%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT018-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 01:00:43 PM UTC 2026
% Result : Unsatisfiable 26.33s 3.76s
% Output : Proof 26.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 14
% Syntax : Number of formulae : 129 ( 113 unt; 0 def)
% Number of atoms : 149 ( 110 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 29 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-4 aty)
% Number of variables : 92 ( 6 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t27,axiom,
sFlat0 = compose(b,c),
introduced(definition) ).
cnf(t104,plain,
compose(b,c) = sFlat0,
inference(orient,[status(thm)],[t27]) ).
cnf(t28,axiom,
sFlat1 = compose(a,compose(b,c)),
introduced(definition) ).
cnf(t6161,plain,
sFlat1 = compose(a,sFlat0),
inference(step,[status(thm)],[t28,t104]) ).
cnf(t111,plain,
compose(a,sFlat0) = sFlat1,
inference(orient,[status(thm)],[t6161]) ).
cnf(f19,negated_conjecture,
~ there_exists(compose(a,compose(b,c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_bc_exists) ).
fof(f19_nnf,plain,
~ there_exists(compose(a,compose(b,c))),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
~ there_exists(compose(a,compose(b,c))),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
~ there_exists(compose(a,compose(b,c))),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t10,plain,
there_exists(compose(a,compose(b,c))) = false,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t81,plain,
there_exists(compose(a,compose(b,c))) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(t29,axiom,
sFlat2 = there_exists(compose(a,compose(b,c))),
introduced(definition) ).
cnf(t6154,plain,
sFlat2 = false,
inference(step,[status(thm)],[t29,t81]) ).
cnf(t92,plain,
false = sFlat2,
inference(orient,[status(thm)],[t6154]) ).
cnf(t6155,plain,
there_exists(compose(a,compose(b,c))) = sFlat2,
inference(step,[status(thm)],[t81,t92]) ).
cnf(t93,plain,
there_exists(compose(a,compose(b,c))) = sFlat2,
inference(orient,[status(thm)],[t6155]) ).
cnf(t6160,plain,
there_exists(compose(a,sFlat0)) = sFlat2,
inference(step,[status(thm)],[t93,t104]) ).
cnf(t110,plain,
there_exists(compose(a,sFlat0)) = sFlat2,
inference(rw,[status(thm)],[t6160]) ).
cnf(t6166,plain,
there_exists(sFlat1) = sFlat2,
inference(step,[status(thm)],[t110,t111]) ).
cnf(t162,plain,
there_exists(sFlat1) = sFlat2,
inference(orient,[status(thm)],[t6166]) ).
cnf(f7,axiom,
( there_exists(compose(X,Y))
| domain(X) != codomain(Y)
| ~ there_exists(domain(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition2) ).
fof(f7_nnf,plain,
! [X,Y] :
( there_exists(compose(X,Y))
| domain(X) != codomain(Y)
| ~ there_exists(domain(X)) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( there_exists(compose(X,Y))
| domain(X) != codomain(Y)
| ~ there_exists(domain(X)) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( there_exists(compose(X0,X1))
| domain(X0) != codomain(X1)
| ~ there_exists(domain(X0)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t25,plain,
ifeq(there_exists(domain(X1)),true,ifeq(domain(X1),codomain(X2),there_exists(compose(X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t62,plain,
ifeq(there_exists(domain(X1)),true,ifeq(domain(X1),codomain(X2),there_exists(compose(X1,X2)),true),true) = true,
inference(orient,[status(thm)],[t25]) ).
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(t20,plain,
ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t49,plain,
ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) = true,
inference(orient,[status(thm)],[t20]) ).
cnf(f17,hypothesis,
there_exists(compose(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_ab_exists) ).
fof(f17_nnf,plain,
there_exists(compose(a,b)),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
there_exists(compose(a,b)),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(t7,plain,
there_exists(compose(a,b)) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t39,plain,
there_exists(compose(a,b)) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t51,plain,
true = ifeq(true,true,there_exists(domain(a)),true),
inference(cp,[status(thm)],[t49,t39]) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t32,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t6163,plain,
true = there_exists(domain(a)),
inference(step,[status(thm)],[t51,t32]) ).
cnf(t136,plain,
there_exists(domain(a)) = true,
inference(orient,[status(thm)],[t6163]) ).
cnf(t145,plain,
true = ifeq(true,true,ifeq(domain(a),codomain(X1),there_exists(compose(a,X1)),true),true),
inference(cp,[status(thm)],[t62,t136]) ).
cnf(t6717,plain,
true = ifeq(domain(a),codomain(X1),there_exists(compose(a,X1)),true),
inference(step,[status(thm)],[t145,t32]) ).
cnf(t6018,plain,
ifeq(domain(a),codomain(X1),there_exists(compose(a,X1)),true) = true,
inference(orient,[status(thm)],[t6717]) ).
