%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT011-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 6.12s 1.24s
% Output : Proof 6.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 67 ( 59 unt; 0 def)
% Number of atoms : 83 ( 50 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 24 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 63 ( 6 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t19,axiom,
sFlat0 = domain(a),
introduced(definition) ).
cnf(t128,plain,
domain(a) = sFlat0,
inference(orient,[status(thm)],[t19]) ).
cnf(t20,axiom,
sFlat1 = domain(domain(a)),
introduced(definition) ).
cnf(t124,plain,
domain(domain(a)) = sFlat1,
inference(orient,[status(thm)],[t20]) ).
cnf(t316,plain,
domain(sFlat0) = sFlat1,
inference(step,[status(thm)],[t124,t128]) ).
cnf(t132,plain,
domain(sFlat0) = sFlat1,
inference(rw,[status(thm)],[t316]) ).
cnf(t137,plain,
domain(sFlat0) = sFlat1,
inference(orient,[status(thm)],[t132]) ).
cnf(f17,axiom,
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_is_well_defined) ).
fof(f17_nnf,plain,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t11,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(t22,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(orient,[status(thm)],[t11]) ).
cnf(f13,axiom,
product(X,domain(X),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_on_domain) ).
fof(f13_nnf,plain,
! [X] : product(X,domain(X),X),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X] : product(X,domain(X),X),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
product(X0,domain(X0),X0),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t5,plain,
product(X1,domain(X1),X1) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t46,plain,
product(X1,domain(X1),X1) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t140,plain,
true = product(sFlat0,sFlat1,sFlat0),
inference(cp,[status(thm)],[t46,t137]) ).
cnf(t194,plain,
product(sFlat0,sFlat1,sFlat0) = true,
inference(orient,[status(thm)],[t140]) ).
cnf(t195,plain,
X1 = ifeq(true,true,ifeq(product(sFlat0,sFlat1,X1),true,sFlat0,X1),X1),
inference(cp,[status(thm)],[t22,t194]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t21,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t327,plain,
X1 = ifeq(product(sFlat0,sFlat1,X1),true,sFlat0,X1),
inference(step,[status(thm)],[t195,t21]) ).
cnf(t304,plain,
ifeq(product(sFlat0,sFlat1,X1),true,sFlat0,X1) = X1,
inference(orient,[status(thm)],[t327]) ).
cnf(f15,axiom,
( product(X,Y,Y)
| ~ identity_map(X)
| ~ defined(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity1) ).
fof(f15_nnf,plain,
! [X,Y] :
( product(X,Y,Y)
| ~ identity_map(X)
| ~ defined(X,Y) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X,Y] :
( product(X,Y,Y)
| ~ identity_map(X)
| ~ defined(X,Y) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( product(X0,X1,X1)
| ~ identity_map(X0)
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(t9,plain,
ifeq(defined(X1,X2),true,ifeq(identity_map(X1),true,product(X1,X2,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t44,plain,
ifeq(defined(X1,X2),true,ifeq(identity_map(X1),true,product(X1,X2,X2),true),true) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(f11,axiom,
defined(X,domain(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mapping_from_x_to_its_domain) ).
fof(f11_nnf,plain,
! [X] : defined(X,domain(X)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : defined(X,domain(X)),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
defined(X0,domain(X0)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t2,plain,
defined(X1,domain(X1)) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t84,plain,
defined(X1,domain(X1)) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t139,plain,
true = defined(sFlat0,sFlat1),
inference(cp,[status(thm)],[t84,t137]) ).
cnf(t161,plain,
defined(sFlat0,sFlat1) = true,
inference(orient,[status(thm)],[t139]) ).
cnf(t164,plain,
true = ifeq(true,true,ifeq(identity_map(sFlat0),true,product(sFlat0,sFlat1,sFlat1),true),true),
inference(cp,[status(thm)],[t44,t161]) ).
cnf(t317,plain,
true = ifeq(identity_map(sFlat0),true,product(sFlat0,sFlat1,sFlat1),true),
inference(step,[status(thm)],[t164,t21]) ).
cnf(f9,axiom,
identity_map(domain(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_is_an_identity_map) ).
fof(f9_nnf,plain,
! [X] : identity_map(domain(X)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X] : identity_map(domain(X)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
identity_map(domain(X0)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(t1,plain,
identity_map(domain(X1)) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t116,plain,
identity_map(domain(X1)) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t129,plain,
true = identity_map(sFlat0),
inference(cp,[status(thm)],[t116,t128]) ).
cnf(t133,plain,
identity_map(sFlat0) = true,
inference(orient,[status(thm)],[t129]) ).
cnf(t318,plain,
true = ifeq(true,true,product(sFlat0,sFlat1,sFlat1),true),
inference(step,[status(thm)],[t317,t133]) ).
cnf(t319,plain,
true = product(sFlat0,sFlat1,sFlat1),
inference(step,[status(thm)],[t318,t21]) ).
cnf(t211,plain,
product(sFlat0,sFlat1,sFlat1) = true,
inference(orient,[status(thm)],[t319]) ).
cnf(t306,plain,
sFlat1 = ifeq(true,true,sFlat0,sFlat1),
inference(cp,[status(thm)],[t304,t211]) ).
cnf(t328,plain,
sFlat1 = sFlat0,
inference(step,[status(thm)],[t306,t21]) ).
cnf(t307,plain,
sFlat1 = sFlat0,
inference(orient,[status(thm)],[t328]) ).
cnf(t329,plain,
domain(sFlat0) = sFlat0,
inference(step,[status(thm)],[t137,t307]) ).
cnf(t308,plain,
domain(sFlat0) = sFlat0,
inference(orient,[status(thm)],[t329]) ).
cnf(f18,negated_conjecture,
domain(domain(a)) != domain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_is_idempotent) ).
fof(f18_nnf,plain,
domain(domain(a)) != domain(a),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
domain(domain(a)) != domain(a),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
domain(domain(a)) != domain(a),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(goal_0,negated_conjecture,
domain(domain(a)) != domain(a),
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(g0_0,plain,
domain(sFlat0) != domain(a),
inference(rw,[status(thm)],[goal_0,t128]) ).
cnf(g0_1,plain,
sFlat0 != domain(a),
inference(rw,[status(thm)],[g0_0,t308]) ).
cnf(g0_2,plain,
sFlat0 != sFlat0,
inference(rw,[status(thm)],[g0_1,t128]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n017.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Fri Sep 25 06:50:17 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.12/1.24 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.12/1.24 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------