TSTP Solution File: GRP707-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP707-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 11:49:06 EDT 2022
% Result : Unsatisfiable 0.87s 1.13s
% Output : Refutation 0.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 10
% Syntax : Number of clauses : 156 ( 156 unt; 0 nHn; 156 RR)
% Number of literals : 156 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(mult(u,ld(u,v)),v),
file('GRP707-1.p',unknown),
[] ).
cnf(2,axiom,
equal(ld(u,mult(u,v)),v),
file('GRP707-1.p',unknown),
[] ).
cnf(3,axiom,
equal(mult(rd(u,v),v),u),
file('GRP707-1.p',unknown),
[] ).
cnf(4,axiom,
equal(rd(mult(u,v),v),u),
file('GRP707-1.p',unknown),
[] ).
cnf(5,axiom,
equal(mult(u,unit),u),
file('GRP707-1.p',unknown),
[] ).
cnf(6,axiom,
equal(mult(unit,u),u),
file('GRP707-1.p',unknown),
[] ).
cnf(7,axiom,
equal(mult(mult(mult(u,v),v),w),mult(u,mult(v,mult(v,w)))),
file('GRP707-1.p',unknown),
[] ).
cnf(8,axiom,
equal(mult(u,mult(u,mult(u,u))),unit),
file('GRP707-1.p',unknown),
[] ).
cnf(9,axiom,
equal(mult(mult(u,u),v),mult(v,mult(u,u))),
file('GRP707-1.p',unknown),
[] ).
cnf(10,axiom,
~ equal(mult(mult(a,b),a),mult(a,mult(b,a))),
file('GRP707-1.p',unknown),
[] ).
cnf(28,plain,
equal(ld(unit,u),u),
inference(spr,[status(thm),theory(equality)],[6,2]),
[iquote('0:SpR:6.0,2.0')] ).
cnf(30,plain,
equal(ld(rd(u,v),u),v),
inference(spr,[status(thm),theory(equality)],[3,2]),
[iquote('0:SpR:3.0,2.0')] ).
cnf(36,plain,
equal(rd(u,ld(v,u)),v),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(56,plain,
equal(mult(u,mult(u,u)),ld(u,unit)),
inference(spr,[status(thm),theory(equality)],[8,2]),
[iquote('0:SpR:8.0,2.0')] ).
cnf(69,plain,
equal(ld(u,ld(u,unit)),mult(u,u)),
inference(spr,[status(thm),theory(equality)],[56,2]),
[iquote('0:SpR:56.0,2.0')] ).
cnf(77,plain,
equal(rd(mult(u,mult(v,v)),u),mult(v,v)),
inference(spr,[status(thm),theory(equality)],[9,4]),
[iquote('0:SpR:9.0,4.0')] ).
cnf(78,plain,
equal(ld(mult(u,u),mult(v,mult(u,u))),v),
inference(spr,[status(thm),theory(equality)],[9,2]),
[iquote('0:SpR:9.0,2.0')] ).
cnf(84,plain,
equal(ld(u,mult(mult(v,v),u)),mult(v,v)),
inference(spr,[status(thm),theory(equality)],[9,2]),
[iquote('0:SpR:9.0,2.0')] ).
cnf(118,plain,
equal(mult(rd(unit,u),rd(unit,u)),ld(rd(unit,u),u)),
inference(spr,[status(thm),theory(equality)],[30,69]),
[iquote('0:SpR:30.0,69.0')] ).
cnf(133,plain,
equal(rd(ld(u,unit),u),mult(u,u)),
inference(spr,[status(thm),theory(equality)],[56,77]),
[iquote('0:SpR:56.0,77.0')] ).
cnf(145,plain,
equal(mult(rd(unit,u),rd(unit,u)),rd(u,rd(unit,u))),
inference(spr,[status(thm),theory(equality)],[30,133]),
[iquote('0:SpR:30.0,133.0')] ).
cnf(150,plain,
equal(rd(u,rd(unit,u)),ld(rd(unit,u),u)),
inference(rew,[status(thm),theory(equality)],[118,145]),
[iquote('0:Rew:118.0,145.0')] ).
cnf(167,plain,
equal(mult(ld(rd(unit,u),u),rd(unit,u)),u),
inference(spr,[status(thm),theory(equality)],[150,3]),
[iquote('0:SpR:150.0,3.0')] ).
