%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT005-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 4.51s 2.17s
% Output : Proof 4.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 13
% Syntax : Number of formulae : 118 ( 90 unt; 0 def)
% Number of atoms : 146 ( 98 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 63 ( 35 ~; 28 |; 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 : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 92 ( 10 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t28,axiom,
sFlat0 = domain(a),
introduced(definition) ).
cnf(t91,plain,
domain(a) = sFlat0,
inference(orient,[status(thm)],[t28]) ).
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(t22,plain,
ifeq(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t77,plain,
ifeq(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
inference(orient,[status(thm)],[t22]) ).
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(t5,plain,
compose(X1,domain(X1)) = X1,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t35,plain,
compose(X1,domain(X1)) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(f19,hypothesis,
( compose(d,Y) = Y
| ~ there_exists(compose(d,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dy_equals_y) ).
fof(f19_nnf,plain,
! [Y] :
( compose(d,Y) = Y
| ~ there_exists(compose(d,Y)) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [Y] :
( compose(d,Y) = Y
| ~ there_exists(compose(d,Y)) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( compose(d,X0) = X0
| ~ there_exists(compose(d,X0)) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t21,plain,
ifeq(there_exists(compose(d,X1)),true,compose(d,X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t32,plain,
ifeq(there_exists(compose(d,X1)),true,compose(d,X1),X1) = X1,
inference(orient,[status(thm)],[t21]) ).
cnf(t36,plain,
domain(d) = ifeq(there_exists(d),true,compose(d,domain(d)),domain(d)),
inference(cp,[status(thm)],[t32,t35]) ).
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(t15,plain,
ifeq(there_exists(domain(X1)),true,there_exists(X1),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t57,plain,
ifeq(there_exists(domain(X1)),true,there_exists(X1),true) = true,
inference(orient,[status(thm)],[t15]) ).
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(t14,plain,
ifeq(there_exists(codomain(X1)),true,there_exists(X1),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t58,plain,
ifeq(there_exists(codomain(X1)),true,there_exists(X1),true) = true,
inference(orient,[status(thm)],[t14]) ).
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(t17,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t81,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(orient,[status(thm)],[t17]) ).
cnf(f18,hypothesis,
( compose(X,d) = X
| ~ there_exists(compose(X,d)) ),
file('/export/starexec/sandbox2/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(t20,plain,
ifeq(there_exists(compose(X1,d)),true,compose(X1,d),X1) = X1,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t31,plain,
ifeq(there_exists(compose(X1,d)),true,compose(X1,d),X1) = X1,
inference(orient,[status(thm)],[t20]) ).
cnf(f17,hypothesis,
there_exists(compose(a,d)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ad_exists) ).
fof(f17_nnf,plain,
there_exists(compose(a,d)),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
there_exists(compose(a,d)),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(t8,plain,
there_exists(compose(a,d)) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t61,plain,
there_exists(compose(a,d)) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t69,plain,
a = ifeq(true,true,compose(a,d),a),
inference(cp,[status(thm)],[t31,t61]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t29,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t231,plain,
a = compose(a,d),
inference(step,[status(thm)],[t69,t29]) ).
cnf(t130,plain,
compose(a,d) = a,
inference(orient,[status(thm)],[t231]) ).
cnf(t131,plain,
compose(a,compose(d,X1)) = compose(a,X1),
inference(cp,[status(thm)],[t81,t130]) ).
cnf(t167,plain,
compose(a,compose(d,X1)) = compose(a,X1),
inference(orient,[status(thm)],[t131]) ).
cnf(t168,plain,
compose(a,domain(d)) = compose(a,d),
inference(cp,[status(thm)],[t167,t35]) ).
cnf(t239,plain,
compose(a,domain(d)) = a,
inference(step,[status(thm)],[t168,t130]) ).
cnf(t171,plain,
compose(a,domain(d)) = a,
inference(orient,[status(thm)],[t239]) ).
cnf(t173,plain,
codomain(domain(d)) = ifeq(there_exists(a),true,domain(a),codomain(domain(d))),
inference(cp,[status(thm)],[t77,t171]) ).
cnf(f13,axiom,
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ),
file('/export/starexec/sandbox2/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(t18,plain,
ifeq(there_exists(compose(X1,X2)),true,there_exists(codomain(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t51,plain,
ifeq(there_exists(compose(X1,X2)),true,there_exists(codomain(X1)),true) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(t66,plain,
true = ifeq(true,true,there_exists(codomain(a)),true),
inference(cp,[status(thm)],[t51,t61]) ).
cnf(t227,plain,
true = there_exists(codomain(a)),
inference(step,[status(thm)],[t66,t29]) ).
cnf(t108,plain,
there_exists(codomain(a)) = true,
inference(orient,[status(thm)],[t227]) ).
cnf(t111,plain,
true = ifeq(true,true,there_exists(a),true),
inference(cp,[status(thm)],[t58,t108]) ).
