%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT010-4 : 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 6.99s 1.52s
% Output : Proof 6.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 76 ( 64 unt; 0 def)
% Number of atoms : 88 ( 64 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 32 ( 20 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 59 ( 5 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t29,axiom,
sFlat0 = compose(a,b),
introduced(definition) ).
cnf(t40,plain,
compose(a,b) = sFlat0,
inference(orient,[status(thm)],[t29]) ).
cnf(t30,axiom,
sFlat1 = codomain(compose(a,b)),
introduced(definition) ).
cnf(t238,plain,
sFlat1 = codomain(sFlat0),
inference(step,[status(thm)],[t30,t40]) ).
cnf(t95,plain,
codomain(sFlat0) = sFlat1,
inference(orient,[status(thm)],[t238]) ).
cnf(t31,axiom,
sFlat2 = codomain(a),
introduced(definition) ).
cnf(t90,plain,
codomain(a) = sFlat2,
inference(orient,[status(thm)],[t31]) ).
cnf(f6,axiom,
( domain(X) = codomain(Y)
| ~ there_exists(compose(X,Y)) ),
file('/export/starexec/sandbox2/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(t24,plain,
ifeq(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t85,plain,
ifeq(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
inference(orient,[status(thm)],[t24]) ).
cnf(f8,axiom,
compose(X,compose(Y,Z)) = compose(compose(X,Y),Z),
file('/export/starexec/sandbox2/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(t18,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t36,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(orient,[status(thm)],[t18]) ).
cnf(f10,axiom,
compose(codomain(X),X) = X,
file('/export/starexec/sandbox2/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(t5,plain,
compose(codomain(X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t33,plain,
compose(codomain(X1),X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t91,plain,
a = compose(sFlat2,a),
inference(cp,[status(thm)],[t33,t90]) ).
cnf(t104,plain,
compose(sFlat2,a) = a,
inference(orient,[status(thm)],[t91]) ).
cnf(t105,plain,
compose(sFlat2,compose(a,X1)) = compose(a,X1),
inference(cp,[status(thm)],[t36,t104]) ).
cnf(t214,plain,
compose(sFlat2,compose(a,X1)) = compose(a,X1),
inference(orient,[status(thm)],[t105]) ).
cnf(t215,plain,
compose(a,b) = compose(sFlat2,sFlat0),
inference(cp,[status(thm)],[t214,t40]) ).
cnf(t278,plain,
sFlat0 = compose(sFlat2,sFlat0),
inference(step,[status(thm)],[t215,t40]) ).
cnf(t220,plain,
compose(sFlat2,sFlat0) = sFlat0,
inference(orient,[status(thm)],[t278]) ).
cnf(t222,plain,
codomain(sFlat0) = ifeq(there_exists(sFlat0),true,domain(sFlat2),codomain(sFlat0)),
inference(cp,[status(thm)],[t85,t220]) ).
cnf(t279,plain,
sFlat1 = ifeq(there_exists(sFlat0),true,domain(sFlat2),codomain(sFlat0)),
inference(step,[status(thm)],[t222,t95]) ).
cnf(f11,hypothesis,
there_exists(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',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(t7,plain,
there_exists(compose(a,b)) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t229,plain,
there_exists(sFlat0) = true,
inference(step,[status(thm)],[t7,t40]) ).
cnf(t43,plain,
there_exists(sFlat0) = true,
inference(orient,[status(thm)],[t229]) ).
cnf(t280,plain,
sFlat1 = ifeq(true,true,domain(sFlat2),codomain(sFlat0)),
inference(step,[status(thm)],[t279,t43]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t34,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t281,plain,
sFlat1 = domain(sFlat2),
inference(step,[status(thm)],[t280,t34]) ).
cnf(t106,plain,
codomain(a) = ifeq(there_exists(a),true,domain(sFlat2),codomain(a)),
inference(cp,[status(thm)],[t85,t104]) ).
cnf(t241,plain,
sFlat2 = ifeq(there_exists(a),true,domain(sFlat2),codomain(a)),
inference(step,[status(thm)],[t106,t90]) ).
cnf(f5,axiom,
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
file('/export/starexec/sandbox2/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(hi11,axiom,
there_exists(compose(a,b)) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h1,plain,
there_exists(domain(a)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi11]) ).
cnf(f3,axiom,
( there_exists(X)
| ~ there_exists(domain(X)) ),
file('/export/starexec/sandbox2/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(t0,plain,
there_exists(a) = true,
inference(hyper_resolution,[status(thm)],[hi3,h1]) ).
cnf(t42,plain,
there_exists(a) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t242,plain,
sFlat2 = ifeq(true,true,domain(sFlat2),codomain(a)),
inference(step,[status(thm)],[t241,t42]) ).
cnf(t243,plain,
sFlat2 = domain(sFlat2),
inference(step,[status(thm)],[t242,t34]) ).
cnf(t109,plain,
domain(sFlat2) = sFlat2,
inference(orient,[status(thm)],[t243]) ).
cnf(t282,plain,
sFlat1 = sFlat2,
inference(step,[status(thm)],[t281,t109]) ).
cnf(t224,plain,
sFlat2 = sFlat1,
inference(orient,[status(thm)],[t282]) ).
cnf(t283,plain,
codomain(a) = sFlat1,
inference(step,[status(thm)],[t90,t224]) ).
cnf(t225,plain,
codomain(a) = sFlat1,
inference(orient,[status(thm)],[t283]) ).
cnf(f12,negated_conjecture,
codomain(compose(a,b)) != codomain(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_of_ab_equals_codomain_of_a) ).
fof(f12_nnf,plain,
codomain(compose(a,b)) != codomain(a),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
codomain(compose(a,b)) != codomain(a),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
codomain(compose(a,b)) != codomain(a),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
codomain(compose(a,b)) != codomain(a),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(g0_0,plain,
codomain(sFlat0) != codomain(a),
inference(rw,[status(thm)],[goal_0,t40]) ).
cnf(g0_1,plain,
sFlat1 != codomain(a),
inference(rw,[status(thm)],[g0_0,t95]) ).
cnf(g0_2,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_1,t225]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT010-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 06:54:17 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.99/1.52 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.99/1.52 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------