%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT018-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 01:00:43 PM UTC 2026
% Result : Unsatisfiable 7.31s 7.00s
% Output : Proof 7.31s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t46,axiom,
sFlat0 = compose(b,c),
introduced(definition) ).
cnf(t57,plain,
compose(b,c) = sFlat0,
inference(orient,[status(thm)],[t46]) ).
cnf(t47,axiom,
sFlat1 = compose(a,compose(b,c)),
introduced(definition) ).
cnf(t685,plain,
sFlat1 = compose(a,sFlat0),
inference(step,[status(thm)],[t47,t57]) ).
cnf(t59,plain,
compose(a,sFlat0) = sFlat1,
inference(orient,[status(thm)],[t685]) ).
cnf(t48,axiom,
sFlat2 = there_exists(compose(a,compose(b,c))),
introduced(definition) ).
cnf(t699,plain,
sFlat2 = there_exists(compose(a,sFlat0)),
inference(step,[status(thm)],[t48,t57]) ).
cnf(t700,plain,
sFlat2 = there_exists(sFlat1),
inference(step,[status(thm)],[t699,t59]) ).
cnf(t133,plain,
there_exists(sFlat1) = sFlat2,
inference(orient,[status(thm)],[t700]) ).
cnf(f7,axiom,
( there_exists(compose(X,Y))
| domain(X) != codomain(Y)
| ~ there_exists(domain(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition2) ).
fof(f7_nnf,plain,
! [X,Y] :
( there_exists(compose(X,Y))
| domain(X) != codomain(Y)
| ~ there_exists(domain(X)) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( there_exists(compose(X,Y))
| domain(X) != codomain(Y)
| ~ there_exists(domain(X)) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( there_exists(compose(X0,X1))
| domain(X0) != codomain(X1)
| ~ there_exists(domain(X0)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t45,plain,
ifeq(there_exists(domain(X1)),true,ifeq(domain(X1),codomain(X2),there_exists(compose(X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t103,plain,
ifeq(there_exists(domain(X1)),true,ifeq(domain(X1),codomain(X2),there_exists(compose(X1,X2)),true),true) = true,
inference(orient,[status(thm)],[t45]) ).
cnf(t109,plain,
true = ifeq(there_exists(domain(a)),true,ifeq(domain(a),codomain(sFlat0),there_exists(sFlat1),true),true),
inference(cp,[status(thm)],[t103,t59]) ).
cnf(f5,axiom,
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_domain) ).
fof(f5_nnf,plain,
! [X,Y] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
ifeq(there_exists(compose(X0,X1)),true,there_exists(domain(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f11,hypothesis,
there_exists(compose(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_ab_exists) ).
fof(f11_nnf,plain,
there_exists(compose(a,b)),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
there_exists(compose(a,b)),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(hi11,axiom,
there_exists(compose(a,b)) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t4,plain,
there_exists(domain(a)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi11]) ).
cnf(t69,plain,
there_exists(domain(a)) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t786,plain,
true = ifeq(true,true,ifeq(domain(a),codomain(sFlat0),there_exists(sFlat1),true),true),
inference(step,[status(thm)],[t109,t69]) ).
cnf(t16,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t51,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(t787,plain,
true = ifeq(domain(a),codomain(sFlat0),there_exists(sFlat1),true),
inference(step,[status(thm)],[t786,t51]) ).
cnf(f6,axiom,
( domain(X) = codomain(Y)
| ~ there_exists(compose(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).
fof(f6_nnf,plain,
! [X,Y] :
( domain(X) = codomain(Y)
| ~ there_exists(compose(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( domain(X) = codomain(Y)
| ~ there_exists(compose(X,Y)) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( domain(X0) = codomain(X1)
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t39,plain,
ifeq(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t126,plain,
ifeq(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
inference(orient,[status(thm)],[t39]) ).
cnf(f8,axiom,
compose(X,compose(Y,Z)) = compose(compose(X,Y),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_compose) ).
fof(f8_nnf,plain,
! [X,Y,Z] : compose(X,compose(Y,Z)) = compose(compose(X,Y),Z),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,Z] : compose(X,compose(Y,Z)) = compose(compose(X,Y),Z),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t29,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t53,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(orient,[status(thm)],[t29]) ).
cnf(f10,axiom,
compose(codomain(X),X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).
fof(f10_nnf,plain,
! [X] : compose(codomain(X),X) = X,
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X] : compose(codomain(X),X) = X,
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
compose(codomain(X0),X0) = X0,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(t9,plain,
compose(codomain(X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t50,plain,
compose(codomain(X1),X1) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t56,plain,
compose(codomain(X1),compose(X1,X2)) = compose(X1,X2),
inference(cp,[status(thm)],[t53,t50]) ).
cnf(t331,plain,
compose(codomain(X1),compose(X1,X2)) = compose(X1,X2),
inference(orient,[status(thm)],[t56]) ).
cnf(t342,plain,
compose(b,c) = compose(codomain(b),sFlat0),
inference(cp,[status(thm)],[t331,t57]) ).
cnf(t747,plain,
sFlat0 = compose(codomain(b),sFlat0),
inference(step,[status(thm)],[t342,t57]) ).
cnf(hi6,axiom,
ifeq(there_exists(compose(X0,X1)),true,domain(X0),codomain(X1)) = codomain(X1),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t2,plain,
domain(a) = codomain(b),
inference(hyper_resolution,[status(thm)],[hi6,hi11]) ).
