%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT004-1 : 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 01:00:35 PM UTC 2026
% Result : Unsatisfiable 43.73s 11.85s
% Output : Proof 43.73s
% 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(f18,hypothesis,
( X = Y
| ~ product(Y,a,W)
| ~ product(X,a,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product1) ).
fof(f18_nnf,plain,
! [X,W,Y] :
( X = Y
| ~ product(Y,a,W)
| ~ product(X,a,W) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,W,Y] :
( X = Y
| ~ product(Y,a,W)
| ~ product(X,a,W) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( X0 = X2
| ~ product(X2,a,X1)
| ~ product(X0,a,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t247,plain,
ifeq(product(X1,a,X2),true,ifeq(product(X3,a,X2),true,X1,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t265,plain,
ifeq(product(X1,a,X2),true,ifeq(product(X3,a,X2),true,X1,X3),X3) = X3,
inference(orient,[status(thm)],[t247]) ).
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(h,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hc_equals_d) ).
fof(f21_nnf,plain,
product(h,c,d),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c21,plain,
product(h,c,d),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(hi21,axiom,
product(h,c,d) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(h25,plain,
defined(h,c) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi21]) ).
cnf(f5,axiom,
( defined(X,Y)
| ~ defined(X,Yz)
| ~ product(Y,Z,Yz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom3) ).
fof(f5_nnf,plain,
! [Y,Z,Yz,X] :
( defined(X,Y)
| ~ defined(X,Yz)
| ~ product(Y,Z,Yz) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [Y,Z,Yz,X] :
( defined(X,Y)
| ~ defined(X,Yz)
| ~ product(Y,Z,Yz) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( defined(X3,X0)
| ~ defined(X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
ifeq(product(X0,X1,X2),true,ifeq(defined(X3,X2),true,defined(X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
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(h61,plain,
defined(h,a) = true,
inference(hyper_resolution,[status(thm)],[hi5,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(t120,plain,
product(h,a,compose(h,a)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h61]) ).
cnf(t379,plain,
product(h,a,compose(h,a)) = true,
inference(orient,[status(thm)],[t120]) ).
cnf(t380,plain,
X1 = ifeq(true,true,ifeq(product(X1,a,compose(h,a)),true,h,X1),X1),
inference(cp,[status(thm)],[t265,t379]) ).
cnf(t55,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t262,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t55]) ).
cnf(t2335,plain,
X1 = ifeq(product(X1,a,compose(h,a)),true,h,X1),
inference(step,[status(thm)],[t380,t262]) ).
cnf(t2156,plain,
ifeq(product(X1,a,compose(h,a)),true,h,X1) = X1,
inference(orient,[status(thm)],[t2335]) ).
cnf(t243,plain,
ifeq(defined(X1,X2),true,product(X1,X2,compose(X1,X2)),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t949,plain,
ifeq(defined(X1,X2),true,product(X1,X2,compose(X1,X2)),true) = true,
inference(orient,[status(thm)],[t243]) ).
cnf(f19,hypothesis,
( X = Y
| ~ product(Y,b,W)
| ~ product(X,b,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_product2) ).
fof(f19_nnf,plain,
! [X,W,Y] :
( X = Y
| ~ product(Y,b,W)
| ~ product(X,b,W) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X,W,Y] :
( X = Y
| ~ product(Y,b,W)
| ~ product(X,b,W) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( X0 = X2
| ~ product(X2,b,X1)
| ~ product(X0,b,X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t248,plain,
ifeq(product(X1,b,X2),true,ifeq(product(X3,b,X2),true,X1,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t269,plain,
ifeq(product(X1,b,X2),true,ifeq(product(X3,b,X2),true,X1,X3),X3) = X3,
inference(orient,[status(thm)],[t248]) ).
cnf(h166,plain,
product(h,a,compose(h,a)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h61]) ).
cnf(f7,axiom,
( product(Xy,Z,Xyz)
| ~ product(X,Y,Xy)
| ~ product(X,Yz,Xyz)
| ~ product(Y,Z,Yz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',category_theory_axiom5) ).
fof(f7_nnf,plain,
! [Y,Z,Yz,X,Xyz,Xy] :
( product(Xy,Z,Xyz)
| ~ product(X,Y,Xy)
| ~ product(X,Yz,Xyz)
| ~ product(Y,Z,Yz) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [Y,Z,Yz,X,Xyz,Xy] :
( product(Xy,Z,Xyz)
| ~ product(X,Y,Xy)
| ~ product(X,Yz,Xyz)
| ~ product(Y,Z,Yz) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( product(X5,X1,X4)
| ~ product(X3,X0,X5)
| ~ product(X3,X2,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X3,X2,X4),true,ifeq(product(X3,X0,X5),true,product(X5,X1,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t109,plain,
product(compose(h,a),b,d) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi20,hi21,h166]) ).
