%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET677+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 : n014.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 8.77s 1.72s
% Output : Proof 8.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 23 unt; 0 def)
% Number of atoms : 144 ( 33 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 160 ( 64 ~; 52 |; 23 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-4 aty)
% Number of variables : 64 ( 2 sgn 40 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,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/sandbox/benchmark/theBenchmark.p',p5) ).
fof(f4_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)],[f4]) ).
fof(f4_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)],[f4_nnf]) ).
cnf(c8,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)],[f4_sk]) ).
cnf(hi8,axiom,
ifeq(ilf_type(X0,set_type),true,ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X1,identity_relation_of_type(X0)),true,ilf_type(X1,relation_type(X0,X0)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
fof(f34,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,identity_relation_of_type(B))
=> ( subset(identity_relation_of(B),C)
=> ( B = range(B,B,C)
& B = domain(B,B,C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_44) ).
fof(f34_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,identity_relation_of_type(B))
=> ( subset(identity_relation_of(B),C)
=> ( B = range(B,B,C)
& B = domain(B,B,C) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f34_nnf,plain,
? [B] :
( ? [C] :
( ( B != range(B,B,C)
| B != domain(B,B,C) )
& subset(identity_relation_of(B),C)
& ilf_type(C,identity_relation_of_type(B)) )
& ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f34_neg]) ).
fof(f34_sk,plain,
( ( sk13 != range(sk13,sk13,sk14)
| sk13 != domain(sk13,sk13,sk14) )
& subset(identity_relation_of(sk13),sk14)
& ilf_type(sk14,identity_relation_of_type(sk13))
& ilf_type(sk13,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13,sk14])],[f34_nnf]) ).
cnf(c64,plain,
ilf_type(sk13,set_type),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(hi61,negated_conjecture,
ilf_type(sk13,set_type) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
fof(f33,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p34) ).
fof(f33_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c63,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(hi60,axiom,
ilf_type(X0,set_type) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(c65,plain,
ilf_type(sk14,identity_relation_of_type(sk13)),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(hi62,negated_conjecture,
ilf_type(sk14,identity_relation_of_type(sk13)) = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(h45,plain,
ilf_type(sk14,relation_type(sk13,sk13)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi61,hi60,hi62]) ).
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(identity_relation_of(C),D)
=> ( C = range(B,C,D)
& subset(C,domain(B,C,D)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f1_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( C = range(B,C,D)
& subset(C,domain(B,C,D)) )
| ~ subset(identity_relation_of(C),D)
| ~ 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] :
( ( C = range(B,C,D)
& subset(C,domain(B,C,D)) )
| ~ subset(identity_relation_of(C),D)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c3,plain,
( X1 = range(X0,X1,X2)
| ~ subset(identity_relation_of(X1),X2)
| ~ 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(hi3,axiom,
ifeq(ilf_type(X0,set_type),true,ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X2,relation_type(X0,X1)),true,ifeq(subset(identity_relation_of(X1),X2),true,X1,range(X0,X1,X2)),range(X0,X1,X2)),range(X0,X1,X2)),range(X0,X1,X2)) = range(X0,X1,X2),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(c66,plain,
subset(identity_relation_of(sk13),sk14),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(hi63,negated_conjecture,
subset(identity_relation_of(sk13),sk14) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h129,plain,
sk13 = range(sk13,sk13,sk14),
inference(hyper_resolution,[status(thm)],[hi3,hi61,hi61,h45,hi63]) ).
fof(f0,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( subset(identity_relation_of(C),D)
=> ( subset(C,range(C,B,D))
& C = domain(C,B,D) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f0_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( subset(C,range(C,B,D))
& C = domain(C,B,D) )
| ~ subset(identity_relation_of(C),D)
| ~ ilf_type(D,relation_type(C,B)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C,D] :
( ( subset(C,range(C,B,D))
& C = domain(C,B,D) )
| ~ subset(identity_relation_of(C),D)
| ~ ilf_type(D,relation_type(C,B))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( X1 = domain(X1,X0,X2)
| ~ subset(identity_relation_of(X1),X2)
| ~ ilf_type(X2,relation_type(X1,X0))
| ~ 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,relation_type(X1,X0)),true,ifeq(subset(identity_relation_of(X1),X2),true,X1,domain(X1,X0,X2)),domain(X1,X0,X2)),domain(X1,X0,X2)),domain(X1,X0,X2)) = domain(X1,X0,X2),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h132,plain,
sk13 = domain(sk13,sk13,sk14),
inference(hyper_resolution,[status(thm)],[hi0,hi61,hi61,h45,hi63]) ).
cnf(c67,plain,
( sk13 != range(sk13,sk13,sk14)
| sk13 != domain(sk13,sk13,sk14) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(hi66,negated_conjecture,
ifeq(sk13,domain(sk13,sk13,sk14),ifeq(sk13,range(sk13,sk13,sk14),false,true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi66,h132,h129]) ).
cnf(t522,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f22,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',p23) ).
fof(f22_nnf,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c43,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
fof(f27,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',p28) ).
fof(f27_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)],[f27]) ).
fof(f27_sk,plain,
! [B,C] :
( ( ( ( member(sk12(B),B)
& ilf_type(sk12(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,[sk12])],[f27_nnf]) ).
cnf(c55,plain,
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c43,c55,c67]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t522]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET677+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 11:38:32 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.77/1.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.77/1.72 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------