TSTP Solution File: GRP755-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP755-1 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sat Jul 16 11:49:17 EDT 2022
% Result : Unsatisfiable 131.09s 131.26s
% Output : Refutation 131.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 10
% Syntax : Number of clauses : 63 ( 33 unt; 29 nHn; 63 RR)
% Number of literals : 97 ( 0 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP755-1.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP755-1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP755-1.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP755-1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(u,unit),u),
file('GRP755-1.p',unknown),
[] ).
cnf(6,axiom,
equal(mult(unit,u),u),
file('GRP755-1.p',unknown),
[] ).
cnf(7,axiom,
( equal(mult(mult(u,v),w),mult(u,mult(w,v)))
| equal(mult(mult(u,w),v),mult(u,mult(w,v))) ),
file('GRP755-1.p',unknown),
[] ).
cnf(8,axiom,
( equal(mult(mult(u,v),w),mult(u,mult(w,v)))
| equal(mult(mult(u,v),w),mult(u,mult(v,w))) ),
file('GRP755-1.p',unknown),
[] ).
cnf(9,axiom,
equal(ld(u,unit),i(u)),
file('GRP755-1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(mult(i(b),i(a)),i(mult(a,b))),
file('GRP755-1.p',unknown),
[] ).
cnf(16,plain,
equal(rd(u,u),unit),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(31,plain,
equal(ld(rd(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(39,plain,
equal(mult(u,i(u)),unit),
inference(spr,[status(thm),theory(equality)],[9,1]),
[iquote('0:SpR:9.0,1.0')] ).
cnf(55,plain,
equal(i(rd(unit,u)),u),
inference(spr,[status(thm),theory(equality)],[31,9]),
[iquote('0:SpR:31.0,9.0')] ).
cnf(103,plain,
( equal(mult(mult(u,i(u)),v),mult(u,mult(v,i(u))))
| equal(mult(u,mult(i(u),v)),mult(unit,v)) ),
inference(spr,[status(thm),theory(equality)],[39,8]),
[iquote('0:SpR:39.0,8.1')] ).
cnf(104,plain,
( equal(mult(mult(rd(u,v),v),w),mult(rd(u,v),mult(w,v)))
| equal(mult(rd(u,v),mult(v,w)),mult(u,w)) ),
inference(spr,[status(thm),theory(equality)],[3,8]),
[iquote('0:SpR:3.0,8.1')] ).
cnf(110,plain,
( equal(mult(u,mult(v,i(u))),v)
| equal(mult(u,mult(i(u),v)),v) ),
inference(rew,[status(thm),theory(equality)],[6,103,39]),
[iquote('0:Rew:6.0,103.1,6.0,103.0,39.0,103.0')] ).
cnf(113,plain,
( equal(mult(rd(u,v),mult(w,v)),mult(u,w))
| equal(mult(rd(u,v),mult(v,w)),mult(u,w)) ),
inference(rew,[status(thm),theory(equality)],[3,104]),
[iquote('0:Rew:3.0,104.0')] ).
cnf(124,plain,
( ~ equal(mult(u,mult(v,v)),mult(u,mult(v,v)))
| equal(mult(mult(u,v),v),mult(u,mult(v,v))) ),
inference(eqf,[status(thm),theory(equality)],[7]),
[iquote('0:EqF:7.1,7.0')] ).
cnf(144,plain,
( equal(mult(mult(u,v),w),mult(u,mult(w,v)))
| equal(rd(mult(u,mult(w,v)),v),mult(u,w)) ),
inference(spr,[status(thm),theory(equality)],[7,4]),
[iquote('0:SpR:7.1,4.0')] ).
cnf(168,plain,
equal(mult(mult(u,v),v),mult(u,mult(v,v))),
inference(obv,[status(thm),theory(equality)],[124]),
[iquote('0:Obv:124.0')] ).
cnf(175,plain,
equal(rd(mult(u,mult(v,v)),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[168,4]),
[iquote('0:SpR:168.0,4.0')] ).
