%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET704+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 02:43:50 PM UTC 2026
% Result : Theorem 82.20s 11.72s
% Output : Proof 82.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 36 unt; 0 def)
% Number of atoms : 98 ( 29 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 79 ( 34 ~; 23 |; 15 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 74 ( 4 sgn 34 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f0_nnf,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,X] :
( ( ( ~ member(sk0(A,B),B)
& member(sk0(A,B),A) )
| subset(A,B) )
& ( member(X,B)
| ~ member(X,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c2,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t165,plain,
ifeq(member(sk0(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t831,plain,
ifeq(member(sk0(X1,X2),X2),true,subset(X1,X2),true) = true,
inference(orient,[status(thm)],[t165]) ).
fof(f10,axiom,
! [X,A] :
( member(X,product(A))
<=> ! [Y] :
( member(Y,A)
=> member(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product) ).
fof(f10_nnf,plain,
! [X,A] :
( ( ? [Y] :
( ~ member(X,Y)
& member(Y,A) )
| member(X,product(A)) )
& ( ! [Y] :
( member(X,Y)
| ~ member(Y,A) )
| ~ member(X,product(A)) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,A,Y] :
( ( ( ~ member(X,sk2(X,A))
& member(sk2(X,A),A) )
| member(X,product(A)) )
& ( member(X,Y)
| ~ member(Y,A)
| ~ member(X,product(A)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f10_nnf]) ).
cnf(c26,plain,
( member(X0,X2)
| ~ member(X2,X1)
| ~ member(X0,product(X1)) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t237,plain,
ifeq(member(X1,product(X2)),true,ifeq(member(X3,X2),true,member(X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(t711,plain,
ifeq(member(X1,product(X2)),true,ifeq(member(X3,X2),true,member(X1,X3),true),true) = true,
inference(orient,[status(thm)],[t237]) ).
fof(f11,conjecture,
! [A,X] :
( member(X,A)
=> subset(product(A),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI42) ).
fof(f11_neg,negated_conjecture,
~ ! [A,X] :
( member(X,A)
=> subset(product(A),X) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [A,X] :
( ~ subset(product(A),X)
& member(X,A) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
( ~ subset(product(sk3),sk4)
& member(sk4,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f11_nnf]) ).
cnf(c29,plain,
member(sk4,sk3),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t4,plain,
member(sk4,sk3) = true,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(t293,plain,
member(sk4,sk3) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t737,plain,
true = ifeq(member(X1,product(sk3)),true,ifeq(true,true,member(X1,sk4),true),true),
inference(cp,[status(thm)],[t711,t293]) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t5953,plain,
true = ifeq(member(X1,product(sk3)),true,member(X1,sk4),true),
inference(step,[status(thm)],[t737,t258]) ).
cnf(t5359,plain,
ifeq(member(X1,product(sk3)),true,member(X1,sk4),true) = true,
inference(orient,[status(thm)],[t5953]) ).
cnf(c1,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t110,plain,
or(subset(X1,X2),member(sk0(X1,X2),X1)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t390,plain,
or(subset(X1,X2),member(sk0(X1,X2),X1)) = true,
inference(orient,[status(thm)],[t110]) ).
cnf(c30,plain,
~ subset(product(sk3),sk4),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t11,plain,
subset(product(sk3),sk4) = false,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(t937,plain,
subset(product(sk3),sk4) = false,
inference(orient,[status(thm)],[t11]) ).
cnf(t946,plain,
true = or(false,member(sk0(product(sk3),sk4),product(sk3))),
inference(cp,[status(thm)],[t390,t937]) ).
cnf(t7,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t257,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t5538,plain,
true = member(sk0(product(sk3),sk4),product(sk3)),
inference(step,[status(thm)],[t946,t257]) ).
cnf(t1308,plain,
member(sk0(product(sk3),sk4),product(sk3)) = true,
inference(orient,[status(thm)],[t5538]) ).
cnf(t5360,plain,
true = ifeq(true,true,member(sk0(product(sk3),sk4),sk4),true),
inference(cp,[status(thm)],[t5359,t1308]) ).
cnf(t5954,plain,
true = member(sk0(product(sk3),sk4),sk4),
inference(step,[status(thm)],[t5360,t258]) ).
cnf(t5361,plain,
member(sk0(product(sk3),sk4),sk4) = true,
inference(orient,[status(thm)],[t5954]) ).
cnf(t5364,plain,
true = ifeq(true,true,subset(product(sk3),sk4),true),
inference(cp,[status(thm)],[t831,t5361]) ).
cnf(t5955,plain,
true = subset(product(sk3),sk4),
inference(step,[status(thm)],[t5364,t258]) ).
cnf(t5956,plain,
true = false,
inference(step,[status(thm)],[t5955,t937]) ).
cnf(t5375,plain,
false = true,
inference(orient,[status(thm)],[t5956]) ).
fof(f5,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
fof(f5_nnf,plain,
! [X] : ~ member(X,empty_set),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : ~ member(X,empty_set),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c14,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f6,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( ~ member(B,A)
& member(B,E) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).
fof(f6_nnf,plain,
! [B,A,E] :
( ( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [B,E,A] :
( ( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c16,plain,
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c14,c16,c30]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t5375]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET704+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.42 % Computer : n007.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Thu Sep 24 11:40:52 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 82.20/11.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 82.20/11.72 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------