cnf(220,plain,
equal(mult(u,mult(v,mult(v,unit))),mult(mult(u,v),v)),
inference(spr,[status(thm),theory(equality)],[7,5]),
[iquote('0:SpR:7.0,5.0')] ).
cnf(235,plain,
equal(mult(unit,mult(u,mult(u,v))),mult(mult(u,u),v)),
inference(spr,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpR:6.0,7.0')] ).
cnf(242,plain,
equal(mult(ld(rd(unit,u),u),mult(rd(unit,u),mult(rd(unit,u),v))),mult(mult(u,rd(unit,u)),v)),
inference(spr,[status(thm),theory(equality)],[167,7]),
[iquote('0:SpR:167.0,7.0')] ).
cnf(244,plain,
equal(mult(mult(u,mult(u,u)),v),mult(u,mult(u,mult(u,v)))),
inference(spr,[status(thm),theory(equality)],[9,7]),
[iquote('0:SpR:9.0,7.0')] ).
cnf(246,plain,
equal(mult(mult(u,v),v),mult(u,mult(v,v))),
inference(rew,[status(thm),theory(equality)],[5,220]),
[iquote('0:Rew:5.0,220.0')] ).
cnf(247,plain,
equal(mult(mult(u,mult(v,v)),w),mult(u,mult(v,mult(v,w)))),
inference(rew,[status(thm),theory(equality)],[246,7]),
[iquote('0:Rew:246.0,7.0')] ).
cnf(248,plain,
equal(mult(mult(u,u),v),mult(u,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[6,235]),
[iquote('0:Rew:6.0,235.0')] ).
cnf(249,plain,
equal(mult(u,mult(u,v)),mult(v,mult(u,u))),
inference(rew,[status(thm),theory(equality)],[248,9]),
[iquote('0:Rew:248.0,9.0')] ).
cnf(251,plain,
equal(ld(u,mult(v,mult(v,u))),mult(v,v)),
inference(rew,[status(thm),theory(equality)],[248,84]),
[iquote('0:Rew:248.0,84.0')] ).
cnf(258,plain,
equal(mult(u,mult(u,mult(u,v))),mult(ld(u,unit),v)),
inference(rew,[status(thm),theory(equality)],[56,244]),
[iquote('0:Rew:56.0,244.0')] ).
cnf(297,plain,
equal(rd(mult(u,mult(v,v)),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[246,4]),
[iquote('0:SpR:246.0,4.0')] ).
cnf(299,plain,
equal(mult(mult(u,mult(v,v)),v),mult(mult(u,v),mult(v,v))),
inference(spr,[status(thm),theory(equality)],[246]),
[iquote('0:SpR:246.0,246.0')] ).
cnf(302,plain,
equal(ld(mult(u,u),mult(v,mult(mult(u,u),mult(u,u)))),mult(v,mult(u,u))),
inference(spr,[status(thm),theory(equality)],[246,78]),
[iquote('0:SpR:246.0,78.0')] ).
cnf(305,plain,
equal(mult(u,mult(ld(u,v),ld(u,v))),mult(v,ld(u,v))),
inference(spr,[status(thm),theory(equality)],[1,246]),
[iquote('0:SpR:1.0,246.0')] ).
cnf(307,plain,
equal(mult(rd(u,v),mult(v,v)),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[3,246]),
[iquote('0:SpR:3.0,246.0')] ).
cnf(311,plain,
equal(mult(u,mult(u,rd(v,u))),mult(v,u)),
inference(rew,[status(thm),theory(equality)],[249,307]),
[iquote('0:Rew:249.0,307.0')] ).
cnf(312,plain,
equal(mult(u,mult(v,mult(v,v))),mult(v,mult(v,mult(u,v)))),
inference(rew,[status(thm),theory(equality)],[247,299,249]),
[iquote('0:Rew:247.0,299.0,249.0,299.0')] ).
cnf(313,plain,
equal(mult(u,mult(u,mult(v,u))),mult(v,ld(u,unit))),
inference(rew,[status(thm),theory(equality)],[56,312]),
[iquote('0:Rew:56.0,312.0')] ).
cnf(317,plain,
equal(ld(mult(u,u),mult(v,mult(u,ld(u,unit)))),mult(v,mult(u,u))),
inference(rew,[status(thm),theory(equality)],[313,302,249]),
[iquote('0:Rew:313.0,302.0,249.0,302.0')] ).
