%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU198+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 : n007.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 08:45:23 AM UTC 2026
% Result : Theorem 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 48 ( 18 ~; 15 |; 9 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 23 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(t115_relat_1,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_rng(relation_rng_restriction(B,C)))
<=> ( in(A,relation_rng(C))
& in(A,B) ) ) ),
file('theBenchmark.p',t115_relat_1) ).
fof(t116_relat_1,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),A) ),
file('theBenchmark.p',t116_relat_1) ).
fof(t116_relat_1_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_rng(relation_rng_restriction(A,B)),A) ),
inference(assume_negation,[status(cth)],[t116_relat_1]) ).
fof(nnf_3,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ in(sK0(A,B),B)
& in(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_3]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| ~ in(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_34,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_35,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_55,plain,
( in(B,C)
| ~ in(B,relation_rng(relation_rng_restriction(C,A)))
| ~ relation(A) ),
inference(clausify,[status(thm)],[t115_relat_1]) ).
fof(nnf_30,plain,
? [A,B] :
( ~ subset(relation_rng(relation_rng_restriction(A,B)),A)
& relation(B) ),
inference(fof_nnf,[status(thm)],[t116_relat_1_neg]) ).
fof(sk_t116_relat_1_neg,plain,
( ~ subset(relation_rng(relation_rng_restriction(sK2,sK1)),sK2)
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK2),skolemize(B,sK1)],[nnf_30]) ).
cnf(c_67,negated_conjecture,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_t116_relat_1_neg]) ).
cnf(c_68,negated_conjecture,
~ subset(relation_rng(relation_rng_restriction(sK2,sK1)),sK2),
inference(split_conjunct,[status(thm)],[sk_t116_relat_1_neg]) ).
cnf(c_119,plain,
in(sK0(relation_rng(relation_rng_restriction(sK2,sK1)),sK2),relation_rng(relation_rng_restriction(sK2,sK1))),
inference(resolve,[status(thm)],[c_68,c_34]) ).
cnf(c_121,negated_conjecture,
~ in(sK0(relation_rng(relation_rng_restriction(sK2,sK1)),sK2),sK2),
inference(resolve,[status(thm)],[c_35,c_68]) ).
cnf(c_452,plain,
( in(sK0(relation_rng(relation_rng_restriction(sK2,sK1)),sK2),sK2)
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_119,c_55]) ).
cnf(c_453,negated_conjecture,
in(sK0(relation_rng(relation_rng_restriction(sK2,sK1)),sK2),sK2),
inference(resolve,[status(thm)],[c_67,c_452]) ).
cnf(c_451,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_121,c_453]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU198+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n007.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 26 08:46:24 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.38 % Process 3338381 was started by sandbox2 on n007,
% 0.08/0.38 % Sat Sep 26 08:46:24 2026
% 0.08/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 0.13/0.44
% 0.13/0.44 % SZS status Theorem for theBenchmark
% 0.13/0.44
% 0.13/0.44 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.13/0.44 % Length of proof is 11.
% 0.13/0.44 % Level of proof is 3.
% 0.13/0.44 % Maximum clause weight is 11.000.
% 0.13/0.44 % Given clauses 113.
% 0.13/0.44
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------