%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET653+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 : n001.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 02:43:43 PM UTC 2026
% Result : Theorem 3.75s 0.94s
% Output : Proof 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 32 unt; 0 def)
% Number of atoms : 156 ( 21 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 165 ( 65 ~; 53 |; 21 &)
% ( 1 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 86 ( 4 sgn 50 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,D))
=> ( subset(B,C)
=> ilf_type(E,relation_type(C,D)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_15) ).
fof(f22_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,D))
=> ( subset(B,C)
=> ilf_type(E,relation_type(C,D)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f22_nnf,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ~ ilf_type(E,relation_type(C,D))
& subset(B,C)
& ilf_type(E,relation_type(B,D)) )
& ilf_type(D,set_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f22_neg]) ).
fof(f22_sk,plain,
( ~ ilf_type(sk12,relation_type(sk10,sk11))
& subset(sk9,sk10)
& ilf_type(sk12,relation_type(sk9,sk11))
& ilf_type(sk11,set_type)
& ilf_type(sk10,set_type)
& ilf_type(sk9,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10,sk11,sk12])],[f22_nnf]) ).
cnf(c45,plain,
~ ilf_type(sk12,relation_type(sk10,sk11)),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t67,plain,
ifeq(ilf_type(sk12,relation_type(sk10,sk11)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(range_of(D),C)
& subset(domain_of(D),B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f1_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( subset(range_of(D),C)
& subset(domain_of(D),B) )
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D] :
( ( subset(range_of(D),C)
& subset(domain_of(D),B) )
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(ilf_type(X0,set_type),true,ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X2,relation_type(X0,X1)),true,subset(domain_of(X2),X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(c40,plain,
ilf_type(sk9,set_type),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi38,negated_conjecture,
ilf_type(sk9,set_type) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(c42,plain,
ilf_type(sk11,set_type),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi40,negated_conjecture,
ilf_type(sk11,set_type) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(c43,plain,
ilf_type(sk12,relation_type(sk9,sk11)),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi41,negated_conjecture,
ilf_type(sk12,relation_type(sk9,sk11)) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(h15,plain,
subset(domain_of(sk12),sk9) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi38,hi40,hi41]) ).
fof(f0,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f0_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( subset(B,D)
| ~ subset(C,D)
| ~ subset(B,C)
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C,D] :
( subset(B,D)
| ~ subset(C,D)
| ~ subset(B,C)
| ~ ilf_type(D,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ 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,ifeq(ilf_type(X2,set_type),true,ifeq(subset(X0,X1),true,ifeq(subset(X1,X2),true,subset(X0,X2),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
fof(f21,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
fof(f21_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c39,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi37,axiom,
ilf_type(X0,set_type) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(c41,plain,
ilf_type(sk10,set_type),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi39,negated_conjecture,
ilf_type(sk10,set_type) = true,
inference(equality_encoding,[status(esa)],[c41]) ).
cnf(c44,plain,
subset(sk9,sk10),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi42,negated_conjecture,
subset(sk9,sk10) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(h16,plain,
subset(domain_of(sk12),sk10) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi37,hi38,hi39,h15,hi42]) ).
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,D))
=> ( subset(domain_of(E),C)
=> ilf_type(E,relation_type(C,D)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f2_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ilf_type(E,relation_type(C,D))
| ~ subset(domain_of(E),C)
| ~ ilf_type(E,relation_type(B,D)) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C,D,E] :
( ilf_type(E,relation_type(C,D))
| ~ subset(domain_of(E),C)
| ~ ilf_type(E,relation_type(B,D))
| ~ ilf_type(D,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
( ilf_type(X3,relation_type(X1,X2))
| ~ subset(domain_of(X3),X1)
| ~ ilf_type(X3,relation_type(X0,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi3,axiom,
ifeq(ilf_type(X0,set_type),true,ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X2,set_type),true,ifeq(ilf_type(X3,relation_type(X0,X2)),true,ifeq(subset(domain_of(X3),X1),true,ilf_type(X3,relation_type(X1,X2)),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t18,plain,
ilf_type(sk12,relation_type(sk10,sk11)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi38,hi39,hi40,hi41,h16]) ).
cnf(t119,plain,
ilf_type(sk12,relation_type(sk10,sk11)) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t321,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t67,t119]) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t112,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t322,plain,
false = true,
inference(step,[status(thm)],[t321,t112]) ).
cnf(t198,plain,
false = true,
inference(orient,[status(thm)],[t322]) ).
fof(f13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).
fof(f13_nnf,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c22,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
fof(f16,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).
fof(f16_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)],[f16]) ).
fof(f16_sk,plain,
! [B,C] :
( ( ( ( member(sk5(B),B)
& ilf_type(sk5(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,[sk5])],[f16_nnf]) ).
cnf(c27,plain,
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c22,c27,c45]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t198]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET653+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 11:40:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.75/0.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.75/0.94 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------