%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT006-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 0.34s 21.92s
% Output : Proof 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 85 ( 69 unt; 0 def)
% Number of atoms : 101 ( 73 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 : 5 ( 2 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 : 79 ( 5 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(d,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',da_exists) ).
fof(f11_nnf,plain,
there_exists(compose(d,a)),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
there_exists(compose(d,a)),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(hi11,axiom,
there_exists(compose(d,a)) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t2,plain,
domain(d) = codomain(a),
inference(hyper_resolution,[status(thm)],[hi6,hi11]) ).
cnf(t93,plain,
codomain(a) = domain(d),
inference(orient,[status(thm)],[t2]) ).
cnf(f13,hypothesis,
( compose(d,X) = X
| ~ there_exists(compose(d,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dx_equals_x) ).
fof(f13_nnf,plain,
! [X] :
( compose(d,X) = X
| ~ there_exists(compose(d,X)) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X] :
( compose(d,X) = X
| ~ there_exists(compose(d,X)) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( compose(d,X0) = X0
| ~ there_exists(compose(d,X0)) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t27,plain,
ifeq(there_exists(compose(d,X1)),true,compose(d,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t39,plain,
ifeq(there_exists(compose(d,X1)),true,compose(d,X1),X1) = X1,
inference(orient,[status(thm)],[t27]) ).
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(t20,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t43,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(orient,[status(thm)],[t20]) ).
cnf(f9,axiom,
compose(X,domain(X)) = X,
file('/export/starexec/sandbox2/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(t4,plain,
compose(X1,domain(X1)) = X1,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t33,plain,
compose(X1,domain(X1)) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t45,plain,
compose(X1,compose(domain(X1),X2)) = compose(X1,X2),
inference(cp,[status(thm)],[t43,t33]) ).
cnf(t125,plain,
compose(X1,compose(domain(X1),X2)) = compose(X1,X2),
inference(orient,[status(thm)],[t45]) ).
cnf(t127,plain,
compose(X1,domain(domain(X1))) = compose(X1,domain(X1)),
inference(cp,[status(thm)],[t125,t33]) ).
cnf(t167,plain,
compose(X1,domain(domain(X1))) = X1,
inference(step,[status(thm)],[t127,t33]) ).
cnf(t134,plain,
compose(X1,domain(domain(X1))) = X1,
inference(orient,[status(thm)],[t167]) ).
cnf(t140,plain,
domain(domain(d)) = ifeq(there_exists(d),true,compose(d,domain(domain(d))),domain(domain(d))),
inference(cp,[status(thm)],[t39,t134]) ).
cnf(t28,plain,
ifeq(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t96,plain,
ifeq(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
inference(orient,[status(thm)],[t28]) ).
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(t34,plain,
compose(codomain(X1),X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t94,plain,
a = compose(domain(d),a),
inference(cp,[status(thm)],[t34,t93]) ).
cnf(t101,plain,
compose(domain(d),a) = a,
inference(orient,[status(thm)],[t94]) ).
cnf(t103,plain,
codomain(a) = ifeq(there_exists(a),true,domain(domain(d)),codomain(a)),
inference(cp,[status(thm)],[t96,t101]) ).
cnf(t161,plain,
domain(d) = ifeq(there_exists(a),true,domain(domain(d)),codomain(a)),
inference(step,[status(thm)],[t103,t93]) ).
cnf(t8,plain,
there_exists(compose(d,a)) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(hi13,axiom,
ifeq(there_exists(compose(d,X0)),true,compose(d,X0),X0) = X0,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t1,plain,
compose(d,a) = a,
inference(hyper_resolution,[status(thm)],[hi13,hi11]) ).
cnf(t53,plain,
compose(d,a) = a,
inference(orient,[status(thm)],[t1]) ).
cnf(t154,plain,
there_exists(a) = true,
inference(step,[status(thm)],[t8,t53]) ).
cnf(t58,plain,
there_exists(a) = true,
inference(orient,[status(thm)],[t154]) ).
cnf(t162,plain,
domain(d) = ifeq(true,true,domain(domain(d)),codomain(a)),
inference(step,[status(thm)],[t161,t58]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t35,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t163,plain,
domain(d) = domain(domain(d)),
inference(step,[status(thm)],[t162,t35]) ).
cnf(t106,plain,
domain(domain(d)) = domain(d),
inference(orient,[status(thm)],[t163]) ).
cnf(t168,plain,
domain(d) = ifeq(there_exists(d),true,compose(d,domain(domain(d))),domain(domain(d))),
inference(step,[status(thm)],[t140,t106]) ).
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(h2,plain,
there_exists(domain(d)) = 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(d) = true,
inference(hyper_resolution,[status(thm)],[hi3,h2]) ).
cnf(t57,plain,
there_exists(d) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t169,plain,
domain(d) = ifeq(true,true,compose(d,domain(domain(d))),domain(domain(d))),
inference(step,[status(thm)],[t168,t57]) ).
cnf(t170,plain,
domain(d) = compose(d,domain(domain(d))),
inference(step,[status(thm)],[t169,t35]) ).
cnf(t171,plain,
domain(d) = d,
inference(step,[status(thm)],[t170,t134]) ).
cnf(t143,plain,
domain(d) = d,
inference(orient,[status(thm)],[t171]) ).
cnf(t172,plain,
codomain(a) = d,
inference(step,[status(thm)],[t93,t143]) ).
cnf(t144,plain,
codomain(a) = d,
inference(orient,[status(thm)],[t172]) ).
cnf(f14,negated_conjecture,
codomain(a) != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_of_a_is_d) ).
fof(f14_nnf,plain,
codomain(a) != d,
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
codomain(a) != d,
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
codomain(a) != d,
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(goal_0,negated_conjecture,
codomain(a) != d,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(g0_0,plain,
d != d,
inference(rw,[status(thm)],[goal_0,t144]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT006-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.29/21.06 % CPULimit : 300
% 0.29/21.06 % WCLimit : 300
% 0.29/21.06 % DateTime : Fri Sep 25 06:54:22 UTC 2026
% 0.29/21.07 % CPUTime :
% 0.29/21.07 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.34/21.92 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.34/21.92 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------