cnf(318,plain,
equal(mult(u,mult(v,v)),ld(mult(v,v),u)),
inference(rew,[status(thm),theory(equality)],[5,317,1]),
[iquote('0:Rew:5.0,317.0,1.0,317.0')] ).
cnf(321,plain,
equal(mult(mult(u,v),v),ld(mult(v,v),u)),
inference(rew,[status(thm),theory(equality)],[318,246]),
[iquote('0:Rew:318.0,246.0')] ).
cnf(322,plain,
equal(ld(mult(u,u),u),ld(u,unit)),
inference(rew,[status(thm),theory(equality)],[318,56]),
[iquote('0:Rew:318.0,56.0')] ).
cnf(326,plain,
equal(ld(mult(ld(u,v),ld(u,v)),u),mult(v,ld(u,v))),
inference(rew,[status(thm),theory(equality)],[318,305]),
[iquote('0:Rew:318.0,305.0')] ).
cnf(330,plain,
equal(mult(ld(mult(u,u),v),w),mult(v,mult(u,mult(u,w)))),
inference(rew,[status(thm),theory(equality)],[318,247]),
[iquote('0:Rew:318.0,247.0')] ).
cnf(335,plain,
equal(rd(ld(mult(u,u),v),u),mult(v,u)),
inference(rew,[status(thm),theory(equality)],[318,297]),
[iquote('0:Rew:318.0,297.0')] ).
cnf(338,plain,
equal(mult(u,mult(u,v)),ld(mult(u,u),v)),
inference(rew,[status(thm),theory(equality)],[318,249]),
[iquote('0:Rew:318.0,249.0')] ).
cnf(343,plain,
equal(mult(ld(rd(unit,u),u),ld(mult(rd(unit,u),rd(unit,u)),v)),mult(mult(u,rd(unit,u)),v)),
inference(rew,[status(thm),theory(equality)],[338,242]),
[iquote('0:Rew:338.0,242.0')] ).
cnf(345,plain,
equal(ld(mult(u,u),mult(u,v)),mult(ld(u,unit),v)),
inference(rew,[status(thm),theory(equality)],[338,258]),
[iquote('0:Rew:338.0,258.0')] ).
cnf(346,plain,
equal(ld(mult(u,u),rd(v,u)),mult(v,u)),
inference(rew,[status(thm),theory(equality)],[338,311]),
[iquote('0:Rew:338.0,311.0')] ).
cnf(348,plain,
equal(mult(mult(u,u),v),ld(mult(u,u),v)),
inference(rew,[status(thm),theory(equality)],[338,248]),
[iquote('0:Rew:338.0,248.0')] ).
cnf(352,plain,
equal(ld(u,ld(mult(v,v),u)),mult(v,v)),
inference(rew,[status(thm),theory(equality)],[338,251]),
[iquote('0:Rew:338.0,251.0')] ).
cnf(356,plain,
equal(mult(ld(mult(u,u),v),w),mult(v,ld(mult(u,u),w))),
inference(rew,[status(thm),theory(equality)],[338,330]),
[iquote('0:Rew:338.0,330.0')] ).
cnf(364,plain,
equal(mult(ld(rd(unit,u),u),ld(ld(rd(unit,u),u),v)),mult(mult(u,rd(unit,u)),v)),
inference(rew,[status(thm),theory(equality)],[118,343]),
[iquote('0:Rew:118.0,343.0')] ).
cnf(365,plain,
equal(mult(mult(u,rd(unit,u)),v),v),
inference(rew,[status(thm),theory(equality)],[1,364]),
[iquote('0:Rew:1.0,364.0')] ).
cnf(383,plain,
equal(mult(u,rd(unit,u)),unit),
inference(spr,[status(thm),theory(equality)],[365,5]),
[iquote('0:SpR:365.0,5.0')] ).
cnf(413,plain,
equal(ld(u,ld(mult(u,u),v)),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[338,2]),
[iquote('0:SpR:338.0,2.0')] ).
cnf(414,plain,
equal(mult(u,ld(mult(u,u),v)),ld(mult(u,u),mult(u,v))),
inference(spr,[status(thm),theory(equality)],[338]),
[iquote('0:SpR:338.0,338.0')] ).
cnf(424,plain,
equal(mult(u,ld(mult(u,u),v)),mult(ld(u,unit),v)),
inference(rew,[status(thm),theory(equality)],[345,414]),
[iquote('0:Rew:345.0,414.0')] ).