cnf(186,plain,
equal(mult(u,mult(i(u),i(u))),mult(unit,i(u))),
inference(spr,[status(thm),theory(equality)],[39,168]),
[iquote('0:SpR:39.0,168.0')] ).
cnf(194,plain,
equal(mult(u,mult(i(u),i(u))),i(u)),
inference(rew,[status(thm),theory(equality)],[6,186]),
[iquote('0:Rew:6.0,186.0')] ).
cnf(199,plain,
equal(mult(i(u),i(u)),ld(u,i(u))),
inference(spr,[status(thm),theory(equality)],[194,2]),
[iquote('0:SpR:194.0,2.0')] ).
cnf(355,plain,
equal(mult(rd(u,mult(v,v)),v),rd(u,v)),
inference(spr,[status(thm),theory(equality)],[3,175]),
[iquote('0:SpR:3.0,175.0')] ).
cnf(492,plain,
equal(mult(rd(u,ld(v,i(v))),i(v)),rd(u,i(v))),
inference(spr,[status(thm),theory(equality)],[199,355]),
[iquote('0:SpR:199.0,355.0')] ).
cnf(2376,plain,
( equal(mult(mult(u,i(v)),v),mult(u,mult(v,i(v))))
| equal(rd(mult(u,unit),i(v)),mult(u,v)) ),
inference(spr,[status(thm),theory(equality)],[39,144]),
[iquote('0:SpR:39.0,144.1')] ).
cnf(2408,plain,
( equal(mult(mult(u,i(v)),v),u)
| equal(rd(u,i(v)),mult(u,v)) ),
inference(rew,[status(thm),theory(equality)],[5,2376,39]),
[iquote('0:Rew:5.0,2376.1,5.0,2376.0,39.0,2376.0')] ).
cnf(6434,plain,
( equal(mult(u,mult(v,i(u))),v)
| equal(mult(i(u),v),ld(u,v)) ),
inference(spr,[status(thm),theory(equality)],[110,2]),
[iquote('0:SpR:110.1,2.0')] ).
cnf(7445,plain,
( equal(mult(ld(u,i(u)),u),i(u))
| equal(rd(i(u),i(u)),mult(i(u),u)) ),
inference(spr,[status(thm),theory(equality)],[199,2408]),
[iquote('0:SpR:199.0,2408.0')] ).
cnf(7462,plain,
( equal(mult(ld(u,i(u)),u),i(u))
| equal(mult(i(u),u),unit) ),
inference(rew,[status(thm),theory(equality)],[16,7445]),
[iquote('0:Rew:16.0,7445.1')] ).
cnf(7642,plain,
( equal(mult(i(u),u),unit)
| equal(mult(rd(v,ld(u,i(u))),mult(u,ld(u,i(u)))),mult(v,u))
| equal(mult(rd(v,ld(u,i(u))),i(u)),mult(v,u)) ),
inference(spr,[status(thm),theory(equality)],[7462,113]),
[iquote('0:SpR:7462.0,113.1')] ).
cnf(7671,plain,
( equal(mult(i(u),u),unit)
| equal(rd(v,i(u)),mult(v,u))
| equal(rd(v,i(u)),mult(v,u)) ),
inference(rew,[status(thm),theory(equality)],[492,7642,1]),
[iquote('0:Rew:492.0,7642.2,492.0,7642.1,1.0,7642.1')] ).
cnf(7672,plain,
( equal(mult(i(u),u),unit)
| equal(rd(v,i(u)),mult(v,u)) ),
inference(obv,[status(thm),theory(equality)],[7671]),
[iquote('0:Obv:7671.1')] ).
cnf(7771,plain,
( equal(rd(u,i(v)),mult(u,v))
| equal(mult(rd(w,i(v)),mult(v,i(v))),mult(w,v))
| equal(mult(rd(w,i(v)),unit),mult(w,v)) ),
inference(spr,[status(thm),theory(equality)],[7672,113]),
[iquote('0:SpR:7672.0,113.1')] ).
