TSTP Solution File: GRP715+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP715+1 : TPTP v8.1.0. Released v4.0.0.
% 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 11:49:09 EDT 2022
% Result : Theorem 2.40s 2.59s
% Output : Refutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of clauses : 58 ( 56 unt; 0 nHn; 58 RR)
% Number of literals : 60 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
equal(mult(u,unit),u),
file('GRP715+1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(unit,u),u),
file('GRP715+1.p',unknown),
[] ).
cnf(4,axiom,
equal(mult(op_a,op_b),unit),
file('GRP715+1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(op_b,op_a),unit),
file('GRP715+1.p',unknown),
[] ).
cnf(9,axiom,
equal(mult(mult(u,v),v),mult(u,mult(v,v))),
file('GRP715+1.p',unknown),
[] ).
cnf(11,axiom,
equal(mult(mult(mult(u,v),w),v),mult(u,mult(mult(v,w),v))),
file('GRP715+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(mult(mult(skc3,op_b),op_a),skc3)
| ~ equal(mult(mult(skc2,op_a),op_b),skc2) ),
file('GRP715+1.p',unknown),
[] ).
cnf(36,plain,
equal(mult(op_b,mult(op_a,op_a)),mult(unit,op_a)),
inference(spr,[status(thm),theory(equality)],[5,9]),
[iquote('0:SpR:5.0,9.0')] ).
cnf(37,plain,
equal(mult(op_a,mult(op_b,op_b)),mult(unit,op_b)),
inference(spr,[status(thm),theory(equality)],[4,9]),
[iquote('0:SpR:4.0,9.0')] ).
cnf(41,plain,
equal(mult(op_b,mult(op_a,op_a)),op_a),
inference(rew,[status(thm),theory(equality)],[3,36]),
[iquote('0:Rew:3.0,36.0')] ).
cnf(42,plain,
equal(mult(op_a,mult(op_b,op_b)),op_b),
inference(rew,[status(thm),theory(equality)],[3,37]),
[iquote('0:Rew:3.0,37.0')] ).
cnf(45,plain,
equal(mult(op_b,mult(mult(op_a,op_a),mult(op_a,op_a))),mult(op_a,mult(op_a,op_a))),
inference(spr,[status(thm),theory(equality)],[41,9]),
[iquote('0:SpR:41.0,9.0')] ).
cnf(191,plain,
equal(mult(mult(u,mult(mult(v,w),v)),v),mult(mult(mult(u,v),w),mult(v,v))),
inference(spr,[status(thm),theory(equality)],[11,9]),
[iquote('0:SpR:11.0,9.0')] ).
cnf(194,plain,
equal(mult(u,mult(mult(v,v),v)),mult(mult(u,v),mult(v,v))),
inference(spr,[status(thm),theory(equality)],[11,9]),
[iquote('0:SpR:11.0,9.0')] ).
cnf(196,plain,
equal(mult(mult(u,mult(mult(v,w),v)),w),mult(mult(u,v),mult(mult(w,v),w))),
inference(spr,[status(thm),theory(equality)],[11]),
[iquote('0:SpR:11.0,11.0')] ).
cnf(197,plain,
equal(mult(op_b,mult(mult(op_a,u),op_a)),mult(mult(unit,u),op_a)),
inference(spr,[status(thm),theory(equality)],[5,11]),
[iquote('0:SpR:5.0,11.0')] ).
cnf(199,plain,
equal(mult(op_a,mult(mult(op_b,u),op_b)),mult(mult(unit,u),op_b)),
inference(spr,[status(thm),theory(equality)],[4,11]),
[iquote('0:SpR:4.0,11.0')] ).
cnf(204,plain,
equal(mult(mult(mult(u,mult(v,v)),w),v),mult(mult(u,v),mult(mult(v,w),v))),
inference(spr,[status(thm),theory(equality)],[9,11]),
[iquote('0:SpR:9.0,11.0')] ).
cnf(209,plain,
equal(mult(op_b,mult(mult(op_a,u),op_a)),mult(u,op_a)),
inference(rew,[status(thm),theory(equality)],[3,197]),
[iquote('0:Rew:3.0,197.0')] ).
