%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET625+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 08:36:39 AM UTC 2026
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 64 ( 26 ~; 19 |; 13 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 26 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersect_defn,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersect_defn) ).
fof(subset_defn,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('theBenchmark.p',subset_defn) ).
fof(symmetry_of_intersect,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('theBenchmark.p',symmetry_of_intersect) ).
fof(prove_th101,conjecture,
! [B,C,D] :
( ( subset(C,D)
& intersect(B,C) )
=> intersect(B,D) ),
file('theBenchmark.p',prove_th101) ).
fof(prove_th101_neg,negated_conjecture,
~ ! [B,C,D] :
( ( subset(C,D)
& intersect(B,C) )
=> intersect(B,D) ),
inference(assume_negation,[status(cth)],[prove_th101]) ).
cnf(c_7,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[subset_defn]) ).
fof(nnf_5,plain,
? [B,C,D] :
( ~ intersect(B,D)
& subset(C,D)
& intersect(B,C) ),
inference(fof_nnf,[status(thm)],[prove_th101_neg]) ).
fof(sk_prove_th101_neg,plain,
( ~ intersect(sK2,sK1)
& subset(sK0,sK1)
& intersect(sK2,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1]),skolemize(B,sK2),skolemize(C,sK0),skolemize(D,sK1)],[nnf_5]) ).
cnf(c_10,negated_conjecture,
subset(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_th101_neg]) ).
cnf(c_11,negated_conjecture,
( member(A,sK1)
| ~ member(A,sK0) ),
inference(resolve,[status(thm)],[c_10,c_7]) ).
cnf(c_14,negated_conjecture,
~ intersect(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_th101_neg]) ).
cnf(c_15,negated_conjecture,
intersect(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_prove_th101_neg]) ).
cnf(c_16,plain,
( intersect(B,A)
| ~ intersect(A,B) ),
inference(clausify,[status(thm)],[symmetry_of_intersect]) ).
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(sK3(B,C),C)
& member(sK3(B,C),B) )
| ~ intersect(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3(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(sK3(VAR_0,VAR_1),VAR_1)
| ~ intersect(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK3(VAR_0,VAR_1),VAR_0)
| ~ intersect(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_intersect_defn_sk]) ).
cnf(c_17,plain,
( ~ member(C,B)
| ~ member(C,A)
| intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_18,plain,
( member(sK3(A,B),B)
| ~ intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_19,plain,
( member(sK3(A,B),A)
| ~ intersect(A,B) ),
inference(split_conjunct,[status(thm)],[sk_intersect_defn]) ).
cnf(c_22,negated_conjecture,
~ intersect(sK1,sK2),
inference(resolve,[status(thm)],[c_16,c_14]) ).
cnf(c_23,plain,
member(sK3(sK2,sK0),sK0),
inference(resolve,[status(thm)],[c_18,c_15]) ).
cnf(c_24,plain,
member(sK3(sK2,sK0),sK2),
inference(resolve,[status(thm)],[c_19,c_15]) ).
cnf(c_32,plain,
member(sK3(sK2,sK0),sK1),
inference(resolve,[status(thm)],[c_23,c_11]) ).
cnf(c_40,plain,
( ~ member(A,sK2)
| ~ member(A,sK1) ),
inference(resolve,[status(thm)],[c_17,c_22]) ).
cnf(c_41,plain,
~ member(sK3(sK2,sK0),sK1),
inference(resolve,[status(thm)],[c_40,c_24]) ).
cnf(c_39,plain,
$false,
inference(resolve,[status(thm)],[c_32,c_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET625+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:01:17 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 2579731 was started by sandbox2 on n014,
% 0.12/0.36 % Sat Sep 26 08:01:17 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Theorem for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.37 % Length of proof is 18.
% 0.12/0.37 % Level of proof is 4.
% 0.12/0.37 % Maximum clause weight is 9.000.
% 0.12/0.37 % Given clauses 15.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------