%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET575+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 : Fri Sep 25 02:43:28 PM UTC 2026
% Result : Theorem 3.46s 0.83s
% Output : Proof 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 12 unt; 0 def)
% Number of atoms : 45 ( 10 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 40 ( 17 ~; 11 |; 9 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 30 ( 0 sgn 14 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(f0_nnf,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_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(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
( member(sk0(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi1,axiom,
ifeq(intersect(X0,X1),true,member(sk0(X0,X1),X1),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
fof(f2,conjecture,
! [B,C] :
( intersect(B,C)
=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th15) ).
fof(f2_neg,negated_conjecture,
~ ! [B,C] :
( intersect(B,C)
=> ? [D] :
( member(D,C)
& member(D,B) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f2_nnf,plain,
? [B,C] :
( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
& intersect(B,C) ),
inference(nnf_transformation,[status(thm)],[f2_neg]) ).
fof(f2_sk,plain,
! [D] :
( ( ~ member(D,sk2)
| ~ member(D,sk1) )
& intersect(sk1,sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2])],[f2_nnf]) ).
cnf(c4,plain,
intersect(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi4,negated_conjecture,
intersect(sk1,sk2) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h1,plain,
member(sk0(sk1,sk2),sk2) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi4]) ).
cnf(c0,plain,
( member(sk0(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(intersect(X0,X1),true,member(sk0(X0,X1),X0),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h2,plain,
member(sk0(sk1,sk2),sk1) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi4]) ).
cnf(c5,plain,
( ~ member(X2,sk2)
| ~ member(X2,sk1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi5,negated_conjecture,
ifeq(member(X0,sk1),true,ifeq(member(X0,sk2),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi5,h2,h1]) ).
cnf(t44,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t44]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET575+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n016.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 : Thu Sep 24 11:24:12 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.46/0.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.46/0.83 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------