cnf(210,plain,
equal(mult(op_a,mult(mult(op_b,u),op_b)),mult(u,op_b)),
inference(rew,[status(thm),theory(equality)],[3,199]),
[iquote('0:Rew:3.0,199.0')] ).
cnf(213,plain,
equal(mult(mult(u,v),mult(v,v)),mult(u,mult(v,mult(v,v)))),
inference(rew,[status(thm),theory(equality)],[9,194]),
[iquote('0:Rew:9.0,194.0')] ).
cnf(215,plain,
equal(mult(op_b,mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_a,mult(op_a,op_a))),
inference(rew,[status(thm),theory(equality)],[213,45]),
[iquote('0:Rew:213.0,45.0')] ).
cnf(463,plain,
equal(mult(op_b,mult(op_a,mult(op_a,op_a))),mult(op_a,op_a)),
inference(spr,[status(thm),theory(equality)],[9,209]),
[iquote('0:SpR:9.0,209.0')] ).
cnf(486,plain,
equal(mult(mult(op_a,op_a),op_b),mult(op_a,mult(op_a,op_b))),
inference(spr,[status(thm),theory(equality)],[41,210]),
[iquote('0:SpR:41.0,210.0')] ).
cnf(493,plain,
equal(mult(mult(op_a,op_a),op_b),op_a),
inference(rew,[status(thm),theory(equality)],[2,486,4]),
[iquote('0:Rew:2.0,486.0,4.0,486.0')] ).
cnf(509,plain,
equal(mult(mult(op_a,mult(op_a,op_a)),op_b),mult(op_a,mult(mult(op_a,op_a),op_b))),
inference(spr,[status(thm),theory(equality)],[463,210]),
[iquote('0:SpR:463.0,210.0')] ).
cnf(512,plain,
equal(mult(mult(op_a,mult(op_a,op_a)),op_b),mult(op_a,op_a)),
inference(rew,[status(thm),theory(equality)],[493,509]),
[iquote('0:Rew:493.0,509.0')] ).
cnf(858,plain,
equal(mult(mult(op_a,mult(op_a,op_a)),mult(op_b,op_b)),mult(mult(op_a,op_a),op_b)),
inference(spr,[status(thm),theory(equality)],[512,9]),
[iquote('0:SpR:512.0,9.0')] ).
cnf(862,plain,
equal(mult(mult(op_a,mult(op_a,op_a)),mult(op_b,op_b)),op_a),
inference(rew,[status(thm),theory(equality)],[493,858]),
[iquote('0:Rew:493.0,858.0')] ).
cnf(1577,plain,
equal(mult(mult(mult(u,op_b),op_a),mult(op_b,op_b)),mult(mult(u,mult(unit,op_b)),op_b)),
inference(spr,[status(thm),theory(equality)],[5,191]),
[iquote('0:SpR:5.0,191.0')] ).
cnf(1580,plain,
equal(mult(mult(u,mult(mult(op_a,op_a),op_b)),op_b),mult(mult(mult(u,op_b),mult(op_a,mult(op_a,op_a))),mult(op_b,op_b))),
inference(spr,[status(thm),theory(equality)],[463,191]),
[iquote('0:SpR:463.0,191.0')] ).
cnf(1659,plain,
equal(mult(mult(mult(u,op_b),op_a),mult(op_b,op_b)),mult(u,mult(op_b,op_b))),
inference(rew,[status(thm),theory(equality)],[9,1577,3]),
[iquote('0:Rew:9.0,1577.0,3.0,1577.0')] ).
cnf(1696,plain,
equal(mult(mult(mult(u,op_b),mult(op_a,mult(op_a,op_a))),mult(op_b,op_b)),mult(mult(u,op_a),op_b)),
inference(rew,[status(thm),theory(equality)],[493,1580]),
[iquote('0:Rew:493.0,1580.0')] ).
cnf(1828,plain,
equal(mult(mult(u,mult(op_a,op_b)),mult(op_a,op_a)),mult(mult(u,op_b),mult(mult(mult(op_a,op_a),op_b),mult(op_a,op_a)))),
inference(spr,[status(thm),theory(equality)],[41,196]),
[iquote('0:SpR:41.0,196.0')] ).
