%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : CAT001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 00:07:26 EDT 2022
% Result : Unsatisfiable 26.89s 27.13s
% Output : Refutation 26.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of clauses : 43 ( 15 unt; 0 nHn; 43 RR)
% Number of literals : 89 ( 0 equ; 52 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('CAT001-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(c,u,v)
| ~ product(c,w,v)
| equal(w,u) ),
file('CAT001-1.p',unknown),
[] ).
cnf(3,axiom,
product(b,h,d),
file('CAT001-1.p',unknown),
[] ).
cnf(4,axiom,
product(b,g,d),
file('CAT001-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(g,h),
file('CAT001-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ defined(u,v)
| product(u,v,compose(u,v)) ),
file('CAT001-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ product(u,v,w)
| defined(u,v) ),
file('CAT001-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ defined(u,v)
| ~ product(w,x,u)
| defined(x,v) ),
file('CAT001-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ defined(u,v)
| ~ product(w,v,x)
| ~ product(y,w,u)
| defined(y,x) ),
file('CAT001-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ defined(u,v)
| ~ product(u,w,x)
| ~ product(w,y,v)
| defined(x,y) ),
file('CAT001-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(u,v,w)
| ~ product(u,x,y)
| ~ product(v,z,x)
| product(w,z,y) ),
file('CAT001-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ identity_map(u)
| ~ defined(v,u)
| ~ defined(u,w)
| defined(v,w) ),
file('CAT001-1.p',unknown),
[] ).
cnf(15,axiom,
identity_map(domain__dfg(u)),
file('CAT001-1.p',unknown),
[] ).
cnf(19,axiom,
product(u,domain__dfg(u),u),
file('CAT001-1.p',unknown),
[] ).
cnf(23,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('CAT001-1.p',unknown),
[] ).
cnf(25,plain,
( ~ product(c,h,u)
| ~ product(c,g,u) ),
inference(res,[status(thm),theory(equality)],[2,5]),
[iquote('0:Res:2.2,5.0')] ).
cnf(28,plain,
defined(b,g),
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(c,g)
| ~ product(c,h,compose(c,g)) ),
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(130,plain,
( ~ defined(a,u)
| ~ product(b,v,u)
| defined(c,v) ),
inference(res,[status(thm),theory(equality)],[1,12]),
[iquote('0:Res:1.0,12.1')] ).
cnf(150,plain,
( ~ defined(u,g)
| ~ product(v,b,u)
| defined(v,d) ),
inference(res,[status(thm),theory(equality)],[4,9]),
[iquote('0:Res:4.0,9.1')] ).
cnf(168,plain,
( ~ product(a,u,v)
| ~ product(b,w,u)
| product(c,w,v) ),
inference(res,[status(thm),theory(equality)],[1,13]),
[iquote('0:Res:1.0,13.0')] ).
cnf(466,plain,
( ~ defined(a,d)
| defined(c,g) ),
inference(res,[status(thm),theory(equality)],[4,130]),
[iquote('0:Res:4.0,130.1')] ).
cnf(468,plain,
( ~ defined(a,b)
| defined(c,domain__dfg(b)) ),
inference(res,[status(thm),theory(equality)],[19,130]),
[iquote('0:Res:19.0,130.1')] ).
cnf(473,plain,
defined(c,domain__dfg(b)),
inference(mrr,[status(thm)],[468,30]),
[iquote('0:MRR:468.0,30.0')] ).
cnf(476,plain,
( ~ identity_map(domain__dfg(b))
| ~ defined(domain__dfg(b),u)
| defined(c,u) ),
inference(res,[status(thm),theory(equality)],[473,14]),
[iquote('0:Res:473.0,14.1')] ).
cnf(478,plain,
( ~ defined(domain__dfg(b),u)
| defined(c,u) ),
inference(ssi,[status(thm)],[476,15]),
[iquote('0:SSi:476.0,15.0')] ).
cnf(498,plain,
( ~ defined(c,g)
| defined(a,d) ),
inference(res,[status(thm),theory(equality)],[1,150]),
[iquote('0:Res:1.0,150.1')] ).