cnf(t63,plain,
codomain(b) = domain(a),
inference(orient,[status(thm)],[t2]) ).
cnf(t748,plain,
sFlat0 = compose(domain(a),sFlat0),
inference(step,[status(thm)],[t747,t63]) ).
cnf(t356,plain,
compose(domain(a),sFlat0) = sFlat0,
inference(orient,[status(thm)],[t748]) ).
cnf(t358,plain,
codomain(sFlat0) = ifeq(there_exists(sFlat0),true,domain(domain(a)),codomain(sFlat0)),
inference(cp,[status(thm)],[t126,t356]) ).
cnf(f12,hypothesis,
there_exists(compose(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_bc_exists) ).
fof(f12_nnf,plain,
there_exists(compose(b,c)),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
there_exists(compose(b,c)),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(t13,plain,
there_exists(compose(b,c)) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t686,plain,
there_exists(sFlat0) = true,
inference(step,[status(thm)],[t13,t57]) ).
cnf(t65,plain,
there_exists(sFlat0) = true,
inference(orient,[status(thm)],[t686]) ).
cnf(t749,plain,
codomain(sFlat0) = ifeq(true,true,domain(domain(a)),codomain(sFlat0)),
inference(step,[status(thm)],[t358,t65]) ).
cnf(t750,plain,
codomain(sFlat0) = domain(domain(a)),
inference(step,[status(thm)],[t749,t51]) ).
cnf(t64,plain,
b = compose(domain(a),b),
inference(cp,[status(thm)],[t50,t63]) ).
cnf(t153,plain,
compose(domain(a),b) = b,
inference(orient,[status(thm)],[t64]) ).
cnf(t155,plain,
codomain(b) = ifeq(there_exists(b),true,domain(domain(a)),codomain(b)),
inference(cp,[status(thm)],[t126,t153]) ).
cnf(t706,plain,
domain(a) = ifeq(there_exists(b),true,domain(domain(a)),codomain(b)),
inference(step,[status(thm)],[t155,t63]) ).
cnf(hi12,axiom,
there_exists(compose(b,c)) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h5,plain,
there_exists(domain(b)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi12]) ).
cnf(f3,axiom,
( there_exists(X)
| ~ there_exists(domain(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).
fof(f3_nnf,plain,
! [X] :
( there_exists(X)
| ~ there_exists(domain(X)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] :
( there_exists(X)
| ~ there_exists(domain(X)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( there_exists(X0)
| ~ there_exists(domain(X0)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(there_exists(domain(X0)),true,there_exists(X0),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t1,plain,
there_exists(b) = true,
inference(hyper_resolution,[status(thm)],[hi3,h5]) ).
cnf(t67,plain,
there_exists(b) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t707,plain,
domain(a) = ifeq(true,true,domain(domain(a)),codomain(b)),
inference(step,[status(thm)],[t706,t67]) ).
cnf(t708,plain,
domain(a) = domain(domain(a)),
inference(step,[status(thm)],[t707,t51]) ).
cnf(t158,plain,
domain(domain(a)) = domain(a),
inference(orient,[status(thm)],[t708]) ).
cnf(t751,plain,
codomain(sFlat0) = domain(a),
inference(step,[status(thm)],[t750,t158]) ).
cnf(t360,plain,
codomain(sFlat0) = domain(a),
inference(orient,[status(thm)],[t751]) ).
cnf(t788,plain,
true = ifeq(domain(a),domain(a),there_exists(sFlat1),true),
inference(step,[status(thm)],[t787,t360]) ).
cnf(t789,plain,
true = there_exists(sFlat1),
inference(step,[status(thm)],[t788,t51]) ).
cnf(t790,plain,
true = sFlat2,
inference(step,[status(thm)],[t789,t133]) ).
cnf(t604,plain,
true = sFlat2,
inference(orient,[status(thm)],[t790]) ).
cnf(f13,negated_conjecture,
~ there_exists(compose(a,compose(b,c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_bc_exists) ).
fof(f13_nnf,plain,
~ there_exists(compose(a,compose(b,c))),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
~ there_exists(compose(a,compose(b,c))),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
~ there_exists(compose(a,compose(b,c))),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(goal_0,negated_conjecture,
there_exists(compose(a,compose(b,c))) != true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(g0_0,plain,
there_exists(compose(a,sFlat0)) != true,
inference(rw,[status(thm)],[goal_0,t57]) ).
cnf(g0_1,plain,
there_exists(sFlat1) != true,
inference(rw,[status(thm)],[g0_0,t59]) ).
cnf(g0_2,plain,
sFlat2 != true,
inference(rw,[status(thm)],[g0_1,t133]) ).
cnf(g0_3,plain,
sFlat2 != sFlat2,
inference(rw,[status(thm)],[g0_2,t604]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT018-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.79 % Computer : n006.cluster.edu
% 0.10/5.79 % Model : x86_64 x86_64
% 0.10/5.79 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.79 % Memory : 8046.5625MB
% 0.10/5.79 % OS : Linux 6.8.0-71-generic
% 0.10/5.80 % CPULimit : 300
% 0.10/5.80 % WCLimit : 300
% 0.10/5.80 % DateTime : Fri Sep 25 06:57:51 UTC 2026
% 0.15/5.80 % CPUTime :
% 0.15/5.80 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.31/7.00 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.31/7.00 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------