TSTP Solution File: GRP750-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP750-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 11:49:16 EDT 2022
% Result : Unsatisfiable 150.28s 150.45s
% Output : Refutation 150.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of clauses : 67 ( 67 unt; 0 nHn; 67 RR)
% Number of literals : 67 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP750-1.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP750-1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP750-1.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP750-1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(mult(u,mult(u,u)),mult(v,w)),mult(mult(u,v),mult(mult(u,u),w))),
file('GRP750-1.p',unknown),
[] ).
cnf(6,axiom,
equal(mult(mult(u,v),mult(w,w)),mult(mult(u,w),mult(v,w))),
file('GRP750-1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(mult(mult(a,b),mult(a,c)),mult(mult(a,a),mult(b,c))),
file('GRP750-1.p',unknown),
[] ).
cnf(13,plain,
equal(ld(rd(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(14,plain,
equal(rd(u,ld(v,u)),v),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(18,plain,
equal(rd(mult(mult(u,v),mult(w,v)),mult(v,v)),mult(u,w)),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(26,plain,
equal(rd(mult(mult(u,v),mult(w,w)),mult(v,w)),mult(u,w)),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(27,plain,
equal(ld(mult(u,v),mult(mult(u,w),mult(v,v))),mult(w,v)),
inference(spr,[status(thm),theory(equality)],[6,2]),
[iquote('0:SpR:6.0,2.0')] ).
cnf(37,plain,
equal(mult(mult(rd(u,v),w),mult(v,v)),mult(u,mult(w,v))),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(53,plain,
equal(rd(mult(mult(u,v),w),mult(v,v)),mult(u,rd(w,v))),
inference(spr,[status(thm),theory(equality)],[3,18]),
[iquote('0:SpR:3.0,18.0')] ).
cnf(109,plain,
equal(rd(mult(u,mult(v,v)),mult(w,v)),mult(rd(u,w),v)),
inference(spr,[status(thm),theory(equality)],[3,26]),
[iquote('0:SpR:3.0,26.0')] ).
cnf(135,plain,
equal(ld(mult(u,v),mult(w,mult(v,v))),mult(ld(u,w),v)),
inference(spr,[status(thm),theory(equality)],[1,27]),
[iquote('0:SpR:1.0,27.0')] ).
cnf(232,plain,
equal(rd(mult(mult(u,mult(u,u)),mult(v,w)),mult(mult(u,u),w)),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[5,4]),
[iquote('0:SpR:5.0,4.0')] ).
cnf(233,plain,
equal(ld(mult(u,v),mult(mult(u,mult(u,u)),mult(v,w))),mult(mult(u,u),w)),
inference(spr,[status(thm),theory(equality)],[5,2]),
[iquote('0:SpR:5.0,2.0')] ).
cnf(261,plain,
equal(mult(mult(u,mult(u,u)),mult(v,mult(w,w))),mult(mult(u,v),mult(mult(u,w),mult(u,w)))),
inference(spr,[status(thm),theory(equality)],[6,5]),
[iquote('0:SpR:6.0,5.0')] ).
cnf(309,plain,
equal(rd(mult(u,v),mult(w,w)),mult(rd(u,w),rd(v,w))),
inference(spr,[status(thm),theory(equality)],[3,53]),
[iquote('0:SpR:3.0,53.0')] ).
cnf(492,plain,
equal(rd(mult(u,mult(v,v)),w),mult(rd(u,rd(w,v)),v)),
inference(spr,[status(thm),theory(equality)],[3,109]),
[iquote('0:SpR:3.0,109.0')] ).
cnf(512,plain,
equal(rd(mult(u,mult(v,w)),mult(x,w)),mult(rd(mult(rd(u,w),v),x),w)),
inference(spr,[status(thm),theory(equality)],[37,109]),
[iquote('0:SpR:37.0,109.0')] ).
cnf(529,plain,
equal(mult(rd(mult(rd(mult(u,mult(u,u)),v),w),mult(u,u)),v),mult(u,w)),
inference(rew,[status(thm),theory(equality)],[512,232]),
[iquote('0:Rew:512.0,232.0')] ).
cnf(532,plain,
equal(mult(mult(rd(mult(rd(u,rd(v,u)),u),u),rd(w,u)),v),mult(u,w)),
inference(rew,[status(thm),theory(equality)],[309,529,492]),
[iquote('0:Rew:309.0,529.0,492.0,529.0')] ).