cnf(429,plain,
equal(rd(unit,u),ld(u,unit)),
inference(spr,[status(thm),theory(equality)],[383,2]),
[iquote('0:SpR:383.0,2.0')] ).
cnf(778,plain,
equal(mult(ld(mult(u,u),v),mult(u,v)),ld(mult(mult(u,v),mult(u,v)),u)),
inference(spr,[status(thm),theory(equality)],[338,321]),
[iquote('0:SpR:338.0,321.0')] ).
cnf(790,plain,
equal(mult(u,ld(mult(v,v),mult(v,u))),ld(mult(mult(v,u),mult(v,u)),v)),
inference(rew,[status(thm),theory(equality)],[356,778]),
[iquote('0:Rew:356.0,778.0')] ).
cnf(791,plain,
equal(ld(mult(mult(u,v),mult(u,v)),u),mult(v,mult(ld(u,unit),v))),
inference(rew,[status(thm),theory(equality)],[345,790]),
[iquote('0:Rew:345.0,790.0')] ).
cnf(807,plain,
equal(mult(mult(mult(u,u),v),u),rd(v,u)),
inference(spr,[status(thm),theory(equality)],[2,335]),
[iquote('0:SpR:2.0,335.0')] ).
cnf(818,plain,
equal(mult(ld(mult(u,u),v),u),rd(v,u)),
inference(rew,[status(thm),theory(equality)],[348,807]),
[iquote('0:Rew:348.0,807.0')] ).
cnf(819,plain,
equal(mult(u,ld(v,unit)),rd(u,v)),
inference(rew,[status(thm),theory(equality)],[322,818,356]),
[iquote('0:Rew:322.0,818.0,356.0,818.0')] ).
cnf(833,plain,
equal(ld(u,rd(u,v)),ld(v,unit)),
inference(spr,[status(thm),theory(equality)],[819,2]),
[iquote('0:SpR:819.0,2.0')] ).
cnf(834,plain,
equal(ld(mult(u,u),ld(v,unit)),mult(u,rd(u,v))),
inference(spr,[status(thm),theory(equality)],[819,338]),
[iquote('0:SpR:819.0,338.0')] ).
cnf(904,plain,
equal(ld(mult(u,v),u),ld(v,unit)),
inference(spr,[status(thm),theory(equality)],[4,833]),
[iquote('0:SpR:4.0,833.0')] ).
cnf(907,plain,
equal(ld(ld(u,v),unit),ld(v,u)),
inference(spr,[status(thm),theory(equality)],[36,833]),
[iquote('0:SpR:36.0,833.0')] ).
cnf(1027,plain,
equal(mult(ld(u,v),ld(u,v)),ld(ld(u,v),ld(v,u))),
inference(spr,[status(thm),theory(equality)],[907,69]),
[iquote('0:SpR:907.0,69.0')] ).
cnf(1063,plain,
equal(ld(ld(ld(u,v),ld(v,u)),u),mult(v,ld(u,v))),
inference(rew,[status(thm),theory(equality)],[1027,326]),
[iquote('0:Rew:1027.0,326.0')] ).
cnf(1264,plain,
equal(ld(rd(u,v),mult(u,v)),mult(v,v)),
inference(spr,[status(thm),theory(equality)],[346,352]),
[iquote('0:SpR:346.0,352.0')] ).
cnf(1321,plain,
equal(mult(u,mult(mult(u,u),v)),ld(u,v)),
inference(spr,[status(thm),theory(equality)],[2,413]),
[iquote('0:SpR:2.0,413.0')] ).
cnf(1329,plain,
equal(mult(u,rd(v,u)),ld(u,mult(v,u))),
inference(spr,[status(thm),theory(equality)],[346,413]),
[iquote('0:SpR:346.0,413.0')] ).
cnf(1336,plain,
equal(mult(u,ld(mult(u,u),v)),ld(u,v)),
inference(rew,[status(thm),theory(equality)],[348,1321]),
[iquote('0:Rew:348.0,1321.0')] ).
cnf(1337,plain,
equal(mult(ld(u,unit),v),ld(u,v)),
inference(rew,[status(thm),theory(equality)],[424,1336]),
[iquote('0:Rew:424.0,1336.0')] ).
