%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET575+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 08:36:29 AM UTC 2026
% Result : Theorem 0.02s 0.31s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 4 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 58 ( 25 ~; 18 |; 11 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 23 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersect_defn) ).
fof(symmetry_of_intersect,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('theBenchmark.p',symmetry_of_intersect) ).
fof(prove_th15,conjecture,
! [B,C] :
( intersect(B,C)
=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',prove_th15) ).
fof(prove_th15_neg,negated_conjecture,
~ ! [B,C] :
( intersect(B,C)
=> ? [D] :
( member(D,C)
& member(D,B) ) ),
inference(assume_negation,[status(cth)],[prove_th15]) ).
fof(nnf_1,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ? [X0] :
( member(X0,C)
& member(X0,B) )
| ~ intersect(B,C) ) ),
inference(fof_nnf,[status(thm)],[intersect_defn]) ).
fof(sk_intersect_defn_sk,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ( member(sK0(B,C),C)
& member(sK0(B,C),B) )
| ~ intersect(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(B,C))],[nnf_1]) ).
fof(sk_intersect_defn,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| intersect(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK0(VAR_0,VAR_1),VAR_1)
| ~ intersect(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK0(VAR_0,VAR_1),VAR_0)
| ~ intersect(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_intersect_defn_sk]) ).
cnf(c_4,plain,
( member(sK0(A,B),A)
| ~ intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_5,plain,
( member(sK0(A,B),B)
| ~ intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_7,plain,
( intersect(B,A)
| ~ intersect(A,B) ),
inference(clausify,[status(thm)],[symmetry_of_intersect]) ).
fof(nnf_3,plain,
? [B,C] :
( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
& intersect(B,C) ),
inference(fof_nnf,[status(thm)],[prove_th15_neg]) ).
fof(sk_prove_th15_neg,plain,
( ! [D] :
( ~ member(D,sK2)
| ~ member(D,sK1) )
& intersect(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(B,sK1),skolemize(C,sK2)],[nnf_3]) ).
cnf(c_8,negated_conjecture,
intersect(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_prove_th15_neg]) ).
cnf(c_9,negated_conjecture,
( ~ member(A,sK2)
| ~ member(A,sK1) ),
inference(split_conjunct,[status(thm)],[sk_prove_th15_neg]) ).
cnf(c_10,negated_conjecture,
intersect(sK2,sK1),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_13,plain,
( ~ intersect(A,sK1)
| ~ member(sK0(A,sK1),sK2) ),
inference(resolve,[status(thm)],[c_9,c_5]) ).
cnf(c_20,plain,
( ~ intersect(sK2,sK1)
| ~ intersect(sK2,sK1) ),
inference(resolve,[status(thm)],[c_13,c_4]) ).
cnf(c_21,plain,
~ intersect(sK2,sK1),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_19,plain,
$false,
inference(resolve,[status(thm)],[c_10,c_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET575+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sat Sep 26 07:56:11 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.29 % Process 68777 was started by sandbox on n012,
% 0.02/0.29 % Sat Sep 26 07:56:11 2026
% 0.02/0.29 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.29
% 0.02/0.29 % From the command line: assign(max_seconds, 300).
% 0.02/0.31
% 0.02/0.31 % SZS status Theorem for theBenchmark
% 0.02/0.31
% 0.02/0.31 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.02/0.31 % Length of proof is 11.
% 0.02/0.31 % Level of proof is 3.
% 0.02/0.31 % Maximum clause weight is 8.000.
% 0.02/0.31 % Given clauses 8.
% 0.02/0.31
% 0.02/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------