%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 01:00:38 PM UTC 2026
% Result : Unsatisfiable 8.98s 11.84s
% Output : Proof 8.98s
% 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 = domain(compose(b,a)),
introduced(definition) ).
cnf(t146,plain,
domain(compose(b,a)) = sFlat1,
inference(orient,[status(thm)],[t21]) ).
cnf(t830,plain,
domain(sFlat0) = sFlat1,
inference(step,[status(thm)],[t146,t150]) ).
cnf(t152,plain,
domain(sFlat0) = sFlat1,
inference(rw,[status(thm)],[t830]) ).
cnf(t157,plain,
domain(sFlat0) = sFlat1,
inference(orient,[status(thm)],[t152]) ).
cnf(t22,axiom,
sFlat2 = domain(a),
introduced(definition) ).
cnf(t142,plain,
domain(a) = 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(f2,axiom,
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
file('/export/starexec/sandbox2/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(t13,plain,
ifeq(product(X1,X2,X3),true,ifeq(defined(X3,X4),true,defined(X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t38,plain,
ifeq(product(X1,X2,X3),true,ifeq(defined(X3,X4),true,defined(X2,X4),true),true) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(f13,axiom,
product(X,domain(X),X),
file('/export/starexec/sandbox2/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(t6,plain,
product(X1,domain(X1),X1) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t48,plain,
product(X1,domain(X1),X1) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t145,plain,
true = product(a,sFlat2,a),
inference(cp,[status(thm)],[t48,t142]) ).
cnf(t197,plain,
product(a,sFlat2,a) = true,
inference(orient,[status(thm)],[t145]) ).
cnf(t200,plain,
true = ifeq(true,true,ifeq(defined(a,X1),true,defined(sFlat2,X1),true),true),
inference(cp,[status(thm)],[t38,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(t874,plain,
true = ifeq(defined(a,X1),true,defined(sFlat2,X1),true),
inference(step,[status(thm)],[t200,t23]) ).
cnf(t469,plain,
ifeq(defined(a,X1),true,defined(sFlat2,X1),true) = true,
inference(orient,[status(thm)],[t874]) ).
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(t102,plain,
defined(b,a) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t831,plain,
true = ifeq(true,true,product(b,a,sFlat0),true),
inference(step,[status(thm)],[t151,t102]) ).
cnf(t832,plain,
true = product(b,a,sFlat0),
inference(step,[status(thm)],[t831,t23]) ).
cnf(t214,plain,
product(b,a,sFlat0) = true,
inference(orient,[status(thm)],[t832]) ).
cnf(t217,plain,
true = ifeq(true,true,ifeq(defined(sFlat0,X1),true,defined(a,X1),true),true),
inference(cp,[status(thm)],[t38,t214]) ).
cnf(t884,plain,
true = ifeq(defined(sFlat0,X1),true,defined(a,X1),true),
inference(step,[status(thm)],[t217,t23]) ).
cnf(t527,plain,
ifeq(defined(sFlat0,X1),true,defined(a,X1),true) = true,
inference(orient,[status(thm)],[t884]) ).
cnf(f11,axiom,
defined(X,domain(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mapping_from_x_to_its_domain) ).
fof(f11_nnf,plain,
! [X] : defined(X,domain(X)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : defined(X,domain(X)),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
defined(X0,domain(X0)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t3,plain,
defined(X1,domain(X1)) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t86,plain,
defined(X1,domain(X1)) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t159,plain,
true = defined(sFlat0,sFlat1),
inference(cp,[status(thm)],[t86,t157]) ).
cnf(t181,plain,
defined(sFlat0,sFlat1) = true,
inference(orient,[status(thm)],[t159]) ).
cnf(t528,plain,
true = ifeq(true,true,defined(a,sFlat1),true),
inference(cp,[status(thm)],[t527,t181]) ).
cnf(t885,plain,
true = defined(a,sFlat1),
inference(step,[status(thm)],[t528,t23]) ).
cnf(t537,plain,
defined(a,sFlat1) = true,
inference(orient,[status(thm)],[t885]) ).
cnf(t539,plain,
true = ifeq(true,true,defined(sFlat2,sFlat1),true),
inference(cp,[status(thm)],[t469,t537]) ).
