%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU355+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 08:45:54 AM UTC 2026
% Result : Theorem 0.08s 0.40s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 13 unt; 0 def)
% Number of atoms : 147 ( 4 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 179 ( 69 ~; 70 |; 25 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 80 ( 3 sgn 57 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d8_lattice3,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( relstr_element_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,B)
=> related(A,C,D) ) ) ) ) ),
file('theBenchmark.p',d8_lattice3) ).
fof(d9_lattice3,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( relstr_set_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,B)
=> related(A,D,C) ) ) ) ) ),
file('theBenchmark.p',d9_lattice3) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t6_yellow_0,conjecture,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) ) ) ),
file('theBenchmark.p',t6_yellow_0) ).
fof(t6_yellow_0_neg,negated_conjecture,
~ ! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) ) ) ),
inference(assume_negation,[status(cth)],[t6_yellow_0]) ).
fof(nnf_21,plain,
? [A] :
( ? [B] :
( ( ~ relstr_element_smaller(A,empty_set,B)
| ~ relstr_set_smaller(A,empty_set,B) )
& element(B,the_carrier(A)) )
& rel_str(A) ),
inference(fof_nnf,[status(thm)],[t6_yellow_0_neg]) ).
fof(sk_t6_yellow_0_neg,plain,
( ( ~ relstr_element_smaller(sK0,empty_set,sK3)
| ~ relstr_set_smaller(sK0,empty_set,sK3) )
& element(sK3,the_carrier(sK0))
& rel_str(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK3]),skolemize(A,sK0),skolemize(B,sK3)],[nnf_21]) ).
cnf(c_24,negated_conjecture,
rel_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t6_yellow_0_neg]) ).
fof(nnf_4,plain,
! [A] :
( ! [B,C] :
( ( ( ? [D] :
( ~ related(A,D,C)
& in(D,B)
& element(D,the_carrier(A)) )
| relstr_set_smaller(A,B,C) )
& ( ! [X0] :
( related(A,X0,C)
| ~ in(X0,B)
| ~ element(X0,the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[d9_lattice3]) ).
fof(sk_d9_lattice3_sk,plain,
! [A] :
( ! [B,C] :
( ( ( ( ~ related(A,sK1(A,B,C),C)
& in(sK1(A,B,C),B)
& element(sK1(A,B,C),the_carrier(A)) )
| relstr_set_smaller(A,B,C) )
& ( ! [X0] :
( related(A,X0,C)
| ~ in(X0,B)
| ~ element(X0,the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(D,sK1(A,B,C))],[nnf_4]) ).
fof(sk_d9_lattice3,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ related(VAR_0,sK1(VAR_0,VAR_2,VAR_1),VAR_1)
| relstr_set_smaller(VAR_0,VAR_2,VAR_1)
| ~ element(VAR_1,the_carrier(VAR_0))
| ~ rel_str(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK1(VAR_0,VAR_2,VAR_1),VAR_2)
| relstr_set_smaller(VAR_0,VAR_2,VAR_1)
| ~ element(VAR_1,the_carrier(VAR_0))
| ~ rel_str(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( element(sK1(VAR_0,VAR_2,VAR_1),the_carrier(VAR_0))
| relstr_set_smaller(VAR_0,VAR_2,VAR_1)
| ~ element(VAR_1,the_carrier(VAR_0))
| ~ rel_str(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( related(VAR_0,VAR_3,VAR_1)
| ~ in(VAR_3,VAR_2)
| ~ element(VAR_3,the_carrier(VAR_0))
| ~ relstr_set_smaller(VAR_0,VAR_2,VAR_1)
| ~ element(VAR_1,the_carrier(VAR_0))
| ~ rel_str(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d9_lattice3_sk]) ).
cnf(c_26,plain,
( in(sK1(A,C,B),C)
| relstr_set_smaller(A,C,B)
| ~ element(B,the_carrier(A))
| ~ rel_str(A) ),
inference(split_conjunct,[status(thm)],[sk_d9_lattice3]) ).
fof(nnf_3,plain,
! [A] :
( ! [B,C] :
( ( ( ? [D] :
( ~ related(A,C,D)
& in(D,B)
& element(D,the_carrier(A)) )
| relstr_element_smaller(A,B,C) )
& ( ! [X0] :
( related(A,C,X0)
| ~ in(X0,B)
| ~ element(X0,the_carrier(A)) )
| ~ relstr_element_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[d8_lattice3]) ).
fof(sk_d8_lattice3_sk,plain,
! [A] :
( ! [B,C] :
( ( ( ( ~ related(A,C,sK2(A,B,C))
& in(sK2(A,B,C),B)
& element(sK2(A,B,C),the_carrier(A)) )
| relstr_element_smaller(A,B,C) )
& ( ! [X0] :
( related(A,C,X0)
| ~ in(X0,B)
| ~ element(X0,the_carrier(A)) )
| ~ relstr_element_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(D,sK2(A,B,C))],[nnf_3]) ).
