TSTP Solution File: CAT003-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT003-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Fri Jul 15 00:07:27 EDT 2022
% Result : Unsatisfiable 24.59s 24.80s
% Output : Refutation 24.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of clauses : 49 ( 16 unt; 0 nHn; 49 RR)
% Number of literals : 105 ( 0 equ; 62 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
product(a,b,c),
file('CAT003-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(u,c,v)
| ~ product(w,c,v)
| equal(w,u) ),
file('CAT003-1.p',unknown),
[] ).
cnf(3,axiom,
product(h,a,d),
file('CAT003-1.p',unknown),
[] ).
cnf(4,axiom,
product(g,a,d),
file('CAT003-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(g,h),
file('CAT003-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ defined(u,v)
| product(u,v,compose(u,v)) ),
file('CAT003-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ product(u,v,w)
| defined(u,v) ),
file('CAT003-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ defined(u,v)
| ~ product(w,x,u)
| defined(x,v) ),
file('CAT003-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ defined(u,v)
| ~ product(w,v,x)
| ~ product(y,w,u)
| defined(y,x) ),
file('CAT003-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,u,x)
| product(z,w,y) ),
file('CAT003-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ defined(u,v)
| ~ product(u,w,x)
| ~ product(w,y,v)
| defined(x,y) ),
file('CAT003-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(u,v,w)
| ~ product(u,x,y)
| ~ product(v,z,x)
| product(w,z,y) ),
file('CAT003-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ identity_map(u)
| ~ defined(v,u)
| ~ defined(u,w)
| defined(v,w) ),
file('CAT003-1.p',unknown),
[] ).
cnf(15,axiom,
identity_map(domain__dfg(u)),
file('CAT003-1.p',unknown),
[] ).
cnf(19,axiom,
product(u,domain__dfg(u),u),
file('CAT003-1.p',unknown),
[] ).
cnf(23,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('CAT003-1.p',unknown),
[] ).
cnf(25,plain,
( ~ product(h,c,u)
| ~ product(g,c,u) ),
inference(res,[status(thm),theory(equality)],[2,5]),
[iquote('0:Res:2.2,5.0')] ).
cnf(28,plain,
defined(g,a),
inference(res,[status(thm),theory(equality)],[4,7]),
[iquote('0:Res:4.0,7.0')] ).
cnf(30,plain,
defined(a,b),
inference(res,[status(thm),theory(equality)],[1,7]),
[iquote('0:Res:1.0,7.0')] ).
cnf(34,plain,
( ~ defined(g,c)
| ~ product(h,c,compose(g,c)) ),
inference(res,[status(thm),theory(equality)],[6,25]),
[iquote('0:Res:6.1,25.1')] ).
cnf(61,plain,
( ~ defined(u,v)
| defined(domain__dfg(u),v) ),
inference(res,[status(thm),theory(equality)],[19,8]),
[iquote('0:Res:19.0,8.1')] ).
cnf(80,plain,
( ~ defined(u,v)
| ~ product(u,v,w)
| equal(w,compose(u,v)) ),
inference(res,[status(thm),theory(equality)],[6,23]),
[iquote('0:Res:6.1,23.0')] ).
cnf(83,plain,
( ~ product(u,v,w)
| equal(w,compose(u,v)) ),
inference(mrr,[status(thm)],[80,7]),
[iquote('0:MRR:80.0,7.1')] ).
cnf(127,plain,
( ~ defined(g,u)
| ~ product(a,v,u)
| defined(d,v) ),
inference(res,[status(thm),theory(equality)],[4,12]),
[iquote('0:Res:4.0,12.1')] ).
cnf(128,plain,
( ~ defined(h,u)
| ~ product(a,v,u)
| defined(d,v) ),
inference(res,[status(thm),theory(equality)],[3,12]),
[iquote('0:Res:3.0,12.1')] ).
cnf(149,plain,
( ~ defined(u,b)
| ~ product(v,a,u)
| defined(v,c) ),
inference(res,[status(thm),theory(equality)],[1,9]),
[iquote('0:Res:1.0,9.1')] ).
cnf(162,plain,
( ~ product(g,u,v)
| ~ product(a,w,u)
| product(d,w,v) ),
inference(res,[status(thm),theory(equality)],[4,13]),
[iquote('0:Res:4.0,13.0')] ).
cnf(184,plain,
( ~ product(u,b,v)
| ~ product(w,a,u)
| product(w,c,v) ),
inference(res,[status(thm),theory(equality)],[1,10]),
[iquote('0:Res:1.0,10.0')] ).
cnf(396,plain,
( ~ defined(g,a)
| defined(d,domain__dfg(a)) ),
inference(res,[status(thm),theory(equality)],[19,127]),
[iquote('0:Res:19.0,127.1')] ).
cnf(401,plain,
defined(d,domain__dfg(a)),
inference(mrr,[status(thm)],[396,28]),
[iquote('0:MRR:396.0,28.0')] ).
cnf(404,plain,
( ~ identity_map(domain__dfg(a))
| ~ defined(domain__dfg(a),u)
| defined(d,u) ),
inference(res,[status(thm),theory(equality)],[401,14]),
[iquote('0:Res:401.0,14.1')] ).