cnf(t886,plain,
true = defined(sFlat2,sFlat1),
inference(step,[status(thm)],[t539,t23]) ).
cnf(t555,plain,
defined(sFlat2,sFlat1) = true,
inference(orient,[status(thm)],[t886]) ).
cnf(t558,plain,
true = ifeq(true,true,ifeq(identity_map(sFlat2),true,product(sFlat2,sFlat1,sFlat1),true),true),
inference(cp,[status(thm)],[t46,t555]) ).
cnf(t891,plain,
true = ifeq(identity_map(sFlat2),true,product(sFlat2,sFlat1,sFlat1),true),
inference(step,[status(thm)],[t558,t23]) ).
cnf(f9,axiom,
identity_map(domain(X)),
file('/export/starexec/sandbox2/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(t2,plain,
identity_map(domain(X1)) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t134,plain,
identity_map(domain(X1)) = true,
inference(orient,[status(thm)],[t2]) ).
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(t892,plain,
true = ifeq(true,true,product(sFlat2,sFlat1,sFlat1),true),
inference(step,[status(thm)],[t891,t153]) ).
cnf(t893,plain,
true = product(sFlat2,sFlat1,sFlat1),
inference(step,[status(thm)],[t892,t23]) ).
cnf(t605,plain,
product(sFlat2,sFlat1,sFlat1) = true,
inference(orient,[status(thm)],[t893]) ).
cnf(t606,plain,
X1 = ifeq(true,true,ifeq(product(sFlat2,sFlat1,X1),true,sFlat1,X1),X1),
inference(cp,[status(thm)],[t24,t605]) ).
cnf(t914,plain,
X1 = ifeq(product(sFlat2,sFlat1,X1),true,sFlat1,X1),
inference(step,[status(thm)],[t606,t23]) ).
cnf(t804,plain,
ifeq(product(sFlat2,sFlat1,X1),true,sFlat1,X1) = X1,
inference(orient,[status(thm)],[t914]) ).
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(t559,plain,
true = ifeq(true,true,ifeq(identity_map(sFlat1),true,product(sFlat2,sFlat1,sFlat2),true),true),
inference(cp,[status(thm)],[t45,t555]) ).
cnf(t894,plain,
true = ifeq(identity_map(sFlat1),true,product(sFlat2,sFlat1,sFlat2),true),
inference(step,[status(thm)],[t559,t23]) ).
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(t895,plain,
true = ifeq(true,true,product(sFlat2,sFlat1,sFlat2),true),
inference(step,[status(thm)],[t894,t161]) ).
cnf(t896,plain,
true = product(sFlat2,sFlat1,sFlat2),
inference(step,[status(thm)],[t895,t23]) ).
cnf(t621,plain,
product(sFlat2,sFlat1,sFlat2) = true,
inference(orient,[status(thm)],[t896]) ).
cnf(t806,plain,
sFlat2 = ifeq(true,true,sFlat1,sFlat2),
inference(cp,[status(thm)],[t804,t621]) ).
cnf(t915,plain,
sFlat2 = sFlat1,
inference(step,[status(thm)],[t806,t23]) ).
cnf(t807,plain,
sFlat2 = sFlat1,
inference(orient,[status(thm)],[t915]) ).
cnf(t916,plain,
domain(a) = sFlat1,
inference(step,[status(thm)],[t142,t807]) ).
cnf(t808,plain,
domain(a) = sFlat1,
inference(orient,[status(thm)],[t916]) ).
cnf(f19,negated_conjecture,
domain(compose(b,a)) != domain(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_ba_equals_domain_of_a) ).
fof(f19_nnf,plain,
domain(compose(b,a)) != domain(a),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
domain(compose(b,a)) != domain(a),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
domain(compose(b,a)) != domain(a),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(goal_0,negated_conjecture,
domain(compose(b,a)) != domain(a),
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
domain(sFlat0) != domain(a),
inference(rw,[status(thm)],[goal_0,t150]) ).
cnf(g0_1,plain,
sFlat1 != domain(a),
inference(rw,[status(thm)],[g0_0,t157]) ).
cnf(g0_2,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_1,t808]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/10.39 % Computer : n020.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Fri Sep 25 06:54:46 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.98/11.84 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.98/11.84 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------