cnf(1845,plain,
equal(mult(mult(u,mult(op_a,mult(op_a,op_a))),op_b),mult(mult(u,mult(op_a,op_a)),mult(mult(op_b,mult(op_a,op_a)),op_b))),
inference(spr,[status(thm),theory(equality)],[493,196]),
[iquote('0:SpR:493.0,196.0')] ).
cnf(1853,plain,
equal(mult(mult(u,mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_b,op_b)),mult(mult(u,mult(op_a,mult(op_a,op_a))),mult(mult(mult(op_b,op_b),mult(op_a,mult(op_a,op_a))),mult(op_b,op_b)))),
inference(spr,[status(thm),theory(equality)],[862,196]),
[iquote('0:SpR:862.0,196.0')] ).
cnf(1900,plain,
equal(mult(mult(u,mult(op_a,mult(op_a,op_a))),op_b),mult(u,mult(op_a,op_a))),
inference(rew,[status(thm),theory(equality)],[2,1845,4,41]),
[iquote('0:Rew:2.0,1845.0,4.0,1845.0,41.0,1845.0')] ).
cnf(1909,plain,
equal(mult(mult(u,op_b),mult(op_a,mult(op_a,op_a))),mult(u,mult(op_a,op_a))),
inference(rew,[status(thm),theory(equality)],[2,1828,4,493]),
[iquote('0:Rew:2.0,1828.0,4.0,1828.0,493.0,1828.0')] ).
cnf(1911,plain,
equal(mult(mult(u,mult(op_a,op_a)),mult(op_b,op_b)),mult(mult(u,op_a),op_b)),
inference(rew,[status(thm),theory(equality)],[1909,1696]),
[iquote('0:Rew:1909.0,1696.0')] ).
cnf(1952,plain,
equal(mult(mult(u,mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_b,op_b)),mult(mult(u,mult(op_a,mult(op_a,op_a))),mult(mult(op_b,op_a),op_b))),
inference(rew,[status(thm),theory(equality)],[1911,1853,1909]),
[iquote('0:Rew:1911.0,1853.0,1909.0,1853.0')] ).
cnf(1953,plain,
equal(mult(mult(u,mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_b,op_b)),mult(mult(u,mult(op_a,mult(op_a,op_a))),op_b)),
inference(rew,[status(thm),theory(equality)],[3,1952,5]),
[iquote('0:Rew:3.0,1952.0,5.0,1952.0')] ).
cnf(1954,plain,
equal(mult(mult(u,mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_b,op_b)),mult(u,mult(op_a,op_a))),
inference(rew,[status(thm),theory(equality)],[1900,1953]),
[iquote('0:Rew:1900.0,1953.0')] ).
cnf(6373,plain,
equal(mult(mult(u,mult(mult(op_a,mult(op_a,op_a)),op_b)),op_b),mult(mult(mult(u,op_b),mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_b,op_b))),
inference(spr,[status(thm),theory(equality)],[215,191]),
[iquote('0:SpR:215.0,191.0')] ).
cnf(6379,plain,
equal(mult(mult(mult(u,op_b),mult(op_a,mult(op_a,mult(op_a,op_a)))),mult(op_b,op_b)),mult(mult(u,mult(op_a,op_a)),op_b)),
inference(rew,[status(thm),theory(equality)],[512,6373]),
[iquote('0:Rew:512.0,6373.0')] ).
cnf(6380,plain,
equal(mult(mult(u,mult(op_a,op_a)),op_b),mult(mult(u,op_b),mult(op_a,op_a))),
inference(rew,[status(thm),theory(equality)],[1954,6379]),
[iquote('0:Rew:1954.0,6379.0')] ).
cnf(7264,plain,
equal(mult(mult(u,mult(op_b,op_b)),op_a),mult(mult(u,op_b),mult(mult(op_a,mult(op_b,op_b)),op_a))),
inference(spr,[status(thm),theory(equality)],[1659,11]),
[iquote('0:SpR:1659.0,11.0')] ).
