%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT018-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 01:00:43 PM UTC 2026
% Result : Unsatisfiable 10.75s 2.01s
% Output : Proof 10.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 68 ( 44 unt; 0 def)
% Number of atoms : 124 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 118 ( 62 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 120 ( 6 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
( product(X,Y,compose(X,Y))
| ~ defined(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_composition) ).
fof(f0_nnf,plain,
! [X,Y] :
( product(X,Y,compose(X,Y))
| ~ defined(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( product(X,Y,compose(X,Y))
| ~ defined(X,Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(defined(X0,X1),true,product(X0,X1,compose(X0,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f18,hypothesis,
defined(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_ab_exists) ).
fof(f18_nnf,plain,
defined(a,b),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
defined(a,b),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(hi18,axiom,
defined(a,b) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h0,plain,
product(a,b,compose(a,b)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi18]) ).
cnf(f5,axiom,
( defined(X,Y)
| ~ defined(X,Yz)
| ~ product(Y,Z,Yz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom3) ).
fof(f5_nnf,plain,
! [Y,Z,Yz,X] :
( defined(X,Y)
| ~ defined(X,Yz)
| ~ product(Y,Z,Yz) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [Y,Z,Yz,X] :
( defined(X,Y)
| ~ defined(X,Yz)
| ~ product(Y,Z,Yz) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( defined(X3,X0)
| ~ defined(X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
ifeq(product(X0,X1,X2),true,ifeq(defined(X3,X2),true,defined(X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f14,axiom,
product(codomain(X),X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_on_codomain) ).
fof(f14_nnf,plain,
! [X] : product(codomain(X),X,X),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X] : product(codomain(X),X,X),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
product(codomain(X0),X0,X0),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
product(codomain(X0),X0,X0) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(f19,hypothesis,
defined(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_bc_exists) ).
fof(f19_nnf,plain,
defined(b,c),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
defined(b,c),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(hi19,axiom,
defined(b,c) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h19,plain,
defined(b,codomain(c)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi14,hi19]) ).
cnf(f16,axiom,
( product(X,Y,X)
| ~ identity_map(Y)
| ~ defined(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity2) ).
fof(f16_nnf,plain,
! [X,Y] :
( product(X,Y,X)
| ~ identity_map(Y)
| ~ defined(X,Y) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X,Y] :
( product(X,Y,X)
| ~ identity_map(Y)
| ~ defined(X,Y) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( product(X0,X1,X0)
| ~ identity_map(X1)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,axiom,
ifeq(defined(X0,X1),true,ifeq(identity_map(X1),true,product(X0,X1,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(f10,axiom,
identity_map(codomain(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_is_an_identity_map) ).
fof(f10_nnf,plain,
! [X] : identity_map(codomain(X)),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X] : identity_map(codomain(X)),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
identity_map(codomain(X0)),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
identity_map(codomain(X0)) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h24,plain,
product(b,codomain(c),b) = true,
inference(hyper_resolution,[status(thm)],[hi16,h19,hi10]) ).
cnf(f6,axiom,
( defined(Xy,Z)
| ~ defined(X,Yz)
| ~ product(X,Y,Xy)
| ~ product(Y,Z,Yz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom4) ).
fof(f6_nnf,plain,
! [Y,Z,Yz,X,Xy] :
( defined(Xy,Z)
| ~ defined(X,Yz)
| ~ product(X,Y,Xy)
| ~ product(Y,Z,Yz) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [Y,Z,Yz,X,Xy] :
( defined(Xy,Z)
| ~ defined(X,Yz)
| ~ product(X,Y,Xy)
| ~ product(Y,Z,Yz) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( defined(X4,X1)
| ~ defined(X3,X2)
| ~ product(X3,X0,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X0,X4),true,ifeq(defined(X3,X2),true,defined(X4,X1),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h136,plain,
defined(compose(a,b),codomain(c)) = true,
inference(hyper_resolution,[status(thm)],[hi6,h24,h0,hi18]) ).
cnf(f8,axiom,
( defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z)
| ~ defined(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom6) ).
fof(f8_nnf,plain,
! [X,Y,Z] :
( defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z)
| ~ defined(X,Y) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,Z] :
( defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z)
| ~ defined(X,Y) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( defined(X0,X2)
| ~ identity_map(X1)
| ~ defined(X1,X2)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(defined(X0,X1),true,ifeq(defined(X1,X2),true,ifeq(identity_map(X1),true,defined(X0,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(f12,axiom,
defined(codomain(X),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mapping_from_codomain_of_x_to_x) ).
fof(f12_nnf,plain,
! [X] : defined(codomain(X),X),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X] : defined(codomain(X),X),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
defined(codomain(X0),X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi12,axiom,
defined(codomain(X0),X0) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h256,plain,
defined(compose(a,b),c) = true,
inference(hyper_resolution,[status(thm)],[hi8,h136,hi12,hi10]) ).
cnf(h1,plain,
product(b,c,compose(b,c)) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi19]) ).
cnf(f3,axiom,
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom1) ).
fof(f3_nnf,plain,
! [X,Y,Xy,Z,Yz] :
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,Xy,Z,Yz] :
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( defined(X0,X4)
| ~ defined(X2,X3)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X1,X3,X4),true,ifeq(defined(X2,X3),true,defined(X0,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t13,plain,
defined(a,compose(b,c)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h0,h1,h256]) ).
cnf(t432,plain,
defined(a,compose(b,c)) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(f20,negated_conjecture,
~ defined(a,compose(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_bc_exists) ).
fof(f20_nnf,plain,
~ defined(a,compose(b,c)),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
~ defined(a,compose(b,c)),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
~ defined(a,compose(b,c)),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
defined(a,compose(b,c)) != true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t432]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT018-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 07:02:32 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.75/2.01 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.75/2.01 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------