cnf(t228,plain,
true = there_exists(a),
inference(step,[status(thm)],[t111,t29]) ).
cnf(t117,plain,
there_exists(a) = true,
inference(orient,[status(thm)],[t228]) ).
cnf(t240,plain,
codomain(domain(d)) = ifeq(true,true,domain(a),codomain(domain(d))),
inference(step,[status(thm)],[t173,t117]) ).
cnf(t241,plain,
codomain(domain(d)) = domain(a),
inference(step,[status(thm)],[t240,t29]) ).
cnf(t242,plain,
codomain(domain(d)) = sFlat0,
inference(step,[status(thm)],[t241,t91]) ).
cnf(t175,plain,
codomain(domain(d)) = sFlat0,
inference(orient,[status(thm)],[t242]) ).
cnf(t178,plain,
true = ifeq(there_exists(sFlat0),true,there_exists(domain(d)),true),
inference(cp,[status(thm)],[t58,t175]) ).
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(t19,plain,
ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t48,plain,
ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t67,plain,
true = ifeq(true,true,there_exists(domain(a)),true),
inference(cp,[status(thm)],[t48,t61]) ).
cnf(t229,plain,
true = there_exists(domain(a)),
inference(step,[status(thm)],[t67,t29]) ).
cnf(t230,plain,
true = there_exists(sFlat0),
inference(step,[status(thm)],[t229,t91]) ).
cnf(t123,plain,
there_exists(sFlat0) = true,
inference(orient,[status(thm)],[t230]) ).
cnf(t243,plain,
true = ifeq(true,true,there_exists(domain(d)),true),
inference(step,[status(thm)],[t178,t123]) ).
cnf(t244,plain,
true = there_exists(domain(d)),
inference(step,[status(thm)],[t243,t29]) ).
cnf(t181,plain,
there_exists(domain(d)) = true,
inference(orient,[status(thm)],[t244]) ).
cnf(t184,plain,
true = ifeq(true,true,there_exists(d),true),
inference(cp,[status(thm)],[t57,t181]) ).
cnf(t245,plain,
true = there_exists(d),
inference(step,[status(thm)],[t184,t29]) ).
cnf(t190,plain,
there_exists(d) = true,
inference(orient,[status(thm)],[t245]) ).
cnf(t246,plain,
domain(d) = ifeq(true,true,compose(d,domain(d)),domain(d)),
inference(step,[status(thm)],[t36,t190]) ).
cnf(t247,plain,
domain(d) = compose(d,domain(d)),
inference(step,[status(thm)],[t246,t29]) ).
cnf(t248,plain,
domain(d) = d,
inference(step,[status(thm)],[t247,t35]) ).
cnf(t209,plain,
domain(d) = d,
inference(orient,[status(thm)],[t248]) ).
cnf(t210,plain,
d = compose(d,d),
inference(cp,[status(thm)],[t35,t209]) ).
cnf(t214,plain,
compose(d,d) = d,
inference(orient,[status(thm)],[t210]) ).
cnf(t216,plain,
codomain(d) = ifeq(there_exists(d),true,domain(d),codomain(d)),
inference(cp,[status(thm)],[t77,t214]) ).
cnf(t78,plain,
codomain(d) = ifeq(true,true,domain(a),codomain(d)),
inference(cp,[status(thm)],[t77,t61]) ).
cnf(t225,plain,
codomain(d) = domain(a),
inference(step,[status(thm)],[t78,t29]) ).
cnf(t226,plain,
codomain(d) = sFlat0,
inference(step,[status(thm)],[t225,t91]) ).
cnf(t102,plain,
codomain(d) = sFlat0,
inference(orient,[status(thm)],[t226]) ).
cnf(t249,plain,
sFlat0 = ifeq(there_exists(d),true,domain(d),codomain(d)),
inference(step,[status(thm)],[t216,t102]) ).
cnf(t250,plain,
sFlat0 = ifeq(true,true,domain(d),codomain(d)),
inference(step,[status(thm)],[t249,t190]) ).
cnf(t251,plain,
sFlat0 = domain(d),
inference(step,[status(thm)],[t250,t29]) ).
cnf(t252,plain,
sFlat0 = d,
inference(step,[status(thm)],[t251,t209]) ).
cnf(t218,plain,
d = sFlat0,
inference(orient,[status(thm)],[t252]) ).
cnf(f20,negated_conjecture,
domain(a) != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_a_is_d) ).
fof(f20_nnf,plain,
domain(a) != d,
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
domain(a) != d,
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
domain(a) != d,
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(goal_0,negated_conjecture,
domain(a) != d,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(g0_0,plain,
sFlat0 != d,
inference(rw,[status(thm)],[goal_0,t91]) ).
cnf(g0_1,plain,
sFlat0 != sFlat0,
inference(rw,[status(thm)],[g0_0,t218]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT005-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 06:50:23 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.51/2.17 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.51/2.17 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------