cnf(7796,plain,
( equal(mult(i(u),u),unit)
| equal(mult(i(u),u),unit) ),
inference(spr,[status(thm),theory(equality)],[7672,16]),
[iquote('0:SpR:7672.1,16.0')] ).
cnf(7820,plain,
equal(mult(i(u),u),unit),
inference(obv,[status(thm),theory(equality)],[7796]),
[iquote('0:Obv:7796.0')] ).
cnf(7864,plain,
( equal(rd(u,i(v)),mult(u,v))
| equal(rd(w,i(v)),mult(w,v))
| equal(rd(w,i(v)),mult(w,v)) ),
inference(rew,[status(thm),theory(equality)],[5,7771,39]),
[iquote('0:Rew:5.0,7771.2,5.0,7771.1,39.0,7771.1')] ).
cnf(7865,plain,
( equal(rd(u,i(v)),mult(u,v))
| equal(rd(w,i(v)),mult(w,v)) ),
inference(obv,[status(thm),theory(equality)],[7864]),
[iquote('0:Obv:7864.1')] ).
cnf(7866,plain,
equal(rd(u,i(v)),mult(u,v)),
inference(con,[status(thm)],[7865]),
[iquote('0:Con:7865.1')] ).
cnf(8879,plain,
equal(rd(unit,u),i(u)),
inference(spr,[status(thm),theory(equality)],[7820,4]),
[iquote('0:SpR:7820.0,4.0')] ).
cnf(8925,plain,
( equal(mult(rd(u,v),unit),mult(u,i(v)))
| equal(mult(rd(u,v),mult(v,i(v))),mult(u,i(v))) ),
inference(spr,[status(thm),theory(equality)],[7820,113]),
[iquote('0:SpR:7820.0,113.0')] ).
cnf(8942,plain,
equal(i(i(u)),u),
inference(rew,[status(thm),theory(equality)],[8879,55]),
[iquote('0:Rew:8879.0,55.0')] ).
cnf(9035,plain,
( equal(mult(u,i(v)),rd(u,v))
| equal(mult(u,i(v)),rd(u,v)) ),
inference(rew,[status(thm),theory(equality)],[5,8925,39]),
[iquote('0:Rew:5.0,8925.1,39.0,8925.1,5.0,8925.0')] ).
cnf(9036,plain,
equal(mult(u,i(v)),rd(u,v)),
inference(obv,[status(thm),theory(equality)],[9035]),
[iquote('0:Obv:9035.0')] ).
cnf(9037,plain,
~ equal(rd(i(b),a),i(mult(a,b))),
inference(rew,[status(thm),theory(equality)],[9036,10]),
[iquote('0:Rew:9036.0,10.0')] ).
cnf(9229,plain,
( equal(mult(u,rd(v,u)),v)
| equal(mult(i(u),v),ld(u,v)) ),
inference(rew,[status(thm),theory(equality)],[9036,6434]),
[iquote('0:Rew:9036.0,6434.0')] ).
cnf(9514,plain,
equal(ld(mult(u,v),u),i(v)),
inference(spr,[status(thm),theory(equality)],[7866,31]),
[iquote('0:SpR:7866.0,31.0')] ).
cnf(17895,plain,
( equal(mult(i(u),v),ld(u,v))
| equal(rd(v,u),ld(u,v)) ),
inference(spr,[status(thm),theory(equality)],[9229,2]),
[iquote('0:SpR:9229.0,2.0')] ).
cnf(20450,plain,
( equal(rd(u,v),ld(v,u))
| equal(ld(i(v),ld(v,u)),u) ),
inference(spr,[status(thm),theory(equality)],[17895,2]),
[iquote('0:SpR:17895.0,2.0')] ).
cnf(21722,plain,
( equal(rd(mult(u,v),u),ld(u,mult(u,v)))
| equal(ld(i(u),v),mult(u,v)) ),
inference(spr,[status(thm),theory(equality)],[2,20450]),
[iquote('0:SpR:2.0,20450.1')] ).
