%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 01:00:39 PM UTC 2026
% Result : Unsatisfiable 9.90s 2.01s
% Output : Proof 9.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 14
% Syntax : Number of formulae : 115 ( 95 unt; 0 def)
% Number of atoms : 151 ( 83 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 80 ( 44 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 117 ( 10 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t20,axiom,
sFlat0 = compose(b,a),
introduced(definition) ).
cnf(t150,plain,
compose(b,a) = sFlat0,
inference(orient,[status(thm)],[t20]) ).
cnf(t21,axiom,
sFlat1 = codomain(compose(b,a)),
introduced(definition) ).
cnf(t146,plain,
codomain(compose(b,a)) = sFlat1,
inference(orient,[status(thm)],[t21]) ).
cnf(t892,plain,
codomain(sFlat0) = sFlat1,
inference(step,[status(thm)],[t146,t150]) ).
cnf(t152,plain,
codomain(sFlat0) = sFlat1,
inference(rw,[status(thm)],[t892]) ).
cnf(t157,plain,
codomain(sFlat0) = sFlat1,
inference(orient,[status(thm)],[t152]) ).
cnf(t22,axiom,
sFlat2 = codomain(b),
introduced(definition) ).
cnf(t142,plain,
codomain(b) = sFlat2,
inference(orient,[status(thm)],[t22]) ).
cnf(f17,axiom,
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/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(t12,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t24,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(orient,[status(thm)],[t12]) ).
cnf(f15,axiom,
( product(X,Y,Y)
| ~ identity_map(X)
| ~ defined(X,Y) ),
file('/export/starexec/sandbox2/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(t10,plain,
ifeq(defined(X1,X2),true,ifeq(identity_map(X1),true,product(X1,X2,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t46,plain,
ifeq(defined(X1,X2),true,ifeq(identity_map(X1),true,product(X1,X2,X2),true),true) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(f5,axiom,
( defined(X,Y)
| ~ defined(X,Yz)
| ~ product(Y,Z,Yz) ),
file('/export/starexec/sandbox2/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(t14,plain,
ifeq(product(X1,X2,X3),true,ifeq(defined(X4,X3),true,defined(X4,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t34,plain,
ifeq(product(X1,X2,X3),true,ifeq(defined(X4,X3),true,defined(X4,X1),true),true) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(f14,axiom,
product(codomain(X),X,X),
file('/export/starexec/sandbox2/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(t7,plain,
product(codomain(X1),X1,X1) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t67,plain,
product(codomain(X1),X1,X1) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t145,plain,
true = product(sFlat2,b,b),
inference(cp,[status(thm)],[t67,t142]) ).
cnf(t197,plain,
product(sFlat2,b,b) = true,
inference(orient,[status(thm)],[t145]) ).
cnf(t201,plain,
true = ifeq(true,true,ifeq(defined(X1,b),true,defined(X1,sFlat2),true),true),
inference(cp,[status(thm)],[t34,t197]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t23,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t936,plain,
true = ifeq(defined(X1,b),true,defined(X1,sFlat2),true),
inference(step,[status(thm)],[t201,t23]) ).
cnf(t469,plain,
ifeq(defined(X1,b),true,defined(X1,sFlat2),true) = true,
inference(orient,[status(thm)],[t936]) ).
cnf(f0,axiom,
( product(X,Y,compose(X,Y))
| ~ defined(X,Y) ),
file('/export/starexec/sandbox2/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(t9,plain,
ifeq(defined(X1,X2),true,product(X1,X2,compose(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t47,plain,
ifeq(defined(X1,X2),true,product(X1,X2,compose(X1,X2)),true) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t151,plain,
true = ifeq(defined(b,a),true,product(b,a,sFlat0),true),
inference(cp,[status(thm)],[t47,t150]) ).
cnf(f18,hypothesis,
defined(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ba_defined) ).
fof(f18_nnf,plain,
defined(b,a),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
defined(b,a),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(t0,plain,
defined(b,a) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t118,plain,
defined(b,a) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t893,plain,
true = ifeq(true,true,product(b,a,sFlat0),true),
inference(step,[status(thm)],[t151,t118]) ).
cnf(t894,plain,
true = product(b,a,sFlat0),
inference(step,[status(thm)],[t893,t23]) ).
cnf(t214,plain,
product(b,a,sFlat0) = true,
inference(orient,[status(thm)],[t894]) ).
cnf(t218,plain,
true = ifeq(true,true,ifeq(defined(X1,sFlat0),true,defined(X1,b),true),true),
inference(cp,[status(thm)],[t34,t214]) ).
cnf(t953,plain,
true = ifeq(defined(X1,sFlat0),true,defined(X1,b),true),
inference(step,[status(thm)],[t218,t23]) ).
cnf(t585,plain,
ifeq(defined(X1,sFlat0),true,defined(X1,b),true) = true,
inference(orient,[status(thm)],[t953]) ).
cnf(f12,axiom,
defined(codomain(X),X),
file('/export/starexec/sandbox2/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(t4,plain,
defined(codomain(X1),X1) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t102,plain,
defined(codomain(X1),X1) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t159,plain,
true = defined(sFlat1,sFlat0),
inference(cp,[status(thm)],[t102,t157]) ).
cnf(t181,plain,
defined(sFlat1,sFlat0) = true,
inference(orient,[status(thm)],[t159]) ).
cnf(t587,plain,
true = ifeq(true,true,defined(sFlat1,b),true),
inference(cp,[status(thm)],[t585,t181]) ).
