%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU062+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:44:58 AM UTC 2026
% Result : Theorem 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 60 ( 11 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 64 ( 25 ~; 19 |; 12 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 26 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(t142_funct_1,axiom,
! [A,B] :
( relation(B)
=> ( in(A,relation_rng(B))
<=> relation_inverse_image(B,singleton(A)) != empty_set ) ),
file('theBenchmark.p',t142_funct_1) ).
fof(t143_funct_1,conjecture,
! [A,B] :
( relation(B)
=> ( ! [C] :
~ ( relation_inverse_image(B,singleton(C)) = empty_set
& in(C,A) )
=> subset(A,relation_rng(B)) ) ),
file('theBenchmark.p',t143_funct_1) ).
fof(t143_funct_1_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( ! [C] :
~ ( relation_inverse_image(B,singleton(C)) = empty_set
& in(C,A) )
=> subset(A,relation_rng(B)) ) ),
inference(assume_negation,[status(cth)],[t143_funct_1]) ).
fof(nnf_33,plain,
? [A,B] :
( ~ subset(A,relation_rng(B))
& ! [C] :
( relation_inverse_image(B,singleton(C)) != empty_set
| ~ in(C,A) )
& relation(B) ),
inference(fof_nnf,[status(thm)],[t143_funct_1_neg]) ).
fof(sk_t143_funct_1_neg,plain,
( ~ subset(sK2,relation_rng(sK0))
& ! [C] :
( relation_inverse_image(sK0,singleton(C)) != empty_set
| ~ in(C,sK2) )
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2]),skolemize(A,sK2),skolemize(B,sK0)],[nnf_33]) ).
cnf(c_39,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t143_funct_1_neg]) ).
cnf(c_41,plain,
( relation_inverse_image(A,singleton(B)) = empty_set
| in(B,relation_rng(A))
| ~ relation(A) ),
inference(clausify,[status(thm)],[t142_funct_1]) ).
cnf(c_81,negated_conjecture,
( relation_inverse_image(sK0,singleton(A)) = empty_set
| in(A,relation_rng(sK0)) ),
inference(resolve,[status(thm)],[c_41,c_39]) ).
fof(nnf_5,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(sK1(A,B),B)
& in(sK1(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(C,sK1(A,B))],[nnf_5]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK1(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK1(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_84,plain,
( in(sK1(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_85,plain,
( ~ in(sK1(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_110,negated_conjecture,
( relation_inverse_image(sK0,singleton(A)) != empty_set
| ~ in(A,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t143_funct_1_neg]) ).
cnf(c_111,negated_conjecture,
~ subset(sK2,relation_rng(sK0)),
inference(split_conjunct,[status(thm)],[sk_t143_funct_1_neg]) ).
cnf(c_123,plain,
( relation_inverse_image(sK0,singleton(sK1(A,relation_rng(sK0)))) = empty_set
| subset(A,relation_rng(sK0)) ),
inference(resolve,[status(thm)],[c_85,c_81]) ).
cnf(c_192,plain,
in(sK1(sK2,relation_rng(sK0)),sK2),
inference(resolve,[status(thm)],[c_111,c_84]) ).
cnf(c_280,plain,
relation_inverse_image(sK0,singleton(sK1(sK2,relation_rng(sK0)))) != empty_set,
inference(resolve,[status(thm)],[c_192,c_110]) ).
cnf(c_327,negated_conjecture,
relation_inverse_image(sK0,singleton(sK1(sK2,relation_rng(sK0)))) = empty_set,
inference(resolve,[status(thm)],[c_123,c_111]) ).
cnf(c_326,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_280,c_327]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU062+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n007.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 08:31:54 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 3308015 was started by sandbox on n007,
% 0.07/0.35 % Sat Sep 26 08:31:54 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 0.11/0.39
% 0.11/0.39 % SZS status Theorem for theBenchmark
% 0.11/0.39
% 0.11/0.39 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.11/0.39 % Length of proof is 14.
% 0.11/0.39 % Level of proof is 4.
% 0.11/0.39 % Maximum clause weight is 13.000.
% 0.11/0.39 % Given clauses 111.
% 0.11/0.39
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------