%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET997+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 : n026.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 0.71s 0.52s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 10 unt; 0 def)
% Number of atoms : 97 ( 19 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 112 ( 44 ~; 33 |; 26 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 31 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
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(t19_funct_1,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ! [C] :
~ ( ! [D] :
~ ( C = apply(B,D)
& in(D,relation_dom(B)) )
& in(C,A) )
=> subset(A,relation_rng(B)) ) ),
file('theBenchmark.p',t19_funct_1) ).
fof(t19_funct_1_neg,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( ! [C] :
~ ( ! [D] :
~ ( C = apply(B,D)
& in(D,relation_dom(B)) )
& in(C,A) )
=> subset(A,relation_rng(B)) ) ),
inference(assume_negation,[status(cth)],[t19_funct_1]) ).
cnf(c_35,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]) ).
fof(nnf_31,plain,
? [A,B] :
( ~ subset(A,relation_rng(B))
& ! [C] :
( ? [D] :
( apply(B,D) = C
& in(D,relation_dom(B)) )
| ~ in(C,A) )
& function(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[t19_funct_1_neg]) ).
fof(sk_t19_funct_1_neg_sk,plain,
( ~ subset(sK2,relation_rng(sK0))
& ! [C] :
( ( apply(sK0,sK3(C)) = C
& in(sK3(C),relation_dom(sK0)) )
| ~ in(C,sK2) )
& function(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK3]),skolemize(A,sK2),skolemize(B,sK0),skolemize(D,sK3(C))],[nnf_31]) ).
fof(sk_t19_funct_1_neg,plain,
( ~ subset(sK2,relation_rng(sK0))
& ! [VAR_0] :
( apply(sK0,sK3(VAR_0)) = VAR_0
| ~ in(VAR_0,sK2) )
& ! [VAR_0] :
( in(sK3(VAR_0),relation_dom(sK0))
| ~ in(VAR_0,sK2) )
& function(sK0)
& relation(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_t19_funct_1_neg_sk]) ).
cnf(c_40,negated_conjecture,
function(sK0),
inference(split_conjunct,[status(thm)],[sk_t19_funct_1_neg]) ).
fof(nnf_4,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X3] :
( in(X3,B)
| ~ in(X3,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) )
& ( ! [X3] :
( in(X3,B)
| ~ in(X3,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(C,sK1(A,B))],[nnf_4]) ).
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_44,plain,
( in(sK1(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_45,plain,
( ~ in(sK1(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_78,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t19_funct_1_neg]) ).
cnf(c_79,negated_conjecture,
( in(sK3(A),relation_dom(sK0))
| ~ in(A,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t19_funct_1_neg]) ).
cnf(c_80,negated_conjecture,
( apply(sK0,sK3(A)) = A
| ~ in(A,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t19_funct_1_neg]) ).
cnf(c_81,negated_conjecture,
~ subset(sK2,relation_rng(sK0)),
inference(split_conjunct,[status(thm)],[sk_t19_funct_1_neg]) ).
cnf(c_107,negated_conjecture,
( apply(sK0,C) != B
| ~ in(C,relation_dom(sK0))
| in(B,A)
| relation_rng(sK0) != A
| ~ relation(sK0) ),
inference(resolve,[status(thm)],[c_40,c_35]) ).
cnf(c_108,negated_conjecture,
( apply(sK0,C) != B
| ~ in(C,relation_dom(sK0))
| in(B,A)
| relation_rng(sK0) != A ),
inference(resolve,[status(thm)],[c_78,c_107]) ).
cnf(c_175,plain,
in(sK1(sK2,relation_rng(sK0)),sK2),
inference(resolve,[status(thm)],[c_81,c_44]) ).
cnf(c_177,negated_conjecture,
~ in(sK1(sK2,relation_rng(sK0)),relation_rng(sK0)),
inference(resolve,[status(thm)],[c_45,c_81]) ).
cnf(c_359,plain,
apply(sK0,sK3(sK1(sK2,relation_rng(sK0)))) = sK1(sK2,relation_rng(sK0)),
inference(resolve,[status(thm)],[c_175,c_80]) ).
cnf(c_360,plain,
in(sK3(sK1(sK2,relation_rng(sK0))),relation_dom(sK0)),
inference(resolve,[status(thm)],[c_175,c_79]) ).
cnf(c_640,plain,
( apply(sK0,B) != A
| ~ in(B,relation_dom(sK0))
| in(A,relation_rng(sK0)) ),
inference(xxres,[status(thm)],[c_108]) ).
cnf(c_641,plain,
( apply(sK0,A) != sK1(sK2,relation_rng(sK0))
| ~ in(A,relation_dom(sK0)) ),
inference(resolve,[status(thm)],[c_640,c_177]) ).
cnf(c_642,plain,
apply(sK0,sK3(sK1(sK2,relation_rng(sK0)))) != sK1(sK2,relation_rng(sK0)),
inference(resolve,[status(thm)],[c_641,c_360]) ).
cnf(c_643,plain,
sK1(sK2,relation_rng(sK0)) != sK1(sK2,relation_rng(sK0)),
inference(paramod,[status(thm)],[c_359,c_642]) ).
cnf(c_639,plain,
$false,
inference(copy,[status(thm)],[c_643]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET997+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 08:32:10 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 561400 was started by sandbox on n026,
% 0.09/0.38 % Sat Sep 26 08:32:10 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.39
% 0.15/0.39 % From the command line: assign(max_seconds, 300).
% 0.71/0.52
% 0.71/0.52 % SZS status Theorem for theBenchmark
% 0.71/0.52
% 0.71/0.52 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.71/0.52 % Length of proof is 18.
% 0.71/0.52 % Level of proof is 4.
% 0.71/0.52 % Maximum clause weight is 16.000.
% 0.71/0.52 % Given clauses 161.
% 0.71/0.52
% 0.71/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------