%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 01:00:34 PM UTC 2026
% Result : Unsatisfiable 28.79s 14.30s
% Output : Proof 28.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of formulae : 90 ( 66 unt; 0 def)
% Number of atoms : 134 ( 64 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 94 ( 50 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 133 ( 10 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f19,hypothesis,
( X = Y
| ~ product(b,Y,W)
| ~ product(b,X,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product2) ).
fof(f19_nnf,plain,
! [X,W,Y] :
( X = Y
| ~ product(b,Y,W)
| ~ product(b,X,W) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X,W,Y] :
( X = Y
| ~ product(b,Y,W)
| ~ product(b,X,W) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( X0 = X2
| ~ product(b,X2,X1)
| ~ product(b,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t248,plain,
ifeq(product(b,X1,X2),true,ifeq(product(b,X3,X2),true,X1,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t264,plain,
ifeq(product(b,X1,X2),true,ifeq(product(b,X3,X2),true,X1,X3),X3) = X3,
inference(orient,[status(thm)],[t248]) ).
cnf(f1,axiom,
( defined(X,Y)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_property1) ).
fof(f1_nnf,plain,
! [X,Y,Z] :
( defined(X,Y)
| ~ product(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] :
( defined(X,Y)
| ~ product(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( defined(X0,X1)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(product(X0,X1,X2),true,defined(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f21,hypothesis,
product(c,h,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ch_equals_d) ).
fof(f21_nnf,plain,
product(c,h,d),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c21,plain,
product(c,h,d),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(hi21,axiom,
product(c,h,d) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(h25,plain,
defined(c,h) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi21]) ).
cnf(f2,axiom,
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_property2) ).
fof(f2_nnf,plain,
! [X,Y,Xy,Z] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Xy,Z] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( defined(X1,X3)
| ~ defined(X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(product(X0,X1,X2),true,ifeq(defined(X2,X3),true,defined(X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f20,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_equals_c) ).
fof(f20_nnf,plain,
product(a,b,c),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
product(a,b,c),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(hi20,axiom,
product(a,b,c) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h63,plain,
defined(b,h) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi20,h25]) ).
cnf(f0,axiom,
( product(X,Y,compose(X,Y))
| ~ defined(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_composition) ).
fof(f0_nnf,plain,
! [X,Y] :
( product(X,Y,compose(X,Y))
| ~ defined(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( product(X,Y,compose(X,Y))
| ~ defined(X,Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( product(X0,X1,compose(X0,X1))
| ~ defined(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(defined(X0,X1),true,product(X0,X1,compose(X0,X1)),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t108,plain,
product(b,h,compose(b,h)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h63]) ).
cnf(t354,plain,
product(b,h,compose(b,h)) = true,
inference(orient,[status(thm)],[t108]) ).
cnf(t356,plain,
h = ifeq(product(b,X1,compose(b,h)),true,ifeq(true,true,X1,h),h),
inference(cp,[status(thm)],[t264,t354]) ).
cnf(t50,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t261,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t50]) ).
cnf(t2026,plain,
h = ifeq(product(b,X1,compose(b,h)),true,X1,h),
inference(step,[status(thm)],[t356,t261]) ).
cnf(t1844,plain,
ifeq(product(b,X1,compose(b,h)),true,X1,h) = h,
inference(orient,[status(thm)],[t2026]) ).
cnf(t243,plain,
ifeq(defined(X1,X2),true,product(X1,X2,compose(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t931,plain,
ifeq(defined(X1,X2),true,product(X1,X2,compose(X1,X2)),true) = true,
inference(orient,[status(thm)],[t243]) ).
cnf(f18,hypothesis,
( X = Y
| ~ product(a,Y,W)
| ~ product(a,X,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product1) ).
fof(f18_nnf,plain,
! [X,W,Y] :
( X = Y
| ~ product(a,Y,W)
| ~ product(a,X,W) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,W,Y] :
( X = Y
| ~ product(a,Y,W)
| ~ product(a,X,W) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( X0 = X2
| ~ product(a,X2,X1)
| ~ product(a,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t247,plain,
ifeq(product(a,X1,X2),true,ifeq(product(a,X3,X2),true,X1,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t268,plain,
ifeq(product(a,X1,X2),true,ifeq(product(a,X3,X2),true,X1,X3),X3) = X3,
inference(orient,[status(thm)],[t247]) ).
cnf(h166,plain,
product(b,h,compose(b,h)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h63]) ).
cnf(f4,axiom,
( product(X,Yz,Xyz)
| ~ product(Y,Z,Yz)
| ~ product(Xy,Z,Xyz)
| ~ product(X,Y,Xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom2) ).