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(t21,plain,
ifeq(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t116,plain,
ifeq(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
inference(orient,[status(thm)],[t21]) ).
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(t5,plain,
compose(X1,domain(X1)) = X1,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t30,plain,
compose(X1,domain(X1)) = X1,
inference(orient,[status(thm)],[t5]) ).
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(t97,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(orient,[status(thm)],[t18]) ).
cnf(f10,axiom,
compose(codomain(X),X) = X,
file('/export/starexec/sandbox/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(t6,plain,
compose(codomain(X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t31,plain,
compose(codomain(X1),X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t100,plain,
compose(codomain(X1),compose(X1,X2)) = compose(X1,X2),
inference(cp,[status(thm)],[t97,t31]) ).
cnf(t350,plain,
compose(codomain(X1),compose(X1,X2)) = compose(X1,X2),
inference(orient,[status(thm)],[t100]) ).
cnf(t359,plain,
compose(b,c) = compose(codomain(b),sFlat0),
inference(cp,[status(thm)],[t350,t104]) ).
cnf(t6203,plain,
sFlat0 = compose(codomain(b),sFlat0),
inference(step,[status(thm)],[t359,t104]) ).
cnf(t117,plain,
codomain(b) = ifeq(true,true,domain(a),codomain(b)),
inference(cp,[status(thm)],[t116,t39]) ).
cnf(t6162,plain,
codomain(b) = domain(a),
inference(step,[status(thm)],[t117,t32]) ).
cnf(t130,plain,
codomain(b) = domain(a),
inference(orient,[status(thm)],[t6162]) ).
cnf(t6204,plain,
sFlat0 = compose(domain(a),sFlat0),
inference(step,[status(thm)],[t6203,t130]) ).
cnf(t375,plain,
compose(domain(a),sFlat0) = sFlat0,
inference(orient,[status(thm)],[t6204]) ).
cnf(t378,plain,
codomain(sFlat0) = ifeq(there_exists(sFlat0),true,domain(domain(a)),codomain(sFlat0)),
inference(cp,[status(thm)],[t116,t375]) ).
cnf(f18,hypothesis,
there_exists(compose(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_bc_exists) ).
fof(f18_nnf,plain,
there_exists(compose(b,c)),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
there_exists(compose(b,c)),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(t8,plain,
there_exists(compose(b,c)) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t38,plain,
there_exists(compose(b,c)) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t6159,plain,
there_exists(sFlat0) = true,
inference(step,[status(thm)],[t38,t104]) ).
cnf(t109,plain,
there_exists(sFlat0) = true,
inference(rw,[status(thm)],[t6159]) ).
cnf(t123,plain,
there_exists(sFlat0) = true,
inference(orient,[status(thm)],[t109]) ).
cnf(t6205,plain,
codomain(sFlat0) = ifeq(true,true,domain(domain(a)),codomain(sFlat0)),
inference(step,[status(thm)],[t378,t123]) ).
cnf(t6206,plain,
codomain(sFlat0) = domain(domain(a)),
inference(step,[status(thm)],[t6205,t32]) ).
cnf(t382,plain,
domain(domain(a)) = codomain(sFlat0),
inference(orient,[status(thm)],[t6206]) ).
cnf(t383,plain,
domain(a) = compose(domain(a),codomain(sFlat0)),
inference(cp,[status(thm)],[t30,t382]) ).
cnf(t467,plain,
compose(domain(a),codomain(sFlat0)) = domain(a),
inference(orient,[status(thm)],[t383]) ).
cnf(t469,plain,
codomain(codomain(sFlat0)) = ifeq(there_exists(domain(a)),true,domain(domain(a)),codomain(codomain(sFlat0))),
inference(cp,[status(thm)],[t116,t467]) ).
cnf(t99,plain,
compose(X1,compose(domain(X1),X2)) = compose(X1,X2),
inference(cp,[status(thm)],[t97,t30]) ).