cnf(t357,plain,
product(compose(h,a),b,d) = true,
inference(orient,[status(thm)],[t109]) ).
cnf(t358,plain,
X1 = ifeq(true,true,ifeq(product(X1,b,d),true,compose(h,a),X1),X1),
inference(cp,[status(thm)],[t269,t357]) ).
cnf(t2328,plain,
X1 = ifeq(product(X1,b,d),true,compose(h,a),X1),
inference(step,[status(thm)],[t358,t262]) ).
cnf(t2119,plain,
ifeq(product(X1,b,d),true,compose(h,a),X1) = X1,
inference(orient,[status(thm)],[t2328]) ).
cnf(f22,hypothesis,
product(g,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gc_equals_d) ).
fof(f22_nnf,plain,
product(g,c,d),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
product(g,c,d),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(hi22,axiom,
product(g,c,d) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(h33,plain,
defined(g,c) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi22]) ).
cnf(h124,plain,
defined(g,a) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi20,h33]) ).
cnf(h218,plain,
product(g,a,compose(g,a)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h124]) ).
cnf(t108,plain,
product(compose(g,a),b,d) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi20,hi22,h218]) ).
cnf(t368,plain,
product(compose(g,a),b,d) = true,
inference(orient,[status(thm)],[t108]) ).
cnf(t2120,plain,
compose(g,a) = ifeq(true,true,compose(h,a),compose(g,a)),
inference(cp,[status(thm)],[t2119,t368]) ).
cnf(t2329,plain,
compose(g,a) = compose(h,a),
inference(step,[status(thm)],[t2120,t262]) ).
cnf(t2122,plain,
compose(g,a) = compose(h,a),
inference(orient,[status(thm)],[t2329]) ).
cnf(t2123,plain,
true = ifeq(defined(g,a),true,product(g,a,compose(h,a)),true),
inference(cp,[status(thm)],[t949,t2122]) ).
cnf(t237,plain,
ifeq(product(X1,X2,X3),true,defined(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t417,plain,
ifeq(product(X1,X2,X3),true,defined(X1,X2),true) = true,
inference(orient,[status(thm)],[t237]) ).
cnf(t118,plain,
product(g,a,compose(g,a)) = true,
inference(hyper_resolution,[status(thm)],[hi0,h124]) ).
cnf(t390,plain,
product(g,a,compose(g,a)) = true,
inference(orient,[status(thm)],[t118]) ).
cnf(t423,plain,
true = ifeq(true,true,defined(g,a),true),
inference(cp,[status(thm)],[t417,t390]) ).
cnf(t2185,plain,
true = defined(g,a),
inference(step,[status(thm)],[t423,t262]) ).
cnf(t1048,plain,
defined(g,a) = true,
inference(orient,[status(thm)],[t2185]) ).
cnf(t2331,plain,
true = ifeq(true,true,product(g,a,compose(h,a)),true),
inference(step,[status(thm)],[t2123,t1048]) ).
cnf(t2332,plain,
true = product(g,a,compose(h,a)),
inference(step,[status(thm)],[t2331,t262]) ).
cnf(t2125,plain,
product(g,a,compose(h,a)) = true,
inference(orient,[status(thm)],[t2332]) ).
cnf(t2157,plain,
g = ifeq(true,true,h,g),
inference(cp,[status(thm)],[t2156,t2125]) ).
cnf(t2336,plain,
g = h,
inference(step,[status(thm)],[t2157,t262]) ).
cnf(t2160,plain,
g = h,
inference(orient,[status(thm)],[t2336]) ).
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,t2160]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.44 % Problem : CAT004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.45 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/6.00 % Computer : n026.cluster.edu
% 0.11/6.00 % Model : x86_64 x86_64
% 0.11/6.00 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/6.00 % Memory : 8046.5625MB
% 0.11/6.00 % OS : Linux 6.8.0-71-generic
% 0.11/6.00 % CPULimit : 300
% 0.11/6.00 % WCLimit : 300
% 0.11/6.00 % DateTime : Fri Sep 25 06:54:31 UTC 2026
% 0.11/6.00 % CPUTime :
% 0.11/6.00 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 43.73/11.85 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 43.73/11.85 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------