cnf(533,plain,
equal(mult(mult(rd(u,rd(v,u)),rd(w,u)),v),mult(u,w)),
inference(rew,[status(thm),theory(equality)],[4,532]),
[iquote('0:Rew:4.0,532.0')] ).
cnf(586,plain,
equal(mult(ld(rd(u,v),w),v),ld(u,mult(w,mult(v,v)))),
inference(spr,[status(thm),theory(equality)],[3,135]),
[iquote('0:SpR:3.0,135.0')] ).
cnf(692,plain,
equal(mult(rd(u,rd(v,u)),rd(w,u)),rd(mult(u,w),v)),
inference(spr,[status(thm),theory(equality)],[533,4]),
[iquote('0:SpR:533.0,4.0')] ).
cnf(716,plain,
equal(mult(mult(rd(u,rd(v,u)),w),v),mult(u,mult(w,u))),
inference(spr,[status(thm),theory(equality)],[4,533]),
[iquote('0:SpR:4.0,533.0')] ).
cnf(1101,plain,
equal(rd(ld(u,mult(v,mult(w,w))),w),ld(rd(u,w),v)),
inference(spr,[status(thm),theory(equality)],[586,4]),
[iquote('0:SpR:586.0,4.0')] ).
cnf(1378,plain,
equal(ld(rd(u,rd(v,u)),rd(mult(u,w),v)),rd(w,u)),
inference(spr,[status(thm),theory(equality)],[692,2]),
[iquote('0:SpR:692.0,2.0')] ).
cnf(1400,plain,
equal(rd(mult(u,mult(v,u)),w),mult(rd(u,rd(w,u)),v)),
inference(spr,[status(thm),theory(equality)],[4,692]),
[iquote('0:SpR:4.0,692.0')] ).
cnf(1404,plain,
equal(rd(mult(u,v),mult(w,u)),mult(rd(u,w),rd(v,u))),
inference(spr,[status(thm),theory(equality)],[4,692]),
[iquote('0:SpR:4.0,692.0')] ).
cnf(1443,plain,
equal(mult(mult(rd(u,v),w),mult(v,u)),mult(u,mult(w,u))),
inference(spr,[status(thm),theory(equality)],[4,716]),
[iquote('0:SpR:4.0,716.0')] ).
cnf(1538,plain,
equal(ld(mult(u,v),mult(mult(u,mult(u,u)),w)),mult(mult(u,u),ld(v,w))),
inference(spr,[status(thm),theory(equality)],[1,233]),
[iquote('0:SpR:1.0,233.0')] ).
cnf(2065,plain,
equal(rd(ld(u,mult(v,mult(w,x))),x),ld(rd(u,x),mult(rd(v,x),w))),
inference(spr,[status(thm),theory(equality)],[37,1101]),
[iquote('0:SpR:37.0,1101.0')] ).
cnf(2468,plain,
equal(ld(rd(u,rd(v,u)),rd(w,v)),rd(ld(u,w),u)),
inference(spr,[status(thm),theory(equality)],[1,1378]),
[iquote('0:SpR:1.0,1378.0')] ).
cnf(2554,plain,
equal(mult(rd(u,rd(ld(v,mult(u,mult(w,u))),u)),w),v),
inference(spr,[status(thm),theory(equality)],[1400,14]),
[iquote('0:SpR:1400.0,14.0')] ).
cnf(2603,plain,
equal(mult(rd(u,ld(rd(v,u),mult(rd(u,u),w))),w),v),
inference(rew,[status(thm),theory(equality)],[2065,2554]),
[iquote('0:Rew:2065.0,2554.0')] ).
cnf(2706,plain,
equal(mult(rd(u,v),rd(ld(u,w),u)),rd(w,mult(v,u))),
inference(spr,[status(thm),theory(equality)],[1,1404]),
[iquote('0:SpR:1.0,1404.0')] ).
cnf(2988,plain,
equal(mult(u,mult(ld(rd(u,v),w),u)),mult(w,mult(v,u))),
inference(spr,[status(thm),theory(equality)],[1,1443]),
[iquote('0:SpR:1.0,1443.0')] ).
