def)
% Number of atoms : 148 ( 10 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 145 ( 51 ~; 42 |; 26 &)
% ( 3 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 61 ( 2 sgn 29 !; 6 ?)
% 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(d9_orders_2,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( related(A,B,C)
<=> in(ordered_pair(B,C),the_InternalRel(A)) ) ) ) ),
file('theBenchmark.p',d9_orders_2) ).
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(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t60_yellow_0,conjecture,
! [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(t60_yellow_0_neg,negated_conjecture,
~ ! [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) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t60_yellow_0]) ).
cnf(c_42,plain,
( rel_str(B)
| ~ subrelstr(B,A)
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[dt_m1_yellow_0]) ).
fof(nnf_41,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( ~ 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(fof_nnf,[status(thm)],[t60_yellow_0_neg]) ).
fof(sk_t60_yellow_0_neg,plain,
( ~ related(sK1,sK2,sK3)
& related(sK0,sK4,sK5)
& sK5 = sK3
& sK4 = sK2
& element(sK5,the_carrier(sK0))
& element(sK4,the_carrier(sK0))
& element(sK3,the_carrier(sK1))
& element(sK2,the_carrier(sK1))
& subrelstr(sK0,sK1)
& rel_str(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK2,sK3,sK4,sK5]),skolemize(A,sK1),skolemize(B,sK0),skolemize(C,sK2),skolemize(D,sK3),skolemize(E,sK4),skolemize(F,sK5)],[nnf_41]) ).
cnf(c_44,negated_conjecture,
subrelstr(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t60_yellow_0_neg]) ).
cnf(c_46,plain,
( subset(the_InternalRel(B),the_InternalRel(A))
| ~ subrelstr(B,A)
| ~ rel_str(B)
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[d13_yellow_0]) ).
cnf(c_48,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_52,negated_conjecture,
( subset(the_InternalRel(sK0),the_InternalRel(sK1))
| ~ rel_str(sK0)
| ~ rel_str(sK1) ),
inference(resolve,[status(thm)],[c_46,c_44]) ).
cnf(c_65,negated_conjecture,
( rel_str(sK0)
| ~ rel_str(sK1) ),
inference(resolve,[status(thm)],[c_42,c_44]) ).
cnf(c_71,plain,
( in(ordered_pair(B,C),the_InternalRel(A))
| ~ related(A,B,C)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[d9_orders_2]) ).
cnf(c_72,plain,
( ~ in(ordered_pair(B,C),the_InternalRel(A))
| related(A,B,C)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[d9_orders_2]) ).
cnf(c_88,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_89,plain,
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t4_subset]) ).
cnf(c_90,plain,
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t5_subset]) ).
cnf(c_94,negated_conjecture,
rel_str(sK1),
inference(split_conjunct,[status(thm)],[sk_t60_yellow_0_neg]) ).
cnf(c_95,negated_conjecture,
element(sK2,the_carrier(sK1)),
inference(split_conjunct,[status(thm)],[sk_t60_yellow_0_neg]) ).
cnf(c_96,negated_conjecture,
element(sK3,the_carrier(sK1)),
inference(split_conjunct,[status(thm)],[sk_t60_yellow_0_neg]) ).
cnf(c_97,negated_conjecture,
element(sK4,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t60_yellow_0_neg]) ).
cnf(c_98,negated_conjecture,
element(sK5,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t60_yellow_0_neg]) ).
cnf(c_99,negated_conjecture,
sK4 = sK2,
inference(split_conjunct,[status(thm)],[sk_t60_yellow_0_neg]) ).
cnf(c_100,negated_conjecture,
sK5 = sK3,
inference(split_conjunct,[status(thm)],[sk_t60_yellow_0_neg]) ).
cnf(c_101,negated_conjecture,
related(sK0,sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_t60_yellow_0_neg]) ).
cnf(c_437,negated_conjecture,
related(sK0,sK2,sK5),
inference(paramod,[status(thm)],[c_99,c_101]) ).
cnf(c_102,negated_conjecture,
related(sK0,sK2,sK3),
inference(paramod,[status(thm)],[c_100,c_437]) ).
cnf(c_103,negated_conjecture,
~ related(sK1,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_t60_yellow_0_neg]) ).
cnf(c_107,negated_conjecture,
( ~ rel_str(sK0)
| ~ rel_str(sK1)
| element(the_InternalRel(sK0),powerset(the_InternalRel(sK1))) ),
inference(resolve,[status(thm)],[c_48,c_52]) ).
