%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT006-3 : 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 01:00:36 PM UTC 2026
% Result : Unsatisfiable 15.35s 2.47s
% Output : Proof 15.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 87 ( 63 unt; 0 def)
% Number of atoms : 115 ( 71 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 34 ~; 28 |; 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 : 72 ( 6 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(d,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',da_exists) ).
fof(f17_nnf,plain,
there_exists(compose(d,a)),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
there_exists(compose(d,a)),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(hi17,axiom,
there_exists(compose(d,a)) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
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(h4,plain,
equivalent(compose(d,a),compose(codomain(compose(d,a)),compose(d,a))) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi17,hi10]) ).
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(codomain(compose(d,a)),compose(d,a))) = 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(h71,plain,
equivalent(compose(codomain(compose(d,a)),compose(d,a)),compose(compose(codomain(compose(d,a)),d),a)) = true,
inference(hyper_resolution,[status(thm)],[hi2,h23,hi8]) ).
cnf(h214,plain,
there_exists(compose(compose(codomain(compose(d,a)),d),a)) = true,
inference(hyper_resolution,[status(thm)],[hi11,h71]) ).
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(hi6,axiom,
ifeq(there_exists(compose(X0,X1)),true,domain(X0),codomain(X1)) = codomain(X1),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t68,plain,
domain(compose(codomain(compose(d,a)),d)) = codomain(a),
inference(hyper_resolution,[status(thm)],[hi6,h214]) ).
cnf(f13,axiom,
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_codomain) ).
fof(f13_nnf,plain,
! [X,Y] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( there_exists(codomain(X0))
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
ifeq(there_exists(compose(X0,X1)),true,there_exists(codomain(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h514,plain,
there_exists(codomain(compose(codomain(compose(d,a)),d))) = true,
inference(hyper_resolution,[status(thm)],[hi13,h214]) ).
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(hi4,axiom,
ifeq(there_exists(codomain(X0)),true,there_exists(X0),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h1491,plain,
there_exists(compose(codomain(compose(d,a)),d)) = true,
inference(hyper_resolution,[status(thm)],[hi4,h514]) ).
cnf(t32,plain,
domain(codomain(compose(d,a))) = codomain(d),
inference(hyper_resolution,[status(thm)],[hi6,h1491]) ).
cnf(t67,plain,
domain(codomain(compose(d,a))) = codomain(compose(d,a)),
inference(hyper_resolution,[status(thm)],[hi6,h23]) ).
cnf(t288,plain,
domain(codomain(compose(d,a))) = codomain(compose(d,a)),
inference(orient,[status(thm)],[t67]) ).
cnf(t472,plain,
codomain(compose(d,a)) = codomain(d),
inference(step,[status(thm)],[t32,t288]) ).
cnf(t294,plain,
codomain(compose(d,a)) = codomain(d),
inference(orient,[status(thm)],[t472]) ).
cnf(t478,plain,
domain(compose(codomain(d),d)) = codomain(a),
inference(step,[status(thm)],[t68,t294]) ).
cnf(t14,plain,
compose(codomain(X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t257,plain,
compose(codomain(X1),X1) = X1,
inference(orient,[status(thm)],[t14]) ).
cnf(t479,plain,
domain(d) = codomain(a),
inference(step,[status(thm)],[t478,t257]) ).
cnf(t302,plain,
codomain(a) = domain(d),
inference(orient,[status(thm)],[t479]) ).
cnf(h1,plain,
there_exists(codomain(d)) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi17]) ).
cnf(h9,plain,
there_exists(d) = true,
inference(hyper_resolution,[status(thm)],[hi4,h1]) ).
cnf(h21,plain,
equivalent(d,compose(codomain(d),d)) = true,
inference(hyper_resolution,[status(thm)],[hi2,h9,hi10]) ).
cnf(h63,plain,
there_exists(compose(codomain(d),d)) = true,
inference(hyper_resolution,[status(thm)],[hi11,h21]) ).
cnf(t19,plain,
domain(codomain(d)) = codomain(d),
inference(hyper_resolution,[status(thm)],[hi6,h63]) ).
cnf(t299,plain,
domain(codomain(d)) = codomain(d),
inference(orient,[status(thm)],[t19]) ).
cnf(f18,hypothesis,
( compose(X,d) = X
| ~ there_exists(compose(X,d)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xd_equals_x) ).
fof(f18_nnf,plain,
! [X] :
( compose(X,d) = X
| ~ there_exists(compose(X,d)) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X] :
( compose(X,d) = X
| ~ there_exists(compose(X,d)) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( compose(X0,d) = X0
| ~ there_exists(compose(X0,d)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi18,axiom,
ifeq(there_exists(compose(X0,d)),true,compose(X0,d),X0) = X0,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t92,plain,
compose(codomain(compose(d,a)),d) = codomain(compose(d,a)),
inference(hyper_resolution,[status(thm)],[hi18,h1491]) ).
cnf(t276,plain,
compose(codomain(compose(d,a)),d) = codomain(compose(d,a)),
inference(orient,[status(thm)],[t92]) ).
cnf(t475,plain,
compose(codomain(d),d) = codomain(compose(d,a)),
inference(step,[status(thm)],[t276,t294]) ).
cnf(t476,plain,
d = codomain(compose(d,a)),
inference(step,[status(thm)],[t475,t257]) ).
cnf(t477,plain,
d = codomain(d),
inference(step,[status(thm)],[t476,t294]) ).
cnf(t298,plain,
d = codomain(d),
inference(rw,[status(thm)],[t477]) ).
cnf(t443,plain,
codomain(d) = d,
inference(orient,[status(thm)],[t298]) ).
cnf(t521,plain,
domain(d) = codomain(d),
inference(step,[status(thm)],[t299,t443]) ).
cnf(t522,plain,
domain(d) = d,
inference(step,[status(thm)],[t521,t443]) ).
cnf(t451,plain,
domain(d) = d,
inference(rw,[status(thm)],[t522]) ).
cnf(t458,plain,
domain(d) = d,
inference(orient,[status(thm)],[t451]) ).
cnf(t527,plain,
codomain(a) = d,
inference(step,[status(thm)],[t302,t458]) ).
cnf(t461,plain,
codomain(a) = d,
inference(orient,[status(thm)],[t527]) ).
cnf(f20,negated_conjecture,
codomain(a) != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_of_a_is_d) ).
fof(f20_nnf,plain,
codomain(a) != d,
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
codomain(a) != d,
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
codomain(a) != d,
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
codomain(a) != d,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(g0_0,plain,
d != d,
inference(rw,[status(thm)],[goal_0,t461]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n005.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
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 06:52:32 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 15.35/2.47 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.35/2.47 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------