cnf(1344,plain,
equal(ld(mult(mult(u,v),mult(u,v)),u),mult(v,ld(u,v))),
inference(rew,[status(thm),theory(equality)],[1337,791]),
[iquote('0:Rew:1337.0,791.0')] ).
cnf(1367,plain,
equal(rd(ld(u,v),v),ld(u,unit)),
inference(spr,[status(thm),theory(equality)],[1337,4]),
[iquote('0:SpR:1337.0,4.0')] ).
cnf(1369,plain,
equal(ld(mult(ld(u,unit),ld(u,unit)),v),mult(ld(u,unit),ld(u,v))),
inference(spr,[status(thm),theory(equality)],[1337,338]),
[iquote('0:SpR:1337.0,338.0')] ).
cnf(1370,plain,
equal(ld(mult(u,u),ld(v,unit)),mult(ld(v,u),u)),
inference(spr,[status(thm),theory(equality)],[1337,321]),
[iquote('0:SpR:1337.0,321.0')] ).
cnf(1374,plain,
equal(rd(ld(u,unit),v),ld(u,ld(v,unit))),
inference(spr,[status(thm),theory(equality)],[1337,819]),
[iquote('0:SpR:1337.0,819.0')] ).
cnf(1383,plain,
equal(ld(mult(u,u),ld(v,unit)),ld(v,mult(u,u))),
inference(spr,[status(thm),theory(equality)],[1337,318]),
[iquote('0:SpR:1337.0,318.0')] ).
cnf(1393,plain,
equal(ld(rd(unit,u),v),mult(u,v)),
inference(spr,[status(thm),theory(equality)],[30,1337]),
[iquote('0:SpR:30.0,1337.0')] ).
cnf(1397,plain,
equal(mult(ld(u,v),w),ld(ld(v,u),w)),
inference(spr,[status(thm),theory(equality)],[907,1337]),
[iquote('0:SpR:907.0,1337.0')] ).
cnf(1401,plain,
equal(ld(ld(u,unit),v),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[429,1393]),
[iquote('0:Rew:429.0,1393.0')] ).
cnf(1411,plain,
equal(mult(u,ld(mult(v,v),w)),ld(ld(u,mult(v,v)),w)),
inference(rew,[status(thm),theory(equality)],[1397,356]),
[iquote('0:Rew:1397.0,356.0')] ).
cnf(1415,plain,
equal(mult(u,rd(u,v)),ld(ld(u,v),u)),
inference(rew,[status(thm),theory(equality)],[834,1370,1397]),
[iquote('0:Rew:834.0,1370.0,1397.0,1370.0')] ).
cnf(1419,plain,
equal(ld(mult(u,u),ld(v,unit)),ld(ld(u,v),u)),
inference(rew,[status(thm),theory(equality)],[1415,834]),
[iquote('0:Rew:1415.0,834.0')] ).
cnf(1427,plain,
equal(ld(ld(u,v),u),ld(v,mult(u,u))),
inference(rew,[status(thm),theory(equality)],[1383,1419]),
[iquote('0:Rew:1383.0,1419.0')] ).
cnf(1429,plain,
equal(mult(u,rd(u,v)),ld(v,mult(u,u))),
inference(rew,[status(thm),theory(equality)],[1427,1415]),
[iquote('0:Rew:1427.0,1415.0')] ).
cnf(1463,plain,
equal(mult(ld(u,unit),ld(u,v)),ld(rd(ld(u,unit),u),v)),
inference(rew,[status(thm),theory(equality)],[819,1369]),
[iquote('0:Rew:819.0,1369.0')] ).
cnf(1464,plain,
equal(ld(ld(u,ld(u,unit)),v),ld(ld(unit,u),ld(u,v))),
inference(rew,[status(thm),theory(equality)],[1397,1463,1374]),
[iquote('0:Rew:1397.0,1463.0,1374.0,1463.0')] ).
cnf(1465,plain,
equal(ld(mult(u,u),v),ld(u,ld(u,v))),
inference(rew,[status(thm),theory(equality)],[69,1464,28]),
[iquote('0:Rew:69.0,1464.0,28.0,1464.0')] ).
cnf(1466,plain,
equal(ld(u,ld(u,rd(v,u))),mult(v,u)),
inference(rew,[status(thm),theory(equality)],[1465,346]),
[iquote('0:Rew:1465.0,346.0')] ).
cnf(1469,plain,
equal(mult(u,mult(u,v)),ld(u,ld(u,v))),
inference(rew,[status(thm),theory(equality)],[1465,338]),
[iquote('0:Rew:1465.0,338.0')] ).
