TSTP Solution File: GRP194+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n013.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 : Sat Jul 16 11:46:17 EDT 2022
% Result : Theorem 0.20s 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 22 ( 7 unt; 1 nHn; 22 RR)
% Number of literals : 54 ( 0 equ; 35 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
left_zero(f,f_left_zero),
file('GRP194+1.p',unknown),
[] ).
cnf(2,axiom,
group_member(skf2(u),f),
file('GRP194+1.p',unknown),
[] ).
cnf(3,axiom,
~ left_zero(h,phi(f_left_zero)),
file('GRP194+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ left_zero(u,v)
| group_member(v,u) ),
file('GRP194+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ group_member(u,f)
| group_member(phi(u),h) ),
file('GRP194+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ group_member(u,h)
| equal(phi(skf2(u)),u) ),
file('GRP194+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ group_member(u,v)
| left_zero(v,u)
| group_member(skf3(v,w),v) ),
file('GRP194+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ left_zero(u,v)
| ~ group_member(w,u)
| equal(multiply(u,v,w),v) ),
file('GRP194+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ group_member(u,v)
| ~ equal(multiply(v,u,skf3(v,u)),u)
| left_zero(v,u) ),
file('GRP194+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ group_member(u,f)
| ~ group_member(v,f)
| equal(multiply(h,phi(v),phi(u)),phi(multiply(f,v,u))) ),
file('GRP194+1.p',unknown),
[] ).
cnf(15,plain,
group_member(f_left_zero,f),
inference(res,[status(thm),theory(equality)],[1,4]),
[iquote('0:Res:1.0,4.0')] ).
cnf(39,plain,
( ~ group_member(u,h)
| ~ group_member(skf2(u),f)
| ~ group_member(v,f)
| equal(phi(multiply(f,v,skf2(u))),multiply(h,phi(v),u)) ),
inference(spr,[status(thm),theory(equality)],[6,11]),
[iquote('0:SpR:6.1,11.2')] ).
cnf(42,plain,
( ~ group_member(u,h)
| ~ group_member(v,f)
| equal(phi(multiply(f,v,skf2(u))),multiply(h,phi(v),u)) ),
inference(mrr,[status(thm)],[39,2]),
[iquote('0:MRR:39.1,2.0')] ).
cnf(148,plain,
( ~ left_zero(f,u)
| ~ group_member(skf2(v),f)
| ~ group_member(v,h)
| ~ group_member(u,f)
| equal(multiply(h,phi(u),v),phi(u)) ),
inference(spr,[status(thm),theory(equality)],[8,42]),
[iquote('0:SpR:8.2,42.2')] ).
cnf(152,plain,
( ~ left_zero(f,u)
| ~ group_member(v,h)
| equal(multiply(h,phi(u),v),phi(u)) ),
inference(mrr,[status(thm)],[148,2,4]),
[iquote('0:MRR:148.1,148.3,2.0,4.1')] ).
cnf(178,plain,
( ~ left_zero(f,u)
| ~ group_member(skf3(h,phi(u)),h)
| ~ group_member(phi(u),h)
| ~ equal(phi(u),phi(u))
| left_zero(h,phi(u)) ),
inference(spl,[status(thm),theory(equality)],[152,10]),
[iquote('0:SpL:152.2,10.1')] ).
cnf(181,plain,
( ~ left_zero(f,u)
| ~ group_member(skf3(h,phi(u)),h)
| ~ group_member(phi(u),h)
| left_zero(h,phi(u)) ),
inference(obv,[status(thm),theory(equality)],[178]),
[iquote('0:Obv:178.3')] ).
cnf(182,plain,
( ~ left_zero(f,u)
| ~ group_member(phi(u),h)
| left_zero(h,phi(u)) ),
inference(mrr,[status(thm)],[181,7]),
[iquote('0:MRR:181.1,7.2')] ).
cnf(191,plain,
( ~ left_zero(f,f_left_zero)
| ~ group_member(phi(f_left_zero),h) ),
inference(res,[status(thm),theory(equality)],[182,3]),
[iquote('0:Res:182.2,3.0')] ).
cnf(193,plain,
~ group_member(phi(f_left_zero),h),
inference(mrr,[status(thm)],[191,1]),
[iquote('0:MRR:191.0,1.0')] ).
cnf(200,plain,
~ group_member(f_left_zero,f),
inference(res,[status(thm),theory(equality)],[5,193]),
[iquote('0:Res:5.1,193.0')] ).
cnf(201,plain,
$false,
inference(mrr,[status(thm)],[200,15]),
[iquote('0:MRR:200.0,15.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 12:04:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.47
% 0.20/0.47 SPASS V 3.9
% 0.20/0.47 SPASS beiseite: Proof found.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47 SPASS derived 127 clauses, backtracked 1 clauses, performed 3 splits and kept 74 clauses.
% 0.20/0.47 SPASS allocated 85364 KBytes.
% 0.20/0.47 SPASS spent 0:00:00.12 on the problem.
% 0.20/0.47 0:00:00.04 for the input.
% 0.20/0.47 0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.47 0:00:00.00 for inferences.
% 0.20/0.47 0:00:00.00 for the backtracking.
% 0.20/0.47 0:00:00.02 for the reduction.
% 0.20/0.47
% 0.20/0.47
% 0.20/0.47 Here is a proof with depth 5, length 22 :
% 0.20/0.47 % SZS output start Refutation
% See solution above
% 0.20/0.47 Formulae used in the proof : left_zero_for_f surjective left_zero prove_left_zero_h homomorphism1 homomorphism2
% 0.20/0.47
%------------------------------------------------------------------------------