cnf(728,plain,
( ~ defined(b,u)
| defined(c,u) ),
inference(res,[status(thm),theory(equality)],[61,478]),
[iquote('0:Res:61.1,478.0')] ).
cnf(770,plain,
( ~ defined(b,g)
| defined(a,d) ),
inference(res,[status(thm),theory(equality)],[728,498]),
[iquote('0:Res:728.1,498.0')] ).
cnf(775,plain,
defined(a,d),
inference(mrr,[status(thm)],[770,28]),
[iquote('0:MRR:770.0,28.0')] ).
cnf(776,plain,
defined(c,g),
inference(mrr,[status(thm)],[466,775]),
[iquote('0:MRR:466.0,775.0')] ).
cnf(778,plain,
~ product(c,h,compose(c,g)),
inference(mrr,[status(thm)],[34,776]),
[iquote('0:MRR:34.0,776.0')] ).
cnf(789,plain,
( ~ defined(a,u)
| ~ product(b,v,u)
| product(c,v,compose(a,u)) ),
inference(res,[status(thm),theory(equality)],[6,168]),
[iquote('0:Res:6.1,168.0')] ).
cnf(7685,plain,
( ~ defined(a,u)
| ~ product(b,v,u)
| equal(compose(a,u),compose(c,v)) ),
inference(res,[status(thm),theory(equality)],[789,83]),
[iquote('0:Res:789.2,83.0')] ).
cnf(53880,plain,
( ~ defined(a,d)
| equal(compose(c,g),compose(a,d)) ),
inference(res,[status(thm),theory(equality)],[4,7685]),
[iquote('0:Res:4.0,7685.1')] ).
cnf(53912,plain,
equal(compose(c,g),compose(a,d)),
inference(mrr,[status(thm)],[53880,775]),
[iquote('0:MRR:53880.0,775.0')] ).
cnf(53913,plain,
~ product(c,h,compose(a,d)),
inference(rew,[status(thm),theory(equality)],[53912,778]),
[iquote('0:Rew:53912.0,778.0')] ).
cnf(54484,plain,
( ~ defined(a,d)
| ~ product(b,h,d) ),
inference(res,[status(thm),theory(equality)],[789,53913]),
[iquote('0:Res:789.2,53913.0')] ).
cnf(54485,plain,
$false,
inference(mrr,[status(thm)],[54484,775,3]),
[iquote('0:MRR:54484.0,54484.1,775.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : CAT001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun May 29 22:51:58 EDT 2022
% 0.14/0.35 % CPUTime :
% 26.89/27.13
% 26.89/27.13 SPASS V 3.9
% 26.89/27.13 SPASS beiseite: Proof found.
% 26.89/27.13 % SZS status Theorem
% 26.89/27.13 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.89/27.13 SPASS derived 40039 clauses, backtracked 0 clauses, performed 0 splits and kept 12453 clauses.
% 26.89/27.13 SPASS allocated 106228 KBytes.
% 26.89/27.13 SPASS spent 0:0:25.69 on the problem.
% 26.89/27.13 0:00:00.03 for the input.
% 26.89/27.13 0:00:00.00 for the FLOTTER CNF translation.
% 26.89/27.13 0:00:00.41 for inferences.
% 26.89/27.13 0:00:00.00 for the backtracking.
% 26.89/27.13 0:0:24.96 for the reduction.
% 26.89/27.13
% 26.89/27.13
% 26.89/27.13 Here is a proof with depth 5, length 43 :
% 26.89/27.13 % SZS output start Refutation
% See solution above
% 26.89/27.13 Formulae used in the proof : ab_equals_c cancellation_for_product bh_equals_d bg_equals_d prove_h_equals_g closure_of_composition associative_property1 associative_property2 category_theory_axiom1 category_theory_axiom4 category_theory_axiom5 category_theory_axiom6 domain_is_an_identity_map product_on_domain composition_is_well_defined
% 26.89/27.13
%------------------------------------------------------------------------------