%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU363+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 : n006.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 22.56s 3.61s
% Output : CNFRefutation 22.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 67 ( 31 unt; 0 def)
% Number of atoms : 176 ( 18 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 159 ( 50 ~; 43 |; 36 &)
% ( 4 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 77 ( 2 sgn 35 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc1_relset_1,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('theBenchmark.p',cc1_relset_1) ).
fof(d14_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( subrelstr(B,A)
=> ( full_subrelstr(B,A)
<=> the_InternalRel(B) = relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(B)) ) ) ),
file('theBenchmark.p',d14_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(dt_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(dt_u1_orders_2,axiom,
! [A] :
( rel_str(A)
=> relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) ),
file('theBenchmark.p',dt_u1_orders_2) ).
fof(redefinition_k1_toler_1,axiom,
! [A,B] :
( relation(A)
=> relation_restriction_as_relation_of(A,B) = relation_restriction(A,B) ),
file('theBenchmark.p',redefinition_k1_toler_1) ).
fof(t106_zfmisc_1,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('theBenchmark.p',t106_zfmisc_1) ).
fof(t16_wellord1,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
file('theBenchmark.p',t16_wellord1) ).
fof(t61_yellow_0,conjecture,
! [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(t61_yellow_0_neg,negated_conjecture,
~ ! [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) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t61_yellow_0]) ).
cnf(c_48,plain,
( rel_str(B)
| ~ subrelstr(B,A)
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[dt_m1_yellow_0]) ).
cnf(c_50,plain,
( relation_restriction_as_relation_of(the_InternalRel(A),the_carrier(B)) = the_InternalRel(B)
| ~ full_subrelstr(B,A)
| ~ subrelstr(B,A)
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[d14_yellow_0]) ).
fof(nnf_46,plain,
? [A] :
( ? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( ~ 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(fof_nnf,[status(thm)],[t61_yellow_0_neg]) ).
fof(sk_t61_yellow_0_neg,plain,
( ~ related(sK0,sK2,sK3)
& in(sK3,the_carrier(sK0))
& in(sK2,the_carrier(sK0))
& related(sK1,sK4,sK5)
& sK3 = sK5
& sK2 = sK4
& element(sK3,the_carrier(sK0))
& element(sK2,the_carrier(sK0))
& element(sK5,the_carrier(sK1))
& element(sK4,the_carrier(sK1))
& subrelstr(sK0,sK1)
& full_subrelstr(sK0,sK1)
& rel_str(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK4,sK5,sK2,sK3]),skolemize(A,sK1),skolemize(B,sK0),skolemize(C,sK4),skolemize(D,sK5),skolemize(E,sK2),skolemize(F,sK3)],[nnf_46]) ).
cnf(c_51,negated_conjecture,
subrelstr(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t61_yellow_0_neg]) ).
cnf(c_55,plain,
( relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A))
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[dt_u1_orders_2]) ).
cnf(c_56,plain,
( element(A,powerset(cartesian_product2(B,C)))
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[dt_m2_relset_1]) ).
cnf(c_67,negated_conjecture,
( relation_restriction_as_relation_of(the_InternalRel(sK1),the_carrier(sK0)) = the_InternalRel(sK0)
| ~ full_subrelstr(sK0,sK1)
| ~ rel_str(sK1) ),
inference(resolve,[status(thm)],[c_51,c_50]) ).
cnf(c_69,negated_conjecture,
( rel_str(sK0)
| ~ rel_str(sK1) ),
inference(resolve,[status(thm)],[c_51,c_48]) ).
cnf(c_76,negated_conjecture,
~ related(sK0,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_t61_yellow_0_neg]) ).
cnf(c_77,negated_conjecture,
in(sK3,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t61_yellow_0_neg]) ).
cnf(c_78,negated_conjecture,
in(sK2,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t61_yellow_0_neg]) ).
cnf(c_79,negated_conjecture,
related(sK1,sK4,sK5),
inference(split_conjunct,[status(thm)],[sk_t61_yellow_0_neg]) ).
cnf(c_80,negated_conjecture,
sK3 = sK5,
inference(split_conjunct,[status(thm)],[sk_t61_yellow_0_neg]) ).
cnf(c_81,negated_conjecture,
sK2 = sK4,
inference(split_conjunct,[status(thm)],[sk_t61_yellow_0_neg]) ).
