%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT007-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 12.10s 2.07s
% Output : Proof 12.10s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t20,axiom,
sFlat0 = defined(a,b),
introduced(definition) ).
cnf(t124,plain,
defined(a,b) = sFlat0,
inference(orient,[status(thm)],[t20]) ).
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(t15,plain,
ifeq(defined(X1,X2),true,ifeq(defined(X2,X3),true,ifeq(identity_map(X2),true,defined(X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t42,plain,
ifeq(defined(X1,X2),true,ifeq(defined(X2,X3),true,ifeq(identity_map(X2),true,defined(X1,X3),true),true),true) = true,
inference(orient,[status(thm)],[t15]) ).
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(t4,plain,
defined(codomain(X1),X1) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t100,plain,
defined(codomain(X1),X1) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(f18,hypothesis,
domain(a) = codomain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_a_equals_codomain_of_b) ).
fof(f18_nnf,plain,
domain(a) = codomain(b),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
domain(a) = codomain(b),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(t0,plain,
domain(a) = codomain(b),
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t140,plain,
codomain(b) = domain(a),
inference(orient,[status(thm)],[t0]) ).
cnf(t141,plain,
true = defined(domain(a),b),
inference(cp,[status(thm)],[t100,t140]) ).
cnf(t143,plain,
defined(domain(a),b) = true,
inference(orient,[status(thm)],[t141]) ).
cnf(t153,plain,
true = ifeq(defined(X1,domain(a)),true,ifeq(true,true,ifeq(identity_map(domain(a)),true,defined(X1,b),true),true),true),
inference(cp,[status(thm)],[t42,t143]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t21,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t1982,plain,
true = ifeq(defined(X1,domain(a)),true,ifeq(identity_map(domain(a)),true,defined(X1,b),true),true),
inference(step,[status(thm)],[t153,t21]) ).
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(t2,plain,
identity_map(domain(X1)) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t120,plain,
identity_map(domain(X1)) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t1983,plain,
true = ifeq(defined(X1,domain(a)),true,ifeq(true,true,defined(X1,b),true),true),
inference(step,[status(thm)],[t1982,t120]) ).
cnf(t1984,plain,
true = ifeq(defined(X1,domain(a)),true,defined(X1,b),true),
inference(step,[status(thm)],[t1983,t21]) ).
cnf(t1627,plain,
ifeq(defined(X1,domain(a)),true,defined(X1,b),true) = true,
inference(orient,[status(thm)],[t1984]) ).
cnf(f11,axiom,
defined(X,domain(X)),
file('/export/starexec/sandbox/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(t84,plain,
defined(X1,domain(X1)) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t1628,plain,
true = ifeq(true,true,defined(a,b),true),
inference(cp,[status(thm)],[t1627,t84]) ).
cnf(t1985,plain,
true = defined(a,b),
inference(step,[status(thm)],[t1628,t21]) ).
cnf(t1986,plain,
true = sFlat0,
inference(step,[status(thm)],[t1985,t124]) ).
cnf(t1640,plain,
true = sFlat0,
inference(orient,[status(thm)],[t1986]) ).
cnf(f19,negated_conjecture,
~ defined(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ab_is_defined) ).
fof(f19_nnf,plain,
~ defined(a,b),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
~ defined(a,b),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
~ defined(a,b),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(goal_0,negated_conjecture,
defined(a,b) != true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
sFlat0 != true,
inference(rw,[status(thm)],[goal_0,t124]) ).
cnf(g0_1,plain,
sFlat0 != sFlat0,
inference(rw,[status(thm)],[g0_0,t1640]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT007-1 : 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 : n015.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 06:56:28 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.10/2.07 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.10/2.07 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------