cnf(7297,plain,
equal(mult(mult(u,mult(op_b,op_b)),op_a),mult(u,op_b)),
inference(rew,[status(thm),theory(equality)],[2,7264,5,42]),
[iquote('0:Rew:2.0,7264.0,5.0,7264.0,42.0,7264.0')] ).
cnf(7359,plain,
equal(mult(mult(u,op_a),op_b),mult(u,mult(mult(op_a,mult(op_b,op_b)),op_a))),
inference(spr,[status(thm),theory(equality)],[7297,11]),
[iquote('0:SpR:7297.0,11.0')] ).
cnf(7360,plain,
equal(mult(mult(u,mult(op_a,op_a)),op_b),mult(mult(u,op_a),mult(mult(op_a,mult(op_b,op_b)),op_a))),
inference(spr,[status(thm),theory(equality)],[7297,204]),
[iquote('0:SpR:7297.0,204.0')] ).
cnf(7395,plain,
equal(mult(mult(u,op_a),op_b),u),
inference(rew,[status(thm),theory(equality)],[2,7359,5,42]),
[iquote('0:Rew:2.0,7359.0,5.0,7359.0,42.0,7359.0')] ).
cnf(7398,plain,
( ~ equal(mult(mult(skc3,op_b),op_a),skc3)
| ~ equal(skc2,skc2) ),
inference(rew,[status(thm),theory(equality)],[7395,12]),
[iquote('0:Rew:7395.0,12.1')] ).
cnf(7457,plain,
~ equal(mult(mult(skc3,op_b),op_a),skc3),
inference(obv,[status(thm),theory(equality)],[7398]),
[iquote('0:Obv:7398.1')] ).
cnf(7470,plain,
equal(mult(mult(u,mult(op_a,op_a)),op_b),mult(u,op_a)),
inference(rew,[status(thm),theory(equality)],[2,7360,5,42]),
[iquote('0:Rew:2.0,7360.0,5.0,7360.0,42.0,7360.0')] ).
cnf(7471,plain,
equal(mult(mult(u,op_b),mult(op_a,op_a)),mult(u,op_a)),
inference(rew,[status(thm),theory(equality)],[6380,7470]),
[iquote('0:Rew:6380.0,7470.0')] ).
cnf(7474,plain,
equal(mult(mult(u,mult(op_a,op_a)),op_b),mult(u,op_a)),
inference(rew,[status(thm),theory(equality)],[7471,6380]),
[iquote('0:Rew:7471.0,6380.0')] ).
cnf(7987,plain,
equal(mult(mult(u,op_b),op_a),mult(mult(u,op_a),op_b)),
inference(spr,[status(thm),theory(equality)],[7471,7474]),
[iquote('0:SpR:7471.0,7474.0')] ).
cnf(7991,plain,
equal(mult(mult(u,op_b),op_a),u),
inference(rew,[status(thm),theory(equality)],[7395,7987]),
[iquote('0:Rew:7395.0,7987.0')] ).
cnf(7992,plain,
$false,
inference(unc,[status(thm)],[7991,7457]),
[iquote('0:UnC:7991.0,7457.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP715+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 10:58:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.40/2.59
% 2.40/2.59 SPASS V 3.9
% 2.40/2.59 SPASS beiseite: Proof found.
% 2.40/2.59 % SZS status Theorem
% 2.40/2.59 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.40/2.59 SPASS derived 4500 clauses, backtracked 0 clauses, performed 0 splits and kept 1354 clauses.
% 2.40/2.59 SPASS allocated 98584 KBytes.
% 2.40/2.59 SPASS spent 0:00:02.18 on the problem.
% 2.40/2.59 0:00:00.04 for the input.
% 2.40/2.59 0:00:00.02 for the FLOTTER CNF translation.
% 2.40/2.59 0:00:00.04 for inferences.
% 2.40/2.59 0:00:00.00 for the backtracking.
% 2.40/2.59 0:00:02.05 for the reduction.
% 2.40/2.59
% 2.40/2.59
% 2.40/2.59 Here is a proof with depth 5, length 58 :
% 2.40/2.59 % SZS output start Refutation
% See solution above
% 2.40/2.59 Formulae used in the proof : f08 f09 f10 f11 f07 f06 goals
% 2.40/2.59
%------------------------------------------------------------------------------