%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT016-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 01:00:41 PM UTC 2026
% Result : Unsatisfiable 5.94s 1.23s
% Output : Proof 5.94s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t17,axiom,
sFlat0 = domain(a),
introduced(definition) ).
cnf(t58,plain,
domain(a) = sFlat0,
inference(orient,[status(thm)],[t17]) ).
cnf(t18,axiom,
sFlat1 = there_exists(domain(a)),
introduced(definition) ).
cnf(t40,plain,
there_exists(domain(a)) = sFlat1,
inference(orient,[status(thm)],[t18]) ).
cnf(t90,plain,
there_exists(sFlat0) = sFlat1,
inference(step,[status(thm)],[t40,t58]) ).
cnf(t65,plain,
there_exists(sFlat0) = sFlat1,
inference(rw,[status(thm)],[t90]) ).
cnf(t66,plain,
there_exists(sFlat0) = sFlat1,
inference(orient,[status(thm)],[t65]) ).
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(t13,plain,
ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t27,plain,
ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) = true,
inference(orient,[status(thm)],[t13]) ).
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(t1,plain,
compose(X1,domain(X1)) = X1,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t19,plain,
compose(X1,domain(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t59,plain,
a = compose(a,sFlat0),
inference(cp,[status(thm)],[t19,t58]) ).
cnf(t71,plain,
compose(a,sFlat0) = a,
inference(orient,[status(thm)],[t59]) ).
cnf(t74,plain,
true = ifeq(there_exists(a),true,there_exists(domain(a)),true),
inference(cp,[status(thm)],[t27,t71]) ).
cnf(f11,hypothesis,
there_exists(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_a_exists) ).
fof(f11_nnf,plain,
there_exists(a),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
there_exists(a),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(t0,plain,
there_exists(a) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t23,plain,
there_exists(a) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t91,plain,
true = ifeq(true,true,there_exists(domain(a)),true),
inference(step,[status(thm)],[t74,t23]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t21,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t92,plain,
true = there_exists(domain(a)),
inference(step,[status(thm)],[t91,t21]) ).
cnf(t93,plain,
true = there_exists(sFlat0),
inference(step,[status(thm)],[t92,t58]) ).
cnf(t94,plain,
true = sFlat1,
inference(step,[status(thm)],[t93,t66]) ).
cnf(t76,plain,
true = sFlat1,
inference(orient,[status(thm)],[t94]) ).
cnf(f12,negated_conjecture,
~ there_exists(domain(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_a_exists) ).
fof(f12_nnf,plain,
~ there_exists(domain(a)),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ there_exists(domain(a)),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ there_exists(domain(a)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
there_exists(domain(a)) != true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(g0_0,plain,
there_exists(sFlat0) != true,
inference(rw,[status(thm)],[goal_0,t58]) ).
cnf(g0_1,plain,
sFlat1 != true,
inference(rw,[status(thm)],[g0_0,t66]) ).
cnf(g0_2,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_1,t76]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : CAT016-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 06:57:11 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.94/1.23 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.94/1.23 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------