%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET658+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 : n026.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 02:43:44 PM UTC 2026
% Result : Theorem 10.43s 1.89s
% Output : Proof 10.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 22 unt; 0 def)
% Number of atoms : 87 ( 15 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 83 ( 38 ~; 26 |; 9 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 43 ( 4 sgn 23 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,conjecture,
! [B] :
( ilf_type(B,binary_relation_type)
=> ilf_type(B,relation_type(domain_of(B),range_of(B))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_20) ).
fof(f28_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,binary_relation_type)
=> ilf_type(B,relation_type(domain_of(B),range_of(B))) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f28_nnf,plain,
? [B] :
( ~ ilf_type(B,relation_type(domain_of(B),range_of(B)))
& ilf_type(B,binary_relation_type) ),
inference(nnf_transformation,[status(thm)],[f28_neg]) ).
fof(f28_sk,plain,
( ~ ilf_type(sk12,relation_type(domain_of(sk12),range_of(sk12)))
& ilf_type(sk12,binary_relation_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12])],[f28_nnf]) ).
cnf(c52,plain,
~ ilf_type(sk12,relation_type(domain_of(sk12),range_of(sk12))),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(t45,plain,
ifeq(ilf_type(sk12,relation_type(domain_of(sk12),range_of(sk12))),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
fof(f14,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(B,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
fof(f14_nnf,plain,
! [B] :
( subset(B,B)
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [B] :
( subset(B,B)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c25,plain,
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi24,axiom,
ifeq(ilf_type(X0,set_type),true,subset(X0,X0),true) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
fof(f27,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p28) ).
fof(f27_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c50,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(hi47,axiom,
ilf_type(X0,set_type) = true,
inference(equality_encoding,[status(esa)],[c50]) ).
cnf(h7,plain,
subset(V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi24,hi47]) ).
fof(f0,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(domain_of(C),B)
=> ilf_type(C,relation_type(B,range_of(C))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f0_nnf,plain,
! [B] :
( ! [C] :
( ilf_type(C,relation_type(B,range_of(C)))
| ~ subset(domain_of(C),B)
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C] :
( ilf_type(C,relation_type(B,range_of(C)))
| ~ subset(domain_of(C),B)
| ~ ilf_type(C,binary_relation_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ilf_type(X1,relation_type(X0,range_of(X1)))
| ~ subset(domain_of(X1),X0)
| ~ ilf_type(X1,binary_relation_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,binary_relation_type),true,ifeq(subset(domain_of(X1),X0),true,ilf_type(X1,relation_type(X0,range_of(X1))),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(c51,plain,
ilf_type(sk12,binary_relation_type),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(hi48,negated_conjecture,
ilf_type(sk12,binary_relation_type) = true,
inference(equality_encoding,[status(esa)],[c51]) ).
cnf(t20,plain,
ilf_type(sk12,relation_type(domain_of(sk12),range_of(sk12))) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi47,hi48,h7]) ).
cnf(t95,plain,
ilf_type(sk12,relation_type(domain_of(sk12),range_of(sk12))) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(t349,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t45,t95]) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t91,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t13]) ).
cnf(t350,plain,
false = true,
inference(step,[status(thm)],[t349,t91]) ).
cnf(t212,plain,
false = true,
inference(orient,[status(thm)],[t350]) ).
fof(f18,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',p19) ).
fof(f18_nnf,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c37,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f21,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',p22) ).
fof(f21_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)],[f21]) ).
fof(f21_sk,plain,
! [B,C] :
( ( ( ( member(sk11(B),B)
& ilf_type(sk11(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,[sk11])],[f21_nnf]) ).
cnf(c42,plain,
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c37,c42,c52]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t212]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET658+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 11:38:23 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.43/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.43/1.89 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------