%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET589+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 02:43:31 PM UTC 2026
% Result : Theorem 6.79s 6.35s
% Output : Proof 6.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 21 unt; 0 def)
% Number of atoms : 78 ( 17 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 64 ( 27 ~; 19 |; 12 &)
% ( 1 <=>; 5 =>; 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 : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 77 ( 3 sgn 44 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,conjecture,
! [B,C,D,E] :
( ( subset(D,E)
& subset(B,C) )
=> subset(difference(B,E),difference(C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th48) ).
fof(f6_neg,negated_conjecture,
~ ! [B,C,D,E] :
( ( subset(D,E)
& subset(B,C) )
=> subset(difference(B,E),difference(C,D)) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [B,C,D,E] :
( ~ subset(difference(B,E),difference(C,D))
& subset(D,E)
& subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( ~ subset(difference(sk1,sk4),difference(sk2,sk3))
& subset(sk3,sk4)
& subset(sk1,sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3,sk4])],[f6_nnf]) ).
cnf(c12,plain,
~ subset(difference(sk1,sk4),difference(sk2,sk3)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t24,plain,
ifeq(subset(difference(sk1,sk4),difference(sk2,sk3)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
fof(f2,axiom,
! [B,C,D] :
( subset(B,C)
=> subset(difference(D,C),difference(D,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_subset2) ).
fof(f2_nnf,plain,
! [B,C,D] :
( subset(difference(D,C),difference(D,B))
| ~ subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C,D] :
( subset(difference(D,C),difference(D,B))
| ~ subset(B,C) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( subset(difference(X2,X1),difference(X2,X0))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(subset(X0,X1),true,subset(difference(X2,X1),difference(X2,X0)),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(c11,plain,
subset(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi10,negated_conjecture,
subset(sk3,sk4) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h2,plain,
subset(difference(V0,sk4),difference(V0,sk3)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi10]) ).
fof(f1,axiom,
! [B,C,D] :
( subset(B,C)
=> subset(difference(B,D),difference(C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_subset1) ).
fof(f1_nnf,plain,
! [B,C,D] :
( subset(difference(B,D),difference(C,D))
| ~ subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D] :
( subset(difference(B,D),difference(C,D))
| ~ subset(B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( subset(difference(X0,X2),difference(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(subset(X0,X1),true,subset(difference(X0,X2),difference(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(c10,plain,
subset(sk1,sk2),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi9,negated_conjecture,
subset(sk1,sk2) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h1,plain,
subset(difference(sk1,V0),difference(sk2,V0)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi9]) ).
fof(f0,axiom,
! [B,C,D] :
( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_subset) ).
fof(f0_nnf,plain,
! [B,C,D] :
( subset(B,D)
| ~ subset(C,D)
| ~ subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C,D] :
( subset(B,D)
| ~ subset(C,D)
| ~ subset(B,C) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(subset(X0,X1),true,ifeq(subset(X1,X2),true,subset(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t17,plain,
subset(difference(sk1,sk4),difference(sk2,sk3)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h1,h2]) ).
cnf(t60,plain,
subset(difference(sk1,sk4),difference(sk2,sk3)) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(t184,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t24,t60]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t42,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t185,plain,
false = true,
inference(step,[status(thm)],[t184,t42]) ).
cnf(t181,plain,
false = true,
inference(orient,[status(thm)],[t185]) ).
fof(f3,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f3_nnf,plain,
! [B,C,D] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [D,B,C] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c4,plain,
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c4,c12]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t181]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET589+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/5.39 % Computer : n016.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Thu Sep 24 11:27:04 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.79/6.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.79/6.35 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------