%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT011-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 01:00:39 PM UTC 2026
% Result : Unsatisfiable 6.17s 1.36s
% Output : Proof 6.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 10
% Syntax : Number of formulae : 85 ( 73 unt; 0 def)
% Number of atoms : 97 ( 73 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 38 ( 26 ~; 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 : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 48 ( 6 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t13,axiom,
sFlat0 = domain(a),
introduced(definition) ).
cnf(t48,plain,
domain(a) = sFlat0,
inference(orient,[status(thm)],[t13]) ).
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(t1,plain,
compose(X1,domain(X1)) = X1,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t17,plain,
compose(X1,domain(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t14,axiom,
sFlat1 = domain(domain(a)),
introduced(definition) ).
cnf(t41,plain,
domain(domain(a)) = sFlat1,
inference(orient,[status(thm)],[t14]) ).
cnf(t173,plain,
domain(sFlat0) = sFlat1,
inference(step,[status(thm)],[t41,t48]) ).
cnf(t55,plain,
domain(sFlat0) = sFlat1,
inference(rw,[status(thm)],[t173]) ).
cnf(t64,plain,
domain(sFlat0) = sFlat1,
inference(orient,[status(thm)],[t55]) ).
cnf(t65,plain,
sFlat0 = compose(sFlat0,sFlat1),
inference(cp,[status(thm)],[t17,t64]) ).
cnf(t81,plain,
compose(sFlat0,sFlat1) = sFlat0,
inference(orient,[status(thm)],[t65]) ).
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(t10,plain,
ifeq(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t38,plain,
ifeq(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
inference(orient,[status(thm)],[t10]) ).
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(t2,plain,
compose(codomain(X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t18,plain,
compose(codomain(X1),X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t83,plain,
codomain(sFlat1) = ifeq(there_exists(sFlat0),true,domain(sFlat0),codomain(sFlat1)),
inference(cp,[status(thm)],[t38,t81]) ).
cnf(f11,hypothesis,
there_exists(domain(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_domain_exists) ).
fof(f11_nnf,plain,
there_exists(domain(a)),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
there_exists(domain(a)),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(t0,plain,
there_exists(domain(a)) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t19,plain,
there_exists(domain(a)) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t174,plain,
there_exists(sFlat0) = true,
inference(step,[status(thm)],[t19,t48]) ).
cnf(t56,plain,
there_exists(sFlat0) = true,
inference(rw,[status(thm)],[t174]) ).
cnf(t71,plain,
there_exists(sFlat0) = true,
inference(orient,[status(thm)],[t56]) ).
cnf(t175,plain,
codomain(sFlat1) = ifeq(true,true,domain(sFlat0),codomain(sFlat1)),
inference(step,[status(thm)],[t83,t71]) ).
cnf(t3,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t15,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t176,plain,
codomain(sFlat1) = domain(sFlat0),
inference(step,[status(thm)],[t175,t15]) ).
cnf(t177,plain,
codomain(sFlat1) = sFlat1,
inference(step,[status(thm)],[t176,t64]) ).
cnf(t86,plain,
codomain(sFlat1) = sFlat1,
inference(orient,[status(thm)],[t177]) ).
cnf(t87,plain,
sFlat1 = compose(sFlat1,sFlat1),
inference(cp,[status(thm)],[t18,t86]) ).
cnf(t95,plain,
compose(sFlat1,sFlat1) = sFlat1,
inference(orient,[status(thm)],[t87]) ).
cnf(t97,plain,
codomain(sFlat1) = ifeq(there_exists(sFlat1),true,domain(sFlat1),codomain(sFlat1)),
inference(cp,[status(thm)],[t38,t95]) ).
cnf(t181,plain,
sFlat1 = ifeq(there_exists(sFlat1),true,domain(sFlat1),codomain(sFlat1)),
inference(step,[status(thm)],[t97,t86]) ).