cnf(c_82,negated_conjecture,
element(sK3,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t61_yellow_0_neg]) ).
cnf(c_83,negated_conjecture,
element(sK5,the_carrier(sK0)),
inference(paramod,[status(thm)],[c_80,c_82]) ).
cnf(c_84,negated_conjecture,
element(sK2,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t61_yellow_0_neg]) ).
cnf(c_85,negated_conjecture,
element(sK4,the_carrier(sK0)),
inference(paramod,[status(thm)],[c_81,c_84]) ).
cnf(c_86,negated_conjecture,
element(sK5,the_carrier(sK1)),
inference(split_conjunct,[status(thm)],[sk_t61_yellow_0_neg]) ).
cnf(c_87,negated_conjecture,
element(sK4,the_carrier(sK1)),
inference(split_conjunct,[status(thm)],[sk_t61_yellow_0_neg]) ).
cnf(c_88,negated_conjecture,
full_subrelstr(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t61_yellow_0_neg]) ).
cnf(c_89,negated_conjecture,
rel_str(sK1),
inference(split_conjunct,[status(thm)],[sk_t61_yellow_0_neg]) ).
cnf(c_97,plain,
( ~ in(B,cartesian_product2(C,C))
| ~ in(B,A)
| in(B,relation_restriction(A,C))
| ~ relation(A) ),
inference(clausify,[status(thm)],[t16_wellord1]) ).
cnf(c_100,plain,
( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) ),
inference(clausify,[status(thm)],[t106_zfmisc_1]) ).
cnf(c_103,plain,
( relation_restriction(A,B) = relation_restriction_as_relation_of(A,B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[redefinition_k1_toler_1]) ).
cnf(c_119,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_120,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_122,plain,
( relation(A)
| ~ element(A,powerset(cartesian_product2(B,C))) ),
inference(clausify,[status(thm)],[cc1_relset_1]) ).
cnf(c_125,plain,
( ~ rel_str(A)
| element(the_InternalRel(A),powerset(cartesian_product2(the_carrier(A),the_carrier(A)))) ),
inference(resolve,[status(thm)],[c_56,c_55]) ).
cnf(c_129,negated_conjecture,
in(sK5,the_carrier(sK0)),
inference(paramod,[status(thm)],[c_80,c_77]) ).
cnf(c_19359,negated_conjecture,
~ related(sK0,sK4,sK3),
inference(paramod,[status(thm)],[c_81,c_76]) ).
cnf(c_130,negated_conjecture,
~ related(sK0,sK4,sK5),
inference(paramod,[status(thm)],[c_80,c_19359]) ).
cnf(c_131,negated_conjecture,
in(sK4,the_carrier(sK0)),
inference(paramod,[status(thm)],[c_81,c_78]) ).
cnf(c_19360,negated_conjecture,
( relation_restriction_as_relation_of(the_InternalRel(sK1),the_carrier(sK0)) = the_InternalRel(sK0)
| ~ full_subrelstr(sK0,sK1) ),
inference(resolve,[status(thm)],[c_89,c_67]) ).
cnf(c_132,negated_conjecture,
relation_restriction_as_relation_of(the_InternalRel(sK1),the_carrier(sK0)) = the_InternalRel(sK0),
inference(resolve,[status(thm)],[c_88,c_19360]) ).
cnf(c_133,negated_conjecture,
rel_str(sK0),
inference(resolve,[status(thm)],[c_89,c_69]) ).
cnf(c_19361,negated_conjecture,
( in(ordered_pair(sK4,sK5),the_InternalRel(sK1))
| ~ element(sK5,the_carrier(sK1))
| ~ element(sK4,the_carrier(sK1))
| ~ rel_str(sK1) ),
inference(resolve,[status(thm)],[c_120,c_79]) ).
cnf(c_19362,negated_conjecture,
( in(ordered_pair(sK4,sK5),the_InternalRel(sK1))
| ~ element(sK5,the_carrier(sK1))
| ~ element(sK4,the_carrier(sK1)) ),
inference(resolve,[status(thm)],[c_89,c_19361]) ).
cnf(c_19363,negated_conjecture,
( in(ordered_pair(sK4,sK5),the_InternalRel(sK1))
| ~ element(sK5,the_carrier(sK1)) ),
inference(resolve,[status(thm)],[c_87,c_19362]) ).
