%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT005-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 4.92s 1.18s
% Output : Proof 4.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 40 unt; 0 def)
% Number of atoms : 72 ( 44 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 44 ( 5 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f12,hypothesis,
( compose(X,d) = X
| ~ there_exists(compose(X,d)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xd_equals_x) ).
fof(f12_nnf,plain,
! [X] :
( compose(X,d) = X
| ~ there_exists(compose(X,d)) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X] :
( compose(X,d) = X
| ~ there_exists(compose(X,d)) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( compose(X0,d) = X0
| ~ there_exists(compose(X0,d)) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t21,plain,
ifeq(there_exists(compose(X1,d)),true,compose(X1,d),X1) = X1,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t31,plain,
ifeq(there_exists(compose(X1,d)),true,compose(X1,d),X1) = X1,
inference(orient,[status(thm)],[t21]) ).
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(t29,plain,
compose(codomain(X1),X1) = X1,
inference(orient,[status(thm)],[t5]) ).
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(hi6,axiom,
ifeq(there_exists(compose(X0,X1)),true,domain(X0),codomain(X1)) = codomain(X1),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f11,hypothesis,
there_exists(compose(a,d)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ad_exists) ).
fof(f11_nnf,plain,
there_exists(compose(a,d)),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
there_exists(compose(a,d)),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(hi11,axiom,
there_exists(compose(a,d)) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t2,plain,
domain(a) = codomain(d),
inference(hyper_resolution,[status(thm)],[hi6,hi11]) ).
cnf(t90,plain,
codomain(d) = domain(a),
inference(orient,[status(thm)],[t2]) ).
cnf(t91,plain,
d = compose(domain(a),d),
inference(cp,[status(thm)],[t29,t90]) ).
cnf(t103,plain,
compose(domain(a),d) = d,
inference(orient,[status(thm)],[t91]) ).
cnf(t105,plain,
domain(a) = ifeq(there_exists(d),true,compose(domain(a),d),domain(a)),
inference(cp,[status(thm)],[t31,t103]) ).
cnf(f4,axiom,
( there_exists(X)
| ~ there_exists(codomain(X)) ),
file('/export/starexec/sandbox2/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(t15,plain,
ifeq(there_exists(codomain(X1)),true,there_exists(X1),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t59,plain,
ifeq(there_exists(codomain(X1)),true,there_exists(X1),true) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t92,plain,
true = ifeq(there_exists(domain(a)),true,there_exists(d),true),
inference(cp,[status(thm)],[t59,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(t3,plain,
there_exists(domain(a)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi11]) ).
cnf(t41,plain,
there_exists(domain(a)) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t122,plain,
true = ifeq(true,true,there_exists(d),true),
inference(step,[status(thm)],[t92,t41]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t30,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t123,plain,
true = there_exists(d),
inference(step,[status(thm)],[t122,t30]) ).
cnf(t99,plain,
there_exists(d) = true,
inference(orient,[status(thm)],[t123]) ).
cnf(t124,plain,
domain(a) = ifeq(true,true,compose(domain(a),d),domain(a)),
inference(step,[status(thm)],[t105,t99]) ).
cnf(t125,plain,
domain(a) = compose(domain(a),d),
inference(step,[status(thm)],[t124,t30]) ).
cnf(t126,plain,
domain(a) = d,
inference(step,[status(thm)],[t125,t103]) ).
cnf(t110,plain,
domain(a) = d,
inference(orient,[status(thm)],[t126]) ).
cnf(f14,negated_conjecture,
domain(a) != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_a_is_d) ).
fof(f14_nnf,plain,
domain(a) != d,
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
domain(a) != d,
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
domain(a) != d,
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(goal_0,negated_conjecture,
domain(a) != d,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(g0_0,plain,
d != d,
inference(rw,[status(thm)],[goal_0,t110]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT005-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.34 % Computer : n013.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Fri Sep 25 06:51:51 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.92/1.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.92/1.18 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------