cnf(t954,plain,
true = defined(sFlat1,b),
inference(step,[status(thm)],[t587,t23]) ).
cnf(t595,plain,
defined(sFlat1,b) = true,
inference(orient,[status(thm)],[t954]) ).
cnf(t597,plain,
true = ifeq(true,true,defined(sFlat1,sFlat2),true),
inference(cp,[status(thm)],[t469,t595]) ).
cnf(t955,plain,
true = defined(sFlat1,sFlat2),
inference(step,[status(thm)],[t597,t23]) ).
cnf(t613,plain,
defined(sFlat1,sFlat2) = true,
inference(orient,[status(thm)],[t955]) ).
cnf(t616,plain,
true = ifeq(true,true,ifeq(identity_map(sFlat1),true,product(sFlat1,sFlat2,sFlat2),true),true),
inference(cp,[status(thm)],[t46,t613]) ).
cnf(t960,plain,
true = ifeq(identity_map(sFlat1),true,product(sFlat1,sFlat2,sFlat2),true),
inference(step,[status(thm)],[t616,t23]) ).
cnf(f10,axiom,
identity_map(codomain(X)),
file('/export/starexec/sandbox2/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(t1,plain,
identity_map(codomain(X1)) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t134,plain,
identity_map(codomain(X1)) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t158,plain,
true = identity_map(sFlat1),
inference(cp,[status(thm)],[t134,t157]) ).
cnf(t161,plain,
identity_map(sFlat1) = true,
inference(orient,[status(thm)],[t158]) ).
cnf(t961,plain,
true = ifeq(true,true,product(sFlat1,sFlat2,sFlat2),true),
inference(step,[status(thm)],[t960,t161]) ).
cnf(t962,plain,
true = product(sFlat1,sFlat2,sFlat2),
inference(step,[status(thm)],[t961,t23]) ).
cnf(t663,plain,
product(sFlat1,sFlat2,sFlat2) = true,
inference(orient,[status(thm)],[t962]) ).
cnf(t664,plain,
X1 = ifeq(true,true,ifeq(product(sFlat1,sFlat2,X1),true,sFlat2,X1),X1),
inference(cp,[status(thm)],[t24,t663]) ).
cnf(t983,plain,
X1 = ifeq(product(sFlat1,sFlat2,X1),true,sFlat2,X1),
inference(step,[status(thm)],[t664,t23]) ).
cnf(t866,plain,
ifeq(product(sFlat1,sFlat2,X1),true,sFlat2,X1) = X1,
inference(orient,[status(thm)],[t983]) ).
cnf(f16,axiom,
( product(X,Y,X)
| ~ identity_map(Y)
| ~ defined(X,Y) ),
file('/export/starexec/sandbox2/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(t11,plain,
ifeq(defined(X1,X2),true,ifeq(identity_map(X2),true,product(X1,X2,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t45,plain,
ifeq(defined(X1,X2),true,ifeq(identity_map(X2),true,product(X1,X2,X1),true),true) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t617,plain,
true = ifeq(true,true,ifeq(identity_map(sFlat2),true,product(sFlat1,sFlat2,sFlat1),true),true),
inference(cp,[status(thm)],[t45,t613]) ).
cnf(t963,plain,
true = ifeq(identity_map(sFlat2),true,product(sFlat1,sFlat2,sFlat1),true),
inference(step,[status(thm)],[t617,t23]) ).
cnf(t143,plain,
true = identity_map(sFlat2),
inference(cp,[status(thm)],[t134,t142]) ).
cnf(t153,plain,
identity_map(sFlat2) = true,
inference(orient,[status(thm)],[t143]) ).
cnf(t964,plain,
true = ifeq(true,true,product(sFlat1,sFlat2,sFlat1),true),
inference(step,[status(thm)],[t963,t153]) ).
cnf(t965,plain,
true = product(sFlat1,sFlat2,sFlat1),
inference(step,[status(thm)],[t964,t23]) ).
cnf(t679,plain,
product(sFlat1,sFlat2,sFlat1) = true,
inference(orient,[status(thm)],[t965]) ).
cnf(t868,plain,
sFlat1 = ifeq(true,true,sFlat2,sFlat1),
inference(cp,[status(thm)],[t866,t679]) ).
cnf(t984,plain,
sFlat1 = sFlat2,
inference(step,[status(thm)],[t868,t23]) ).
cnf(t869,plain,
sFlat2 = sFlat1,
inference(orient,[status(thm)],[t984]) ).
cnf(t985,plain,
codomain(b) = sFlat1,
inference(step,[status(thm)],[t142,t869]) ).
cnf(t870,plain,
codomain(b) = sFlat1,
inference(orient,[status(thm)],[t985]) ).
cnf(f19,negated_conjecture,
codomain(compose(b,a)) != codomain(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_of_ba_equals_codomain_of_b) ).
fof(f19_nnf,plain,
codomain(compose(b,a)) != codomain(b),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
codomain(compose(b,a)) != codomain(b),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
codomain(compose(b,a)) != codomain(b),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(goal_0,negated_conjecture,
codomain(compose(b,a)) != codomain(b),
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
codomain(sFlat0) != codomain(b),
inference(rw,[status(thm)],[goal_0,t150]) ).
cnf(g0_1,plain,
sFlat1 != codomain(b),
inference(rw,[status(thm)],[g0_0,t157]) ).
cnf(g0_2,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_1,t870]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n014.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 06:54:04 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.90/2.01 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.90/2.01 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------