cnf(3342,plain,
equal(ld(rd(u,rd(ld(v,w),u)),v),rd(ld(u,w),u)),
inference(spr,[status(thm),theory(equality)],[14,2468]),
[iquote('0:SpR:14.0,2468.0')] ).
cnf(3419,plain,
equal(rd(u,ld(rd(v,u),mult(rd(u,u),w))),rd(v,w)),
inference(spr,[status(thm),theory(equality)],[2603,4]),
[iquote('0:SpR:2603.0,4.0')] ).
cnf(4218,plain,
equal(mult(ld(rd(u,v),w),u),ld(u,mult(w,mult(v,u)))),
inference(spr,[status(thm),theory(equality)],[2988,2]),
[iquote('0:SpR:2988.0,2.0')] ).
cnf(4228,plain,
equal(mult(rd(u,v),rd(mult(ld(rd(u,w),x),u),u)),rd(mult(x,mult(w,u)),mult(v,u))),
inference(spr,[status(thm),theory(equality)],[2988,1404]),
[iquote('0:SpR:2988.0,1404.0')] ).
cnf(4287,plain,
equal(rd(mult(u,mult(v,w)),mult(x,w)),mult(rd(w,x),ld(rd(w,v),u))),
inference(rew,[status(thm),theory(equality)],[4,4228]),
[iquote('0:Rew:4.0,4228.0')] ).
cnf(4288,plain,
equal(mult(rd(mult(rd(u,v),w),x),v),mult(rd(v,x),ld(rd(v,w),u))),
inference(rew,[status(thm),theory(equality)],[512,4287]),
[iquote('0:Rew:512.0,4287.0')] ).
cnf(5500,plain,
equal(ld(rd(u,v),mult(rd(v,v),w)),ld(rd(u,w),v)),
inference(spr,[status(thm),theory(equality)],[3419,13]),
[iquote('0:SpR:3419.0,13.0')] ).
cnf(5548,plain,
equal(rd(u,ld(v,mult(rd(u,u),w))),rd(mult(v,u),w)),
inference(spr,[status(thm),theory(equality)],[4,3419]),
[iquote('0:SpR:4.0,3419.0')] ).
cnf(8402,plain,
equal(mult(rd(u,v),ld(rd(u,w),v)),mult(rd(v,v),w)),
inference(spr,[status(thm),theory(equality)],[5500,1]),
[iquote('0:SpR:5500.0,1.0')] ).
cnf(9345,plain,
equal(rd(u,mult(ld(v,rd(u,u)),w)),rd(mult(mult(v,w),u),mult(w,w))),
inference(spr,[status(thm),theory(equality)],[135,5548]),
[iquote('0:SpR:135.0,5548.0')] ).
cnf(9361,plain,
equal(rd(u,mult(ld(v,rd(u,u)),w)),mult(v,rd(u,w))),
inference(rew,[status(thm),theory(equality)],[4,9345,309]),
[iquote('0:Rew:4.0,9345.0,309.0,9345.0')] ).
cnf(13382,plain,
equal(mult(mult(rd(u,u),v),mult(u,w)),mult(w,mult(ld(rd(w,v),u),w))),
inference(spr,[status(thm),theory(equality)],[8402,1443]),
[iquote('0:SpR:8402.0,1443.0')] ).
cnf(13423,plain,
equal(mult(rd(u,v),rd(ld(u,w),u)),mult(rd(v,v),rd(ld(v,w),u))),
inference(spr,[status(thm),theory(equality)],[3342,8402]),
[iquote('0:SpR:3342.0,8402.0')] ).
cnf(13456,plain,
equal(mult(mult(rd(u,u),v),mult(u,w)),mult(u,mult(v,w))),
inference(rew,[status(thm),theory(equality)],[1,13382,4218]),
[iquote('0:Rew:1.0,13382.0,4218.0,13382.0')] ).
cnf(13463,plain,
equal(mult(rd(u,u),rd(ld(u,v),w)),rd(v,mult(u,w))),
inference(rew,[status(thm),theory(equality)],[2706,13423]),
[iquote('0:Rew:2706.0,13423.0')] ).
cnf(15639,plain,
equal(mult(rd(rd(u,u),v),rd(u,w)),rd(u,mult(v,w))),
inference(spr,[status(thm),theory(equality)],[13,9361]),
[iquote('0:SpR:13.0,9361.0')] ).
