%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT009-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 15.53s 2.43s
% Output : Proof 15.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 85 ( 65 unt; 0 def)
% Number of atoms : 109 ( 69 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 30 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 81 ( 8 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t118,plain,
ifeq(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t307,plain,
ifeq(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
inference(orient,[status(thm)],[t118]) ).
cnf(f4,axiom,
( there_exists(X)
| ~ there_exists(codomain(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_has_elements) ).
fof(f4_nnf,plain,
! [X] :
( there_exists(X)
| ~ there_exists(codomain(X)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] :
( there_exists(X)
| ~ there_exists(codomain(X)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( there_exists(X0)
| ~ there_exists(codomain(X0)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t59,plain,
ifeq(there_exists(codomain(X1)),true,there_exists(X1),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t415,plain,
ifeq(there_exists(codomain(X1)),true,there_exists(X1),true) = true,
inference(orient,[status(thm)],[t59]) ).
cnf(f2,axiom,
( equivalent(X,Y)
| X != Y
| ~ there_exists(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence1) ).
fof(f2_nnf,plain,
! [X,Y] :
( equivalent(X,Y)
| X != Y
| ~ there_exists(X) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] :
( equivalent(X,Y)
| X != Y
| ~ there_exists(X) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( equivalent(X0,X1)
| X0 != X1
| ~ there_exists(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(there_exists(X0),true,ifeq(X0,X1,equivalent(X0,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f17,hypothesis,
there_exists(compose(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_exists) ).
fof(f17_nnf,plain,
there_exists(compose(a,b)),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
there_exists(compose(a,b)),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(hi17,axiom,
there_exists(compose(a,b)) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(f9,axiom,
compose(X,domain(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_domain) ).
fof(f9_nnf,plain,
! [X] : compose(X,domain(X)) = X,
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X] : compose(X,domain(X)) = X,
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
compose(X0,domain(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,axiom,
compose(X0,domain(X0)) = X0,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h4,plain,
equivalent(compose(a,b),compose(compose(a,b),domain(compose(a,b)))) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi17,hi9]) ).
cnf(f11,axiom,
( there_exists(Y)
| ~ equivalent(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_implies_existence3) ).
fof(f11_nnf,plain,
! [X,Y] :
( there_exists(Y)
| ~ equivalent(X,Y) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X,Y] :
( there_exists(Y)
| ~ equivalent(X,Y) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( there_exists(X1)
| ~ equivalent(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
ifeq(equivalent(X0,X1),true,there_exists(X1),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h23,plain,
there_exists(compose(compose(a,b),domain(compose(a,b)))) = true,
inference(hyper_resolution,[status(thm)],[hi11,h4]) ).
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(hi8,axiom,
compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h77,plain,
equivalent(compose(compose(a,b),domain(compose(a,b))),compose(a,compose(b,domain(compose(a,b))))) = true,
inference(hyper_resolution,[status(thm)],[hi2,h23,hi8]) ).
cnf(h233,plain,
there_exists(compose(a,compose(b,domain(compose(a,b))))) = true,
inference(hyper_resolution,[status(thm)],[hi11,h77]) ).
cnf(hi6,axiom,
ifeq(there_exists(compose(X0,X1)),true,domain(X0),codomain(X1)) = codomain(X1),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t51,plain,
codomain(compose(b,domain(compose(a,b)))) = domain(a),
inference(hyper_resolution,[status(thm)],[hi6,h233]) ).
cnf(t274,plain,
codomain(compose(b,domain(compose(a,b)))) = domain(a),
inference(orient,[status(thm)],[t51]) ).
cnf(t419,plain,
true = ifeq(there_exists(domain(a)),true,there_exists(compose(b,domain(compose(a,b)))),true),
inference(cp,[status(thm)],[t415,t274]) ).
