%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 01:00:33 PM UTC 2026
% Result : Unsatisfiable 4.57s 1.25s
% Output : Proof 4.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 80 ( 48 unt; 0 def)
% Number of atoms : 152 ( 34 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 150 ( 78 ~; 72 |; 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 : 10 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 165 ( 9 sgn 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,axiom,
( defined(X,Y)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_property1) ).
fof(f1_nnf,plain,
! [X,Y,Z] :
( defined(X,Y)
| ~ product(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] :
( defined(X,Y)
| ~ product(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( defined(X0,X1)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(product(X0,X1,X2),true,defined(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f21,hypothesis,
product(b,g,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_equals_d) ).
fof(f21_nnf,plain,
product(b,g,d),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c21,plain,
product(b,g,d),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(hi21,axiom,
product(b,g,d) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(h13,plain,
defined(b,g) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi21]) ).
cnf(f2,axiom,
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associative_property2) ).
fof(f2_nnf,plain,
! [X,Y,Xy,Z] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Xy,Z] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( defined(X1,X3)
| ~ defined(X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(product(X0,X1,X2),true,ifeq(defined(X2,X3),true,defined(X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
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(h32,plain,
defined(domain(b),g) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi13,h13]) ).
cnf(f18,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_equals_c) ).
fof(f18_nnf,plain,
product(a,b,c),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
product(a,b,c),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(hi18,axiom,
product(a,b,c) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h6,plain,
defined(a,b) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi18]) ).
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(h31,plain,
defined(c,domain(b)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi13,hi18,h6]) ).
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(f9,axiom,
identity_map(domain(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_is_an_identity_map) ).
fof(f9_nnf,plain,
! [X] : identity_map(domain(X)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X] : identity_map(domain(X)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
identity_map(domain(X0)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,axiom,
identity_map(domain(X0)) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h51,plain,
defined(c,g) = true,
inference(hyper_resolution,[status(thm)],[hi8,h31,h32,hi9]) ).
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(h54,plain,
defined(a,d) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi18,hi21,h51]) ).
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(h59,plain,
product(a,d,compose(a,d)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h54]) ).
cnf(f7,axiom,
( product(Xy,Z,Xyz)
| ~ product(X,Y,Xy)
| ~ product(X,Yz,Xyz)
| ~ product(Y,Z,Yz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',category_theory_axiom5) ).
fof(f7_nnf,plain,
! [Y,Z,Yz,X,Xyz,Xy] :
( product(Xy,Z,Xyz)
| ~ product(X,Y,Xy)
| ~ product(X,Yz,Xyz)
| ~ product(Y,Z,Yz) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [Y,Z,Yz,X,Xyz,Xy] :
( product(Xy,Z,Xyz)
| ~ product(X,Y,Xy)
| ~ product(X,Yz,Xyz)
| ~ product(Y,Z,Yz) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( product(X5,X1,X4)
| ~ product(X3,X0,X5)
| ~ product(X3,X2,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X2,X4),true,ifeq(product(X3,X0,X5),true,product(X5,X1,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(f20,hypothesis,
product(b,h,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bh_equals_d) ).
fof(f20_nnf,plain,
product(b,h,d),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
product(b,h,d),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(hi20,axiom,
product(b,h,d) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h910,plain,
product(c,h,compose(a,d)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi20,h59,hi18]) ).
cnf(h909,plain,
product(c,g,compose(a,d)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi21,h59,hi18]) ).
cnf(f19,hypothesis,
( X1 = X3
| ~ product(c,X3,X2)
| ~ product(c,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product) ).
fof(f19_nnf,plain,
! [X1,X2,X3] :
( X1 = X3
| ~ product(c,X3,X2)
| ~ product(c,X1,X2) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X1,X2,X3] :
( X1 = X3
| ~ product(c,X3,X2)
| ~ product(c,X1,X2) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( X0 = X2
| ~ product(c,X2,X1)
| ~ product(c,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi19,axiom,
ifeq(product(c,X0,X1),true,ifeq(product(c,X2,X1),true,X0,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t0,plain,
h = g,
inference(hyper_resolution,[status(thm)],[hi19,h909,h910]) ).
cnf(t2284,plain,
g = h,
inference(orient,[status(thm)],[t0]) ).
cnf(f22,negated_conjecture,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).
fof(f22_nnf,plain,
h != g,
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
h != g,
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
h != g,
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(goal_0,negated_conjecture,
h != g,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(g0_0,plain,
h != h,
inference(rw,[status(thm)],[goal_0,t2284]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.55 % Computer : n007.cluster.edu
% 0.11/0.55 % Model : x86_64 x86_64
% 0.11/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.55 % Memory : 8046.5625MB
% 0.11/0.55 % OS : Linux 6.8.0-71-generic
% 0.11/0.55 % CPULimit : 300
% 0.11/0.55 % WCLimit : 300
% 0.11/0.55 % DateTime : Fri Sep 25 06:47:08 UTC 2026
% 0.11/0.55 % CPUTime :
% 0.11/0.55 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.57/1.25 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.57/1.25 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------