cnf(19902,plain,
equal(ld(mult(rd(u,u),v),mult(u,mult(v,w))),mult(u,w)),
inference(spr,[status(thm),theory(equality)],[13456,2]),
[iquote('0:SpR:13456.0,2.0')] ).
cnf(20037,plain,
equal(mult(mult(rd(u,u),v),w),mult(u,mult(v,ld(u,w)))),
inference(spr,[status(thm),theory(equality)],[1,13456]),
[iquote('0:SpR:1.0,13456.0')] ).
cnf(21624,plain,
equal(rd(mult(u,v),mult(u,w)),mult(rd(u,u),rd(v,w))),
inference(spr,[status(thm),theory(equality)],[2,13463]),
[iquote('0:SpR:2.0,13463.0')] ).
cnf(23905,plain,
equal(mult(rd(rd(mult(u,v),mult(u,v)),w),u),rd(mult(u,v),mult(w,v))),
inference(spr,[status(thm),theory(equality)],[4,15639]),
[iquote('0:SpR:4.0,15639.0')] ).
cnf(23954,plain,
equal(mult(rd(u,v),ld(rd(u,rd(w,w)),u)),rd(mult(u,w),mult(v,w))),
inference(rew,[status(thm),theory(equality)],[4288,23905,21624]),
[iquote('0:Rew:4288.0,23905.0,21624.0,23905.0')] ).
cnf(23955,plain,
equal(rd(mult(u,v),mult(w,v)),mult(rd(u,w),rd(v,v))),
inference(rew,[status(thm),theory(equality)],[13,23954]),
[iquote('0:Rew:13.0,23954.0')] ).
cnf(31812,plain,
equal(ld(mult(rd(u,u),v),mult(u,w)),mult(u,ld(v,w))),
inference(spr,[status(thm),theory(equality)],[1,19902]),
[iquote('0:SpR:1.0,19902.0')] ).
cnf(31907,plain,
equal(ld(mult(rd(mult(u,v),mult(u,v)),mult(u,w)),mult(mult(u,mult(u,u)),mult(v,mult(w,w)))),mult(mult(u,v),mult(u,w))),
inference(spr,[status(thm),theory(equality)],[261,19902]),
[iquote('0:SpR:261.0,19902.0')] ).
cnf(32132,plain,
equal(mult(mult(u,u),mult(v,ld(ld(u,mult(u,w)),mult(w,w)))),mult(mult(u,v),mult(u,w))),
inference(rew,[status(thm),theory(equality)],[31812,31907,1538,20037,23955]),
[iquote('0:Rew:31812.0,31907.0,1538.0,31907.0,20037.0,31907.0,23955.0,31907.0')] ).
cnf(32133,plain,
equal(mult(mult(u,u),mult(v,w)),mult(mult(u,v),mult(u,w))),
inference(rew,[status(thm),theory(equality)],[2,32132]),
[iquote('0:Rew:2.0,32132.0,2.0,32132.0')] ).
cnf(32134,plain,
$false,
inference(unc,[status(thm)],[32133,7]),
[iquote('0:UnC:32133.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP750-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n020.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 : Tue Jun 14 00:49:35 EDT 2022
% 0.13/0.33 % CPUTime :
% 150.28/150.45
% 150.28/150.45 SPASS V 3.9
% 150.28/150.45 SPASS beiseite: Proof found.
% 150.28/150.45 % SZS status Theorem
% 150.28/150.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 150.28/150.45 SPASS derived 20451 clauses, backtracked 0 clauses, performed 0 splits and kept 11086 clauses.
% 150.28/150.45 SPASS allocated 156271 KBytes.
% 150.28/150.45 SPASS spent 0:2:29.16 on the problem.
% 150.28/150.45 0:00:00.03 for the input.
% 150.28/150.45 0:00:00.00 for the FLOTTER CNF translation.
% 150.28/150.45 0:00:00.31 for inferences.
% 150.28/150.45 0:00:00.00 for the backtracking.
% 150.28/150.45 0:2:28.78 for the reduction.
% 150.28/150.45
% 150.28/150.45
% 150.28/150.45 Here is a proof with depth 10, length 67 :
% 150.28/150.45 % SZS output start Refutation
% See solution above
% 150.28/150.45 Formulae used in the proof : f01 f02 f03 f04 f05 f06 goals
% 150.28/150.45
%------------------------------------------------------------------------------