%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT009-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 01:00:38 PM UTC 2026
% Result : Unsatisfiable 6.04s 1.35s
% Output : Proof 6.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 83 ( 71 unt; 0 def)
% Number of atoms : 95 ( 71 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 32 ( 20 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 62 ( 5 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t29,axiom,
sFlat0 = compose(a,b),
introduced(definition) ).
cnf(t40,plain,
compose(a,b) = sFlat0,
inference(orient,[status(thm)],[t29]) ).
cnf(t30,axiom,
sFlat1 = domain(compose(a,b)),
introduced(definition) ).
cnf(t198,plain,
sFlat1 = domain(sFlat0),
inference(step,[status(thm)],[t30,t40]) ).
cnf(t85,plain,
domain(sFlat0) = sFlat1,
inference(orient,[status(thm)],[t198]) ).
cnf(t31,axiom,
sFlat2 = domain(b),
introduced(definition) ).
cnf(t92,plain,
domain(b) = sFlat2,
inference(orient,[status(thm)],[t31]) ).
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(t24,plain,
ifeq(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t98,plain,
ifeq(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
inference(orient,[status(thm)],[t24]) ).
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(t18,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t36,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(orient,[status(thm)],[t18]) ).
cnf(t41,plain,
compose(a,compose(b,X1)) = compose(sFlat0,X1),
inference(cp,[status(thm)],[t36,t40]) ).
cnf(t175,plain,
compose(a,compose(b,X1)) = compose(sFlat0,X1),
inference(orient,[status(thm)],[t41]) ).
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(t3,plain,
compose(X1,domain(X1)) = X1,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t32,plain,
compose(X1,domain(X1)) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t93,plain,
b = compose(b,sFlat2),
inference(cp,[status(thm)],[t32,t92]) ).
cnf(t123,plain,
compose(b,sFlat2) = b,
inference(orient,[status(thm)],[t93]) ).
cnf(t176,plain,
compose(sFlat0,sFlat2) = compose(a,b),
inference(cp,[status(thm)],[t175,t123]) ).
cnf(t226,plain,
compose(sFlat0,sFlat2) = sFlat0,
inference(step,[status(thm)],[t176,t40]) ).
cnf(t181,plain,
compose(sFlat0,sFlat2) = sFlat0,
inference(orient,[status(thm)],[t226]) ).
cnf(t183,plain,
codomain(sFlat2) = ifeq(there_exists(sFlat0),true,domain(sFlat0),codomain(sFlat2)),
inference(cp,[status(thm)],[t98,t181]) ).
cnf(t125,plain,
codomain(sFlat2) = ifeq(there_exists(b),true,domain(b),codomain(sFlat2)),
inference(cp,[status(thm)],[t98,t123]) ).
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(t16,plain,
ifeq(there_exists(codomain(X1)),true,there_exists(X1),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t64,plain,
ifeq(there_exists(codomain(X1)),true,there_exists(X1),true) = true,
inference(orient,[status(thm)],[t16]) ).
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,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_exists) ).
fof(f11_nnf,plain,
there_exists(compose(a,b)),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
there_exists(compose(a,b)),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(hi11,axiom,
there_exists(compose(a,b)) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t1,plain,
domain(a) = codomain(b),
inference(hyper_resolution,[status(thm)],[hi6,hi11]) ).
cnf(t81,plain,
codomain(b) = domain(a),
inference(orient,[status(thm)],[t1]) ).
cnf(t83,plain,
true = ifeq(there_exists(domain(a)),true,there_exists(b),true),
inference(cp,[status(thm)],[t64,t81]) ).
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(hi5,axiom,
ifeq(there_exists(compose(X0,X1)),true,there_exists(domain(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t2,plain,
there_exists(domain(a)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi11]) ).
cnf(t44,plain,
there_exists(domain(a)) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t200,plain,
true = ifeq(true,true,there_exists(b),true),
inference(step,[status(thm)],[t83,t44]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t34,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t201,plain,
true = there_exists(b),
inference(step,[status(thm)],[t200,t34]) ).
cnf(t105,plain,
there_exists(b) = true,
inference(orient,[status(thm)],[t201]) ).
cnf(t208,plain,
codomain(sFlat2) = ifeq(true,true,domain(b),codomain(sFlat2)),
inference(step,[status(thm)],[t125,t105]) ).
cnf(t209,plain,
codomain(sFlat2) = domain(b),
inference(step,[status(thm)],[t208,t34]) ).
cnf(t210,plain,
codomain(sFlat2) = sFlat2,
inference(step,[status(thm)],[t209,t92]) ).
cnf(t128,plain,
codomain(sFlat2) = sFlat2,
inference(orient,[status(thm)],[t210]) ).
cnf(t227,plain,
sFlat2 = ifeq(there_exists(sFlat0),true,domain(sFlat0),codomain(sFlat2)),
inference(step,[status(thm)],[t183,t128]) ).
cnf(t7,plain,
there_exists(compose(a,b)) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t189,plain,
there_exists(sFlat0) = true,
inference(step,[status(thm)],[t7,t40]) ).
cnf(t43,plain,
there_exists(sFlat0) = true,
inference(orient,[status(thm)],[t189]) ).
cnf(t228,plain,
sFlat2 = ifeq(true,true,domain(sFlat0),codomain(sFlat2)),
inference(step,[status(thm)],[t227,t43]) ).
cnf(t229,plain,
sFlat2 = domain(sFlat0),
inference(step,[status(thm)],[t228,t34]) ).
cnf(t230,plain,
sFlat2 = sFlat1,
inference(step,[status(thm)],[t229,t85]) ).
cnf(t185,plain,
sFlat2 = sFlat1,
inference(orient,[status(thm)],[t230]) ).
cnf(t231,plain,
domain(b) = sFlat1,
inference(step,[status(thm)],[t92,t185]) ).
cnf(t186,plain,
domain(b) = sFlat1,
inference(orient,[status(thm)],[t231]) ).
cnf(f12,negated_conjecture,
domain(compose(a,b)) != domain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_ab_equals_domain_of_b) ).
fof(f12_nnf,plain,
domain(compose(a,b)) != domain(b),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
domain(compose(a,b)) != domain(b),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
domain(compose(a,b)) != domain(b),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
domain(compose(a,b)) != domain(b),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(g0_0,plain,
domain(sFlat0) != domain(b),
inference(rw,[status(thm)],[goal_0,t40]) ).
cnf(g0_1,plain,
sFlat1 != domain(b),
inference(rw,[status(thm)],[g0_0,t85]) ).
cnf(g0_2,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_1,t186]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT009-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 06:55:37 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.04/1.35 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.04/1.35 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------