%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET991+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 08:37:25 AM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 48 ( 13 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 54 ( 22 ~; 15 |; 10 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 7 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d5_funct_1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
file('theBenchmark.p',d5_funct_1) ).
fof(t12_funct_1,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( in(A,relation_dom(B))
=> in(apply(B,A),relation_rng(B)) ) ),
file('theBenchmark.p',t12_funct_1) ).
fof(t12_funct_1_neg,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( in(A,relation_dom(B))
=> in(apply(B,A),relation_rng(B)) ) ),
inference(assume_negation,[status(cth)],[t12_funct_1]) ).
fof(nnf_30,plain,
? [A,B] :
( ~ in(apply(B,A),relation_rng(B))
& in(A,relation_dom(B))
& function(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[t12_funct_1_neg]) ).
fof(sk_t12_funct_1_neg,plain,
( ~ in(apply(sK0,sK1),relation_rng(sK0))
& in(sK1,relation_dom(sK0))
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_30]) ).
cnf(c_35,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t12_funct_1_neg]) ).
cnf(c_38,plain,
( apply(A,D) != C
| ~ in(D,relation_dom(A))
| in(C,B)
| relation_rng(A) != B
| ~ function(A)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_funct_1]) ).
cnf(c_53,negated_conjecture,
~ in(apply(sK0,sK1),relation_rng(sK0)),
inference(split_conjunct,[status(thm)],[sk_t12_funct_1_neg]) ).
cnf(c_54,negated_conjecture,
in(sK1,relation_dom(sK0)),
inference(split_conjunct,[status(thm)],[sk_t12_funct_1_neg]) ).
cnf(c_55,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t12_funct_1_neg]) ).
cnf(c_85,negated_conjecture,
( apply(sK0,C) != B
| ~ in(C,relation_dom(sK0))
| in(B,A)
| relation_rng(sK0) != A
| ~ function(sK0) ),
inference(resolve,[status(thm)],[c_38,c_35]) ).
cnf(c_86,negated_conjecture,
( apply(sK0,C) != B
| ~ in(C,relation_dom(sK0))
| in(B,A)
| relation_rng(sK0) != A ),
inference(resolve,[status(thm)],[c_55,c_85]) ).
cnf(c_228,negated_conjecture,
( apply(sK0,A) != apply(sK0,sK1)
| ~ in(A,relation_dom(sK0))
| relation_rng(sK0) != relation_rng(sK0) ),
inference(resolve,[status(thm)],[c_86,c_53]) ).
cnf(c_229,negated_conjecture,
( apply(sK0,sK1) != apply(sK0,sK1)
| relation_rng(sK0) != relation_rng(sK0) ),
inference(resolve,[status(thm)],[c_228,c_54]) ).
cnf(c_230,plain,
relation_rng(sK0) != relation_rng(sK0),
inference(xxres,[status(thm)],[c_229]) ).
cnf(c_227,plain,
$false,
inference(copy,[status(thm)],[c_230]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET991+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n003.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Sat Sep 26 08:30:55 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 2448017 was started by sandbox2 on n003,
% 0.18/0.43 % Sat Sep 26 08:30:55 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.44
% 0.18/0.44 % From the command line: assign(max_seconds, 300).
% 0.18/0.47
% 0.18/0.47 % SZS status Theorem for theBenchmark
% 0.18/0.47
% 0.18/0.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.18/0.47 % Length of proof is 10.
% 0.18/0.47 % Level of proof is 4.
% 0.18/0.47 % Maximum clause weight is 26.000.
% 0.18/0.47 % Given clauses 31.
% 0.18/0.47
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------