cnf(406,plain,
( ~ defined(domain__dfg(a),u)
| defined(d,u) ),
inference(ssi,[status(thm)],[404,15]),
[iquote('0:SSi:404.0,15.0')] ).
cnf(416,plain,
( ~ defined(a,u)
| defined(d,u) ),
inference(res,[status(thm),theory(equality)],[61,406]),
[iquote('0:Res:61.1,406.0')] ).
cnf(424,plain,
( ~ defined(h,c)
| defined(d,b) ),
inference(res,[status(thm),theory(equality)],[1,128]),
[iquote('0:Res:1.0,128.1')] ).
cnf(527,plain,
( ~ defined(d,b)
| defined(g,c) ),
inference(res,[status(thm),theory(equality)],[4,149]),
[iquote('0:Res:4.0,149.1')] ).
cnf(528,plain,
( ~ defined(d,b)
| defined(h,c) ),
inference(res,[status(thm),theory(equality)],[3,149]),
[iquote('0:Res:3.0,149.1')] ).
cnf(575,plain,
( ~ defined(a,b)
| defined(h,c) ),
inference(res,[status(thm),theory(equality)],[416,528]),
[iquote('0:Res:416.1,528.0')] ).
cnf(577,plain,
defined(h,c),
inference(mrr,[status(thm)],[575,30]),
[iquote('0:MRR:575.0,30.0')] ).
cnf(578,plain,
defined(d,b),
inference(mrr,[status(thm)],[424,577]),
[iquote('0:MRR:424.0,577.0')] ).
cnf(579,plain,
defined(g,c),
inference(mrr,[status(thm)],[527,578]),
[iquote('0:MRR:527.0,578.0')] ).
cnf(581,plain,
~ product(h,c,compose(g,c)),
inference(mrr,[status(thm)],[34,579]),
[iquote('0:MRR:34.0,579.0')] ).
cnf(685,plain,
( ~ defined(g,u)
| ~ product(a,v,u)
| product(d,v,compose(g,u)) ),
inference(res,[status(thm),theory(equality)],[6,162]),
[iquote('0:Res:6.1,162.0')] ).
cnf(840,plain,
( ~ defined(u,b)
| ~ product(v,a,u)
| product(v,c,compose(u,b)) ),
inference(res,[status(thm),theory(equality)],[6,184]),
[iquote('0:Res:6.1,184.0')] ).
cnf(6533,plain,
( ~ defined(g,u)
| ~ product(a,v,u)
| equal(compose(g,u),compose(d,v)) ),
inference(res,[status(thm),theory(equality)],[685,83]),
[iquote('0:Res:685.2,83.0')] ).
cnf(56490,plain,
( ~ defined(g,c)
| equal(compose(g,c),compose(d,b)) ),
inference(res,[status(thm),theory(equality)],[1,6533]),
[iquote('0:Res:1.0,6533.1')] ).
cnf(56522,plain,
equal(compose(g,c),compose(d,b)),
inference(mrr,[status(thm)],[56490,579]),
[iquote('0:MRR:56490.0,579.0')] ).
cnf(56523,plain,
~ product(h,c,compose(d,b)),
inference(rew,[status(thm),theory(equality)],[56522,581]),
[iquote('0:Rew:56522.0,581.0')] ).
cnf(56930,plain,
( ~ defined(d,b)
| ~ product(h,a,d) ),
inference(res,[status(thm),theory(equality)],[840,56523]),
[iquote('0:Res:840.2,56523.0')] ).
cnf(56931,plain,
$false,
inference(mrr,[status(thm)],[56930,578,3]),
[iquote('0:MRR:56930.0,56930.1,578.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : CAT003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun May 29 19:24:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 24.59/24.80
% 24.59/24.80 SPASS V 3.9
% 24.59/24.80 SPASS beiseite: Proof found.
% 24.59/24.80 % SZS status Theorem
% 24.59/24.80 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.59/24.80 SPASS derived 41816 clauses, backtracked 0 clauses, performed 0 splits and kept 13289 clauses.
% 24.59/24.80 SPASS allocated 107592 KBytes.
% 24.59/24.80 SPASS spent 0:0:23.46 on the problem.
% 24.59/24.80 0:00:00.04 for the input.
% 24.59/24.80 0:00:00.00 for the FLOTTER CNF translation.
% 24.59/24.80 0:00:00.35 for inferences.
% 24.59/24.80 0:00:00.00 for the backtracking.
% 24.59/24.80 0:0:22.86 for the reduction.
% 24.59/24.80
% 24.59/24.80
% 24.59/24.80 Here is a proof with depth 5, length 49 :
% 24.59/24.80 % SZS output start Refutation
% See solution above
% 24.59/24.80 Formulae used in the proof : ab_equals_c cancellation_for_product ha_equals_d ga_equals_d prove_h_equals_g closure_of_composition associative_property1 associative_property2 category_theory_axiom1 category_theory_axiom2 category_theory_axiom4 category_theory_axiom5 category_theory_axiom6 domain_is_an_identity_map product_on_domain composition_is_well_defined
% 24.59/24.80
%------------------------------------------------------------------------------