cnf(21778,plain,
( equal(rd(mult(u,v),u),v)
| equal(ld(i(u),v),mult(u,v)) ),
inference(rew,[status(thm),theory(equality)],[2,21722]),
[iquote('0:Rew:2.0,21722.0')] ).
cnf(22382,plain,
( equal(ld(i(u),v),mult(u,v))
| equal(mult(v,u),mult(u,v)) ),
inference(spr,[status(thm),theory(equality)],[21778,3]),
[iquote('0:SpR:21778.0,3.0')] ).
cnf(24282,plain,
( equal(mult(i(u),v),ld(u,v))
| equal(mult(v,i(u)),mult(i(u),v)) ),
inference(spr,[status(thm),theory(equality)],[8942,22382]),
[iquote('0:SpR:8942.0,22382.0')] ).
cnf(24291,plain,
( equal(mult(i(u),v),ld(u,v))
| equal(mult(i(u),v),ld(u,v)) ),
inference(rew,[status(thm),theory(equality)],[17895,24282,9036]),
[iquote('0:Rew:17895.1,24282.1,9036.0,24282.1')] ).
cnf(24292,plain,
equal(mult(i(u),v),ld(u,v)),
inference(obv,[status(thm),theory(equality)],[24291]),
[iquote('0:Obv:24291.0')] ).
cnf(25494,plain,
equal(rd(ld(u,v),v),i(u)),
inference(spr,[status(thm),theory(equality)],[24292,4]),
[iquote('0:SpR:24292.0,4.0')] ).
cnf(25572,plain,
equal(rd(i(u),v),ld(u,i(v))),
inference(spr,[status(thm),theory(equality)],[24292,9036]),
[iquote('0:SpR:24292.0,9036.0')] ).
cnf(25853,plain,
~ equal(ld(b,i(a)),i(mult(a,b))),
inference(rew,[status(thm),theory(equality)],[25572,9037]),
[iquote('0:Rew:25572.0,9037.0')] ).
cnf(26528,plain,
equal(rd(i(u),v),i(mult(v,u))),
inference(spr,[status(thm),theory(equality)],[9514,25494]),
[iquote('0:SpR:9514.0,25494.0')] ).
cnf(26591,plain,
equal(ld(u,i(v)),i(mult(v,u))),
inference(rew,[status(thm),theory(equality)],[25572,26528]),
[iquote('0:Rew:25572.0,26528.0')] ).
cnf(26592,plain,
$false,
inference(unc,[status(thm)],[26591,25853]),
[iquote('0:UnC:26591.0,25853.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP755-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n028.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 15:48:07 EDT 2022
% 0.13/0.33 % CPUTime :
% 131.09/131.26
% 131.09/131.26 SPASS V 3.9
% 131.09/131.26 SPASS beiseite: Proof found.
% 131.09/131.26 % SZS status Theorem
% 131.09/131.26 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 131.09/131.26 SPASS derived 15094 clauses, backtracked 0 clauses, performed 0 splits and kept 7284 clauses.
% 131.09/131.26 SPASS allocated 93489 KBytes.
% 131.09/131.26 SPASS spent 0:2:10.63 on the problem.
% 131.09/131.26 0:00:00.03 for the input.
% 131.09/131.26 0:00:00.00 for the FLOTTER CNF translation.
% 131.09/131.26 0:00:00.31 for inferences.
% 131.09/131.26 0:00:00.00 for the backtracking.
% 131.09/131.26 0:2:10.25 for the reduction.
% 131.09/131.26
% 131.09/131.26
% 131.09/131.26 Here is a proof with depth 10, length 63 :
% 131.09/131.26 % SZS output start Refutation
% See solution above
% 131.09/131.26 Formulae used in the proof : f01 f02 f03 f04 f05 f06 f07 f08 f09 goals
% 131.09/131.26
%------------------------------------------------------------------------------