cnf(c_108,negated_conjecture,
( ~ rel_str(sK0)
| element(the_InternalRel(sK0),powerset(the_InternalRel(sK1))) ),
inference(resolve,[status(thm)],[c_94,c_107]) ).
cnf(c_119,negated_conjecture,
rel_str(sK0),
inference(resolve,[status(thm)],[c_94,c_65]) ).
cnf(c_120,negated_conjecture,
element(sK2,the_carrier(sK0)),
inference(paramod,[status(thm)],[c_99,c_97]) ).
cnf(c_121,negated_conjecture,
element(sK3,the_carrier(sK0)),
inference(paramod,[status(thm)],[c_100,c_98]) ).
cnf(c_123,negated_conjecture,
element(the_InternalRel(sK0),powerset(the_InternalRel(sK1))),
inference(resolve,[status(thm)],[c_119,c_108]) ).
cnf(c_438,negated_conjecture,
( in(ordered_pair(sK2,sK3),the_InternalRel(sK0))
| ~ element(sK3,the_carrier(sK0))
| ~ element(sK2,the_carrier(sK0))
| ~ rel_str(sK0) ),
inference(resolve,[status(thm)],[c_102,c_71]) ).
cnf(c_439,negated_conjecture,
( in(ordered_pair(sK2,sK3),the_InternalRel(sK0))
| ~ element(sK3,the_carrier(sK0))
| ~ element(sK2,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_119,c_438]) ).
cnf(c_440,negated_conjecture,
( in(ordered_pair(sK2,sK3),the_InternalRel(sK0))
| ~ element(sK3,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_120,c_439]) ).
cnf(c_181,negated_conjecture,
in(ordered_pair(sK2,sK3),the_InternalRel(sK0)),
inference(resolve,[status(thm)],[c_121,c_440]) ).
cnf(c_441,negated_conjecture,
( ~ in(ordered_pair(A,B),the_InternalRel(sK1))
| related(sK1,A,B)
| ~ element(B,the_carrier(sK1))
| ~ element(A,the_carrier(sK1)) ),
inference(resolve,[status(thm)],[c_72,c_94]) ).
cnf(c_442,negated_conjecture,
( ~ in(ordered_pair(sK2,A),the_InternalRel(sK1))
| related(sK1,sK2,A)
| ~ element(A,the_carrier(sK1)) ),
inference(resolve,[status(thm)],[c_441,c_95]) ).
cnf(c_443,negated_conjecture,
( ~ in(ordered_pair(sK2,sK3),the_InternalRel(sK1))
| related(sK1,sK2,sK3) ),
inference(resolve,[status(thm)],[c_442,c_96]) ).
cnf(c_182,negated_conjecture,
~ in(ordered_pair(sK2,sK3),the_InternalRel(sK1)),
inference(resolve,[status(thm)],[c_443,c_103]) ).
cnf(c_233,plain,
( ~ empty(the_InternalRel(sK1))
| ~ in(A,the_InternalRel(sK0)) ),
inference(resolve,[status(thm)],[c_123,c_90]) ).
cnf(c_381,plain,
~ empty(the_InternalRel(sK1)),
inference(resolve,[status(thm)],[c_181,c_233]) ).
cnf(c_444,plain,
( in(A,the_InternalRel(sK1))
| ~ element(A,the_InternalRel(sK1)) ),
inference(resolve,[status(thm)],[c_88,c_381]) ).
cnf(c_388,plain,
~ element(ordered_pair(sK2,sK3),the_InternalRel(sK1)),
inference(resolve,[status(thm)],[c_444,c_182]) ).
cnf(c_445,negated_conjecture,
( element(A,the_InternalRel(sK1))
| ~ in(A,the_InternalRel(sK0)) ),
inference(resolve,[status(thm)],[c_89,c_123]) ).
cnf(c_446,negated_conjecture,
~ in(ordered_pair(sK2,sK3),the_InternalRel(sK0)),
inference(resolve,[status(thm)],[c_445,c_388]) ).
cnf(c_436,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_181,c_446]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU362+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n013.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sat Sep 26 09:18:40 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 2424428 was started by sandbox on n013,
% 0.09/0.38 % Sat Sep 26 09:18:40 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 0.09/0.43
% 0.09/0.43 % SZS status Theorem for theBenchmark
% 0.09/0.43
% 0.09/0.43 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.09/0.43 % Length of proof is 41.
% 0.09/0.43 % Level of proof is 9.
% 0.09/0.43 % Maximum clause weight is 30.000.
% 0.09/0.43 % Given clauses 108.
% 0.09/0.43
% 0.09/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------