%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET676+3 : 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 02:43:47 PM UTC 2026
% Result : Theorem 7.72s 1.45s
% Output : Proof 7.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 20 unt; 0 def)
% Number of atoms : 93 ( 14 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 96 ( 43 ~; 31 |; 11 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 51 ( 4 sgn 26 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ilf_type(cross_product(B,B),identity_relation_of_type(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_41) ).
fof(f19_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ilf_type(cross_product(B,B),identity_relation_of_type(B)) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f19_nnf,plain,
? [B] :
( ~ ilf_type(cross_product(B,B),identity_relation_of_type(B))
& ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f19_neg]) ).
fof(f19_sk,plain,
( ~ ilf_type(cross_product(sk11,sk11),identity_relation_of_type(sk11))
& ilf_type(sk11,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f19_nnf]) ).
cnf(c40,plain,
~ ilf_type(cross_product(sk11,sk11),identity_relation_of_type(sk11)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t43,plain,
ifeq(ilf_type(cross_product(sk11,sk11),identity_relation_of_type(sk11)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
fof(f0,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(cross_product(B,C),relation_type(B,C)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f0_nnf,plain,
! [B] :
( ! [C] :
( ilf_type(cross_product(B,C),relation_type(B,C))
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C] :
( ilf_type(cross_product(B,C),relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ilf_type(cross_product(X0,X1),relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(ilf_type(X0,set_type),true,ifeq(ilf_type(X1,set_type),true,ilf_type(cross_product(X0,X1),relation_type(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
fof(f18,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
fof(f18_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c38,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi36,axiom,
ilf_type(X0,set_type) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(h10,plain,
ilf_type(cross_product(V0,V1),relation_type(V0,V1)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi36,hi36]) ).
fof(f3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f3_nnf,plain,
! [B] :
( ! [C] :
( ( ( ~ ilf_type(C,relation_type(B,B))
| ilf_type(C,identity_relation_of_type(B)) )
& ( ilf_type(C,relation_type(B,B))
| ~ ilf_type(C,identity_relation_of_type(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,C] :
( ( ( ~ ilf_type(C,relation_type(B,B))
| ilf_type(C,identity_relation_of_type(B)) )
& ( ilf_type(C,relation_type(B,B))
| ~ ilf_type(C,identity_relation_of_type(B)) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c9,plain,
( ~ ilf_type(X1,relation_type(X0,X0))
| ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi9,axiom,
ifeq(ilf_type(X0,set_type),true,ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X1,relation_type(X0,X0)),true,ilf_type(X1,identity_relation_of_type(X0)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t14,plain,
ilf_type(cross_product(X1,X1),identity_relation_of_type(X1)) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi36,hi36,h10]) ).
cnf(t90,plain,
ilf_type(cross_product(X1,X1),identity_relation_of_type(X1)) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t262,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t43,t90]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t84,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t263,plain,
false = true,
inference(step,[status(thm)],[t262,t84]) ).
cnf(t144,plain,
false = true,
inference(orient,[status(thm)],[t263]) ).
fof(f11,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(f11_nnf,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c22,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
fof(f14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
fof(f14_nnf,plain,
! [B] :
( ( ( ? [C] :
( member(C,B)
& ilf_type(C,set_type) )
| empty(B) )
& ( ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) )
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [B,C] :
( ( ( ( member(sk7(B),B)
& ilf_type(sk7(B),set_type) )
| empty(B) )
& ( ~ member(C,B)
| ~ ilf_type(C,set_type)
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7])],[f14_nnf]) ).
cnf(c27,plain,
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c22,c27,c40]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t144]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET676+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 11:36:37 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.72/1.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.72/1.45 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------