%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 01:00:36 PM UTC 2026
% Result : Unsatisfiable 6.27s 1.26s
% Output : Proof 6.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 44 unt; 0 def)
% Number of atoms : 108 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 94 ( 50 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-4 aty)
% Number of variables : 105 ( 6 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(h3,plain,
identity_map(codomain(a)) = true,
inference(hyper_resolution,[status(thm)],[hi10]) ).
cnf(f18,hypothesis,
defined(h,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ha_defined) ).
fof(f18_nnf,plain,
defined(h,a),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
defined(h,a),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(hi18,axiom,
defined(h,a) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h15,plain,
defined(h,a) = true,
inference(hyper_resolution,[status(thm)],[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(h16,plain,
defined(h,codomain(a)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi14,h15]) ).
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(h20,plain,
product(h,codomain(a),h) = true,
inference(hyper_resolution,[status(thm)],[hi16,h16,h3]) ).
cnf(f19,hypothesis,
identity_map(h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_is_the_identity_map) ).
fof(f19_nnf,plain,
identity_map(h),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
identity_map(h),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(hi19,axiom,
identity_map(h) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(h17,plain,
identity_map(h) = true,
inference(hyper_resolution,[status(thm)],[hi19]) ).
cnf(f15,axiom,
( product(X,Y,Y)
| ~ identity_map(X)
| ~ defined(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity1) ).
fof(f15_nnf,plain,
! [X,Y] :
( product(X,Y,Y)
| ~ identity_map(X)
| ~ defined(X,Y) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Y] :
( product(X,Y,Y)
| ~ identity_map(X)
| ~ defined(X,Y) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( product(X0,X1,X1)
| ~ identity_map(X0)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(defined(X0,X1),true,ifeq(identity_map(X0),true,product(X0,X1,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(h18,plain,
product(h,codomain(a),codomain(a)) = true,
inference(hyper_resolution,[status(thm)],[hi15,h16,h17]) ).
cnf(f4,axiom,
( product(X,Yz,Xyz)
| ~ product(Y,Z,Yz)
| ~ product(Xy,Z,Xyz)
| ~ product(X,Y,Xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom2) ).
fof(f4_nnf,plain,
! [X,Y,Xy,Z,Xyz,Yz] :
( product(X,Yz,Xyz)
| ~ product(Y,Z,Yz)
| ~ product(Xy,Z,Xyz)
| ~ product(X,Y,Xy) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Xy,Z,Xyz,Yz] :
( product(X,Yz,Xyz)
| ~ product(Y,Z,Yz)
| ~ product(Xy,Z,Xyz)
| ~ product(X,Y,Xy) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( product(X0,X5,X4)
| ~ product(X1,X3,X5)
| ~ product(X2,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X2,X3,X4),true,ifeq(product(X1,X3,X5),true,product(X0,X5,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f13,axiom,
product(X,domain(X),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_on_domain) ).
fof(f13_nnf,plain,
! [X] : product(X,domain(X),X),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X] : product(X,domain(X),X),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
product(X0,domain(X0),X0),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
product(X0,domain(X0),X0) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h19,plain,
product(h,codomain(a),codomain(a)) = true,
inference(hyper_resolution,[status(thm)],[hi4,h18,hi13,hi13]) ).
cnf(f17,axiom,
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_is_well_defined) ).
fof(f17_nnf,plain,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi17,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t0,plain,
codomain(a) = h,
inference(hyper_resolution,[status(thm)],[hi17,h19,h20]) ).
cnf(t145,plain,
codomain(a) = h,
inference(orient,[status(thm)],[t0]) ).
cnf(f20,negated_conjecture,
codomain(a) != h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_of_a_is_h) ).
fof(f20_nnf,plain,
codomain(a) != h,
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
codomain(a) != h,
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
codomain(a) != h,
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
codomain(a) != h,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(g0_0,plain,
h != h,
inference(rw,[status(thm)],[goal_0,t145]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 06:52:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.27/1.26 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.27/1.26 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------