fof(f4_nnf,plain,
! [X,Y,Xy,Z,Xyz,Yz] :
( product(X,Yz,Xyz)
| ~ product(Y,Z,Yz)
| ~ product(Xy,Z,Xyz)
| ~ product(X,Y,Xy) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Xy,Z,Xyz,Yz] :
( product(X,Yz,Xyz)
| ~ product(Y,Z,Yz)
| ~ product(Xy,Z,Xyz)
| ~ product(X,Y,Xy) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( product(X0,X5,X4)
| ~ product(X1,X3,X5)
| ~ product(X2,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X2,X3,X4),true,ifeq(product(X1,X3,X5),true,product(X0,X5,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t106,plain,
product(a,compose(b,h),d) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi20,hi21,h166]) ).
cnf(t388,plain,
product(a,compose(b,h),d) = true,
inference(orient,[status(thm)],[t106]) ).
cnf(t389,plain,
X1 = ifeq(true,true,ifeq(product(a,X1,d),true,compose(b,h),X1),X1),
inference(cp,[status(thm)],[t268,t388]) ).
cnf(t2031,plain,
X1 = ifeq(product(a,X1,d),true,compose(b,h),X1),
inference(step,[status(thm)],[t389,t261]) ).
cnf(t1853,plain,
ifeq(product(a,X1,d),true,compose(b,h),X1) = X1,
inference(orient,[status(thm)],[t2031]) ).
cnf(f22,hypothesis,
product(c,g,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cg_equals_d) ).
fof(f22_nnf,plain,
product(c,g,d),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
product(c,g,d),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(hi22,axiom,
product(c,g,d) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(h33,plain,
defined(c,g) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi22]) ).
cnf(h127,plain,
defined(b,g) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi20,h33]) ).
cnf(h218,plain,
product(b,g,compose(b,g)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h127]) ).
cnf(t105,plain,
product(a,compose(b,g),d) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi20,hi22,h218]) ).
cnf(t393,plain,
product(a,compose(b,g),d) = true,
inference(orient,[status(thm)],[t105]) ).
cnf(t1854,plain,
compose(b,g) = ifeq(true,true,compose(b,h),compose(b,g)),
inference(cp,[status(thm)],[t1853,t393]) ).
cnf(t2032,plain,
compose(b,g) = compose(b,h),
inference(step,[status(thm)],[t1854,t261]) ).
cnf(t1856,plain,
compose(b,g) = compose(b,h),
inference(orient,[status(thm)],[t2032]) ).
cnf(t1857,plain,
true = ifeq(defined(b,g),true,product(b,g,compose(b,h)),true),
inference(cp,[status(thm)],[t931,t1856]) ).
cnf(t229,plain,
ifeq(product(X1,X2,X3),true,defined(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t414,plain,
ifeq(product(X1,X2,X3),true,defined(X1,X2),true) = true,
inference(orient,[status(thm)],[t229]) ).
cnf(t107,plain,
product(b,g,compose(b,g)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h127]) ).
cnf(t359,plain,
product(b,g,compose(b,g)) = true,
inference(orient,[status(thm)],[t107]) ).
cnf(t422,plain,
true = ifeq(true,true,defined(b,g),true),
inference(cp,[status(thm)],[t414,t359]) ).
cnf(t1911,plain,
true = defined(b,g),
inference(step,[status(thm)],[t422,t261]) ).
cnf(t1023,plain,
defined(b,g) = true,
inference(orient,[status(thm)],[t1911]) ).
cnf(t2037,plain,
true = ifeq(true,true,product(b,g,compose(b,h)),true),
inference(step,[status(thm)],[t1857,t1023]) ).
cnf(t2038,plain,
true = product(b,g,compose(b,h)),
inference(step,[status(thm)],[t2037,t261]) ).
cnf(t1862,plain,
product(b,g,compose(b,h)) = true,
inference(orient,[status(thm)],[t2038]) ).
cnf(t1863,plain,
h = ifeq(true,true,g,h),
inference(cp,[status(thm)],[t1844,t1862]) ).
cnf(t2039,plain,
h = g,
inference(step,[status(thm)],[t1863,t261]) ).
cnf(t1883,plain,
g = h,
inference(orient,[status(thm)],[t2039]) ).
cnf(f23,negated_conjecture,
h != g,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_h_equals_g) ).
fof(f23_nnf,plain,
h != g,
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
h != g,
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
h != g,
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(goal_0,negated_conjecture,
h != g,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(g0_0,plain,
h != h,
inference(rw,[status(thm)],[goal_0,t1883]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/10.38 % Computer : n026.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Fri Sep 25 06:53:21 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 28.79/14.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.79/14.30 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------