fof(sk_d8_lattice3,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ related(VAR_0,VAR_1,sK2(VAR_0,VAR_2,VAR_1))
| relstr_element_smaller(VAR_0,VAR_2,VAR_1)
| ~ element(VAR_1,the_carrier(VAR_0))
| ~ rel_str(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK2(VAR_0,VAR_2,VAR_1),VAR_2)
| relstr_element_smaller(VAR_0,VAR_2,VAR_1)
| ~ element(VAR_1,the_carrier(VAR_0))
| ~ rel_str(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( element(sK2(VAR_0,VAR_2,VAR_1),the_carrier(VAR_0))
| relstr_element_smaller(VAR_0,VAR_2,VAR_1)
| ~ element(VAR_1,the_carrier(VAR_0))
| ~ rel_str(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( related(VAR_0,VAR_1,VAR_3)
| ~ in(VAR_3,VAR_2)
| ~ element(VAR_3,the_carrier(VAR_0))
| ~ relstr_element_smaller(VAR_0,VAR_2,VAR_1)
| ~ element(VAR_1,the_carrier(VAR_0))
| ~ rel_str(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d8_lattice3_sk]) ).
cnf(c_30,plain,
( in(sK2(A,C,B),C)
| relstr_element_smaller(A,C,B)
| ~ element(B,the_carrier(A))
| ~ rel_str(A) ),
inference(split_conjunct,[status(thm)],[sk_d8_lattice3]) ).
cnf(c_33,negated_conjecture,
( ~ relstr_element_smaller(sK0,empty_set,sK3)
| ~ relstr_set_smaller(sK0,empty_set,sK3) ),
inference(split_conjunct,[status(thm)],[sk_t6_yellow_0_neg]) ).
cnf(c_34,negated_conjecture,
element(sK3,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t6_yellow_0_neg]) ).
cnf(c_36,plain,
( ~ empty(B)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t7_boole]) ).
cnf(c_37,plain,
( empty_set = A
| ~ empty(A) ),
inference(clausify,[status(thm)],[t6_boole]) ).
fof(nnf_14,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(sk_rc1_xboole_0,plain,
empty(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(A,sK4)],[nnf_14]) ).
cnf(c_41,plain,
empty(sK4),
inference(split_conjunct,[status(thm)],[sk_rc1_xboole_0]) ).
cnf(c_49,negated_conjecture,
( in(sK1(sK0,B,A),B)
| relstr_set_smaller(sK0,B,A)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_26,c_24]) ).
cnf(c_57,negated_conjecture,
( in(sK2(sK0,B,A),B)
| relstr_element_smaller(sK0,B,A)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_30,c_24]) ).
cnf(c_104,plain,
empty_set = sK4,
inference(resolve,[status(thm)],[c_41,c_37]) ).
cnf(c_68,plain,
sK4 = empty_set,
inference(copy,[status(thm)],[c_104]) ).
cnf(c_105,plain,
~ in(A,sK4),
inference(resolve,[status(thm)],[c_36,c_41]) ).
cnf(c_69,plain,
~ in(A,empty_set),
inference(paramod,[status(thm)],[c_68,c_105]) ).
cnf(c_73,plain,
( in(sK1(sK0,A,sK3),A)
| relstr_set_smaller(sK0,A,sK3) ),
inference(resolve,[status(thm)],[c_49,c_34]) ).
cnf(c_79,plain,
( in(sK2(sK0,A,sK3),A)
| relstr_element_smaller(sK0,A,sK3) ),
inference(resolve,[status(thm)],[c_57,c_34]) ).
cnf(c_106,negated_conjecture,
( ~ relstr_element_smaller(sK0,empty_set,sK3)
| in(sK1(sK0,empty_set,sK3),empty_set) ),
inference(resolve,[status(thm)],[c_73,c_33]) ).
cnf(c_93,negated_conjecture,
~ relstr_element_smaller(sK0,empty_set,sK3),
inference(resolve,[status(thm)],[c_69,c_106]) ).
cnf(c_107,plain,
in(sK2(sK0,empty_set,sK3),empty_set),
inference(resolve,[status(thm)],[c_93,c_79]) ).
cnf(c_103,plain,
$false,
inference(resolve,[status(thm)],[c_69,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU355+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.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
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 09:17:55 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 918122 was started by sandbox2 on n006,
% 0.08/0.36 % Sat Sep 26 09:17:55 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.40
% 0.08/0.40 % SZS status Theorem for theBenchmark
% 0.08/0.40
% 0.08/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.40 % Length of proof is 22.
% 0.08/0.40 % Level of proof is 5.
% 0.08/0.40 % Maximum clause weight is 14.000.
% 0.08/0.40 % Given clauses 51.
% 0.08/0.40
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------