cnf(c_176,negated_conjecture,
in(ordered_pair(sK4,sK5),the_InternalRel(sK1)),
inference(resolve,[status(thm)],[c_86,c_19363]) ).
cnf(c_190,plain,
element(the_InternalRel(sK1),powerset(cartesian_product2(the_carrier(sK1),the_carrier(sK1)))),
inference(resolve,[status(thm)],[c_125,c_89]) ).
cnf(c_19364,negated_conjecture,
( ~ in(A,B)
| in(ordered_pair(sK4,A),cartesian_product2(the_carrier(sK0),B)) ),
inference(resolve,[status(thm)],[c_100,c_131]) ).
cnf(c_213,negated_conjecture,
in(ordered_pair(sK4,sK5),cartesian_product2(the_carrier(sK0),the_carrier(sK0))),
inference(resolve,[status(thm)],[c_19364,c_129]) ).
cnf(c_19365,negated_conjecture,
( ~ in(ordered_pair(A,B),the_InternalRel(sK0))
| related(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_119,c_133]) ).
cnf(c_19366,negated_conjecture,
( ~ in(ordered_pair(sK4,A),the_InternalRel(sK0))
| related(sK0,sK4,A)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_19365,c_85]) ).
cnf(c_19367,negated_conjecture,
( ~ in(ordered_pair(sK4,sK5),the_InternalRel(sK0))
| related(sK0,sK4,sK5) ),
inference(resolve,[status(thm)],[c_19366,c_83]) ).
cnf(c_217,negated_conjecture,
~ in(ordered_pair(sK4,sK5),the_InternalRel(sK0)),
inference(resolve,[status(thm)],[c_19367,c_130]) ).
cnf(c_16144,plain,
relation(the_InternalRel(sK1)),
inference(resolve,[status(thm)],[c_190,c_122]) ).
cnf(c_16165,plain,
relation_restriction(the_InternalRel(sK1),A) = relation_restriction_as_relation_of(the_InternalRel(sK1),A),
inference(resolve,[status(thm)],[c_16144,c_103]) ).
cnf(c_19368,plain,
( ~ in(A,cartesian_product2(B,B))
| ~ in(A,the_InternalRel(sK1))
| in(A,relation_restriction(the_InternalRel(sK1),B)) ),
inference(resolve,[status(thm)],[c_97,c_16144]) ).
cnf(c_19369,plain,
( ~ in(ordered_pair(sK4,sK5),cartesian_product2(A,A))
| in(ordered_pair(sK4,sK5),relation_restriction(the_InternalRel(sK1),A)) ),
inference(resolve,[status(thm)],[c_19368,c_176]) ).
cnf(c_19370,plain,
in(ordered_pair(sK4,sK5),relation_restriction(the_InternalRel(sK1),the_carrier(sK0))),
inference(resolve,[status(thm)],[c_19369,c_213]) ).
cnf(c_19371,plain,
in(ordered_pair(sK4,sK5),relation_restriction_as_relation_of(the_InternalRel(sK1),the_carrier(sK0))),
inference(paramod,[status(thm)],[c_16165,c_19370]) ).
cnf(c_19372,plain,
in(ordered_pair(sK4,sK5),the_InternalRel(sK0)),
inference(paramod,[status(thm)],[c_132,c_19371]) ).
cnf(c_19358,plain,
$false,
inference(resolve,[status(thm)],[c_217,c_19372]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU363+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 09:19:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 923796 was started by sandbox2 on n006,
% 0.09/0.36 % Sat Sep 26 09:19:28 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 22.56/3.61
% 22.56/3.61 % given #500 (T,wt=22): 16356 finite(f1(f4(c3,c3),f6(c3))). [resolve(457,a,195,a)].
% 22.56/3.61
% 22.56/3.61 % SZS status Theorem for theBenchmark
% 22.56/3.61
% 22.56/3.61 % Proof 1 at 2.29 (+ 0.92) seconds.
% 22.56/3.61 % Length of proof is 50.
% 22.56/3.61 % Level of proof is 6.
% 22.56/3.61 % Maximum clause weight is 31.000.
% 22.56/3.61 % Given clauses 525.
% 22.56/3.61
% 22.56/3.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------