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(t9,plain,
ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t30,plain,
ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t84,plain,
true = ifeq(there_exists(sFlat0),true,there_exists(domain(sFlat0)),true),
inference(cp,[status(thm)],[t30,t81]) ).
cnf(t178,plain,
true = ifeq(true,true,there_exists(domain(sFlat0)),true),
inference(step,[status(thm)],[t84,t71]) ).
cnf(t179,plain,
true = there_exists(domain(sFlat0)),
inference(step,[status(thm)],[t178,t15]) ).
cnf(t180,plain,
true = there_exists(sFlat1),
inference(step,[status(thm)],[t179,t64]) ).
cnf(t91,plain,
there_exists(sFlat1) = true,
inference(orient,[status(thm)],[t180]) ).
cnf(t182,plain,
sFlat1 = ifeq(true,true,domain(sFlat1),codomain(sFlat1)),
inference(step,[status(thm)],[t181,t91]) ).
cnf(t183,plain,
sFlat1 = domain(sFlat1),
inference(step,[status(thm)],[t182,t15]) ).
cnf(t100,plain,
domain(sFlat1) = sFlat1,
inference(orient,[status(thm)],[t183]) ).
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(t7,plain,
ifeq(there_exists(domain(X1)),true,there_exists(X1),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t23,plain,
ifeq(there_exists(domain(X1)),true,there_exists(X1),true) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t52,plain,
true = ifeq(there_exists(sFlat0),true,there_exists(a),true),
inference(cp,[status(thm)],[t23,t48]) ).
cnf(t199,plain,
true = ifeq(true,true,there_exists(a),true),
inference(step,[status(thm)],[t52,t71]) ).
cnf(t200,plain,
true = there_exists(a),
inference(step,[status(thm)],[t199,t15]) ).
cnf(t167,plain,
there_exists(a) = true,
inference(orient,[status(thm)],[t200]) ).
cnf(f12,negated_conjecture,
domain(domain(a)) != domain(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_is_idempotent) ).
fof(f12_nnf,plain,
domain(domain(a)) != domain(a),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
domain(domain(a)) != domain(a),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
domain(domain(a)) != domain(a),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
domain(domain(a)) != domain(a),
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(g0_0,plain,
sFlat0 != domain(a),
inference(rw,[status(thm)],[goal_0,t48]) ).
cnf(g0_1,plain,
compose(sFlat0,sFlat1) != domain(a),
inference(rw,[status(thm)],[g0_0,t81]) ).
cnf(g0_2,plain,
compose(sFlat0,domain(sFlat1)) != domain(a),
inference(rw,[status(thm)],[g0_1,t100]) ).
cnf(g0_3,plain,
compose(sFlat0,domain(sFlat1)) != sFlat1,
inference(rw,[status(thm)],[g0_2]) ).
cnf(g0_4,plain,
compose(sFlat0,domain(sFlat1)) != compose(sFlat1,sFlat1),
inference(rw,[status(thm)],[g0_3,t95]) ).
cnf(g0_5,plain,
compose(sFlat0,domain(sFlat1)) != compose(sFlat1,domain(sFlat1)),
inference(rw,[status(thm)],[g0_4,t100]) ).
cnf(g0_6,plain,
compose(sFlat0,domain(sFlat1)) != compose(ifeq(there_exists(a),true,sFlat0,sFlat1),domain(sFlat1)),
inference(rw,[status(thm)],[g0_5]) ).
cnf(g0_7,plain,
compose(sFlat0,domain(sFlat1)) != compose(ifeq(there_exists(a),there_exists(a),sFlat0,sFlat1),domain(sFlat1)),
inference(rw,[status(thm)],[g0_6,t167]) ).
cnf(g0_8,plain,
compose(sFlat0,domain(sFlat1)) != compose(sFlat0,domain(sFlat1)),
inference(rw,[status(thm)],[g0_7,t15]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT011-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 06:56:03 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.17/1.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.17/1.36 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------