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(hi10,axiom,
compose(codomain(X0),X0) = X0,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h3,plain,
equivalent(compose(a,b),compose(codomain(compose(a,b)),compose(a,b))) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi17,hi10]) ).
cnf(h17,plain,
there_exists(compose(codomain(compose(a,b)),compose(a,b))) = true,
inference(hyper_resolution,[status(thm)],[hi11,h3]) ).
cnf(h60,plain,
equivalent(compose(codomain(compose(a,b)),compose(a,b)),compose(compose(codomain(compose(a,b)),a),b)) = true,
inference(hyper_resolution,[status(thm)],[hi2,h17,hi8]) ).
cnf(h192,plain,
there_exists(compose(compose(codomain(compose(a,b)),a),b)) = true,
inference(hyper_resolution,[status(thm)],[hi11,h60]) ).
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(t67,plain,
there_exists(domain(compose(codomain(compose(a,b)),a))) = true,
inference(hyper_resolution,[status(thm)],[hi5,h192]) ).
cnf(t54,plain,
domain(compose(codomain(compose(a,b)),a)) = codomain(b),
inference(hyper_resolution,[status(thm)],[hi6,h192]) ).
cnf(t272,plain,
domain(compose(codomain(compose(a,b)),a)) = codomain(b),
inference(orient,[status(thm)],[t54]) ).
cnf(t0,plain,
domain(a) = codomain(b),
inference(hyper_resolution,[status(thm)],[hi6,hi17]) ).
cnf(t276,plain,
codomain(b) = domain(a),
inference(orient,[status(thm)],[t0]) ).
cnf(t562,plain,
domain(compose(codomain(compose(a,b)),a)) = domain(a),
inference(step,[status(thm)],[t272,t276]) ).
cnf(t277,plain,
domain(compose(codomain(compose(a,b)),a)) = domain(a),
inference(orient,[status(thm)],[t562]) ).
cnf(t593,plain,
there_exists(domain(a)) = true,
inference(step,[status(thm)],[t67,t277]) ).
cnf(t334,plain,
there_exists(domain(a)) = true,
inference(orient,[status(thm)],[t593]) ).
cnf(t618,plain,
true = ifeq(true,true,there_exists(compose(b,domain(compose(a,b)))),true),
inference(step,[status(thm)],[t419,t334]) ).
cnf(t22,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t260,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t22]) ).
cnf(t619,plain,
true = there_exists(compose(b,domain(compose(a,b)))),
inference(step,[status(thm)],[t618,t260]) ).
cnf(t537,plain,
there_exists(compose(b,domain(compose(a,b)))) = true,
inference(orient,[status(thm)],[t619]) ).
cnf(t542,plain,
codomain(domain(compose(a,b))) = ifeq(true,true,domain(b),codomain(domain(compose(a,b)))),
inference(cp,[status(thm)],[t307,t537]) ).
cnf(t52,plain,
codomain(domain(compose(a,b))) = domain(compose(a,b)),
inference(hyper_resolution,[status(thm)],[hi6,h23]) ).
cnf(t270,plain,
codomain(domain(compose(a,b))) = domain(compose(a,b)),
inference(orient,[status(thm)],[t52]) ).
cnf(t621,plain,
domain(compose(a,b)) = ifeq(true,true,domain(b),codomain(domain(compose(a,b)))),
inference(step,[status(thm)],[t542,t270]) ).
cnf(t622,plain,
domain(compose(a,b)) = domain(b),
inference(step,[status(thm)],[t621,t260]) ).
cnf(t551,plain,
domain(compose(a,b)) = domain(b),
inference(orient,[status(thm)],[t622]) ).
cnf(f18,negated_conjecture,
domain(compose(a,b)) != domain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_ab_equals_domain_of_b) ).
fof(f18_nnf,plain,
domain(compose(a,b)) != domain(b),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
domain(compose(a,b)) != domain(b),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
domain(compose(a,b)) != domain(b),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
domain(compose(a,b)) != domain(b),
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(g0_0,plain,
domain(b) != domain(b),
inference(rw,[status(thm)],[goal_0,t551]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT009-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n005.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 06:53:18 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 15.53/2.43 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.53/2.43 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------