cnf(t279,plain,
compose(X1,compose(domain(X1),X2)) = compose(X1,X2),
inference(orient,[status(thm)],[t99]) ).
cnf(t281,plain,
compose(X1,domain(domain(X1))) = compose(X1,domain(X1)),
inference(cp,[status(thm)],[t279,t30]) ).
cnf(t6188,plain,
compose(X1,domain(domain(X1))) = X1,
inference(step,[status(thm)],[t281,t30]) ).
cnf(t288,plain,
compose(X1,domain(domain(X1))) = X1,
inference(orient,[status(thm)],[t6188]) ).
cnf(t384,plain,
a = compose(a,codomain(sFlat0)),
inference(cp,[status(thm)],[t288,t382]) ).
cnf(t397,plain,
compose(a,codomain(sFlat0)) = a,
inference(orient,[status(thm)],[t384]) ).
cnf(t399,plain,
codomain(codomain(sFlat0)) = ifeq(there_exists(a),true,domain(a),codomain(codomain(sFlat0))),
inference(cp,[status(thm)],[t116,t397]) ).
cnf(f3,axiom,
( there_exists(X)
| ~ there_exists(domain(X)) ),
file('/export/starexec/sandbox/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(t16,plain,
ifeq(there_exists(domain(X1)),true,there_exists(X1),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t59,plain,
ifeq(there_exists(domain(X1)),true,there_exists(X1),true) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t140,plain,
true = ifeq(true,true,there_exists(a),true),
inference(cp,[status(thm)],[t59,t136]) ).
cnf(t6164,plain,
true = there_exists(a),
inference(step,[status(thm)],[t140,t32]) ).
cnf(t146,plain,
there_exists(a) = true,
inference(orient,[status(thm)],[t6164]) ).
cnf(t6209,plain,
codomain(codomain(sFlat0)) = ifeq(true,true,domain(a),codomain(codomain(sFlat0))),
inference(step,[status(thm)],[t399,t146]) ).
cnf(t6210,plain,
codomain(codomain(sFlat0)) = domain(a),
inference(step,[status(thm)],[t6209,t32]) ).
cnf(t401,plain,
codomain(codomain(sFlat0)) = domain(a),
inference(orient,[status(thm)],[t6210]) ).
cnf(t6223,plain,
domain(a) = ifeq(there_exists(domain(a)),true,domain(domain(a)),codomain(codomain(sFlat0))),
inference(step,[status(thm)],[t469,t401]) ).
cnf(t6224,plain,
domain(a) = ifeq(true,true,domain(domain(a)),codomain(codomain(sFlat0))),
inference(step,[status(thm)],[t6223,t136]) ).
cnf(t6225,plain,
domain(a) = domain(domain(a)),
inference(step,[status(thm)],[t6224,t32]) ).
cnf(t6226,plain,
domain(a) = codomain(sFlat0),
inference(step,[status(thm)],[t6225,t382]) ).
cnf(t471,plain,
codomain(sFlat0) = domain(a),
inference(orient,[status(thm)],[t6226]) ).
cnf(t6024,plain,
true = ifeq(domain(a),domain(a),there_exists(compose(a,sFlat0)),true),
inference(cp,[status(thm)],[t6018,t471]) ).
cnf(t6718,plain,
true = there_exists(compose(a,sFlat0)),
inference(step,[status(thm)],[t6024,t32]) ).
cnf(t6719,plain,
true = there_exists(sFlat1),
inference(step,[status(thm)],[t6718,t111]) ).
cnf(t6720,plain,
true = sFlat2,
inference(step,[status(thm)],[t6719,t162]) ).
cnf(t6035,plain,
true = sFlat2,
inference(orient,[status(thm)],[t6720]) ).
cnf(goal_0,negated_conjecture,
there_exists(compose(a,compose(b,c))) != true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
there_exists(compose(a,sFlat0)) != true,
inference(rw,[status(thm)],[goal_0,t104]) ).
cnf(g0_1,plain,
there_exists(sFlat1) != true,
inference(rw,[status(thm)],[g0_0,t111]) ).
cnf(g0_2,plain,
sFlat2 != true,
inference(rw,[status(thm)],[g0_1,t162]) ).
cnf(g0_3,plain,
sFlat2 != sFlat2,
inference(rw,[status(thm)],[g0_2,t6035]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT018-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 07:02:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 26.33/3.76 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.33/3.76 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------