cnf(1470,plain,
equal(mult(mult(u,u),v),ld(u,ld(u,v))),
inference(rew,[status(thm),theory(equality)],[1465,348]),
[iquote('0:Rew:1465.0,348.0')] ).
cnf(1471,plain,
equal(ld(u,ld(u,ld(u,v))),mult(u,v)),
inference(rew,[status(thm),theory(equality)],[1465,413]),
[iquote('0:Rew:1465.0,413.0')] ).
cnf(1475,plain,
equal(ld(u,ld(v,ld(v,u))),mult(v,v)),
inference(rew,[status(thm),theory(equality)],[1465,352]),
[iquote('0:Rew:1465.0,352.0')] ).
cnf(1477,plain,
equal(ld(mult(u,v),ld(mult(u,v),u)),mult(v,ld(u,v))),
inference(rew,[status(thm),theory(equality)],[1465,1344]),
[iquote('0:Rew:1465.0,1344.0')] ).
cnf(1482,plain,
equal(mult(u,ld(v,ld(v,w))),ld(ld(u,mult(v,v)),w)),
inference(rew,[status(thm),theory(equality)],[1465,1411]),
[iquote('0:Rew:1465.0,1411.0')] ).
cnf(1507,plain,
equal(ld(mult(u,v),ld(v,unit)),mult(v,ld(u,v))),
inference(rew,[status(thm),theory(equality)],[904,1477]),
[iquote('0:Rew:904.0,1477.0')] ).
cnf(1557,plain,
equal(rd(u,mult(v,u)),ld(v,unit)),
inference(spr,[status(thm),theory(equality)],[2,1367]),
[iquote('0:SpR:2.0,1367.0')] ).
cnf(1562,plain,
equal(ld(rd(u,v),unit),rd(v,u)),
inference(spr,[status(thm),theory(equality)],[30,1367]),
[iquote('0:SpR:30.0,1367.0')] ).
cnf(1563,plain,
equal(rd(ld(u,unit),v),ld(mult(v,u),unit)),
inference(spr,[status(thm),theory(equality)],[904,1367]),
[iquote('0:SpR:904.0,1367.0')] ).
cnf(1572,plain,
equal(ld(mult(u,v),unit),ld(v,ld(u,unit))),
inference(rew,[status(thm),theory(equality)],[1374,1563]),
[iquote('0:Rew:1374.0,1563.0')] ).
cnf(1637,plain,
equal(mult(rd(u,v),w),ld(rd(v,u),w)),
inference(spr,[status(thm),theory(equality)],[1562,1401]),
[iquote('0:SpR:1562.0,1401.0')] ).
cnf(1639,plain,
equal(rd(u,rd(v,w)),mult(u,rd(w,v))),
inference(spr,[status(thm),theory(equality)],[1562,819]),
[iquote('0:SpR:1562.0,819.0')] ).
cnf(1668,plain,
equal(ld(ld(u,mult(v,v)),mult(v,w)),mult(u,ld(v,w))),
inference(spr,[status(thm),theory(equality)],[2,1482]),
[iquote('0:SpR:2.0,1482.0')] ).
cnf(1763,plain,
equal(ld(ld(u,v),ld(w,unit)),rd(ld(v,u),w)),
inference(spr,[status(thm),theory(equality)],[907,1374]),
[iquote('0:SpR:907.0,1374.0')] ).
cnf(1801,plain,
equal(ld(ld(u,ld(u,v)),unit),ld(mult(u,v),ld(u,unit))),
inference(spr,[status(thm),theory(equality)],[1469,1572]),
[iquote('0:SpR:1469.0,1572.0')] ).
cnf(1810,plain,
equal(ld(mult(u,v),ld(u,unit)),ld(ld(u,v),u)),
inference(rew,[status(thm),theory(equality)],[907,1801]),
[iquote('0:Rew:907.0,1801.0')] ).
cnf(1811,plain,
equal(ld(mult(u,v),ld(u,unit)),ld(v,mult(u,u))),
inference(rew,[status(thm),theory(equality)],[1427,1810]),
[iquote('0:Rew:1427.0,1810.0')] ).
cnf(1911,plain,
equal(ld(ld(u,unit),mult(v,mult(u,v))),mult(mult(u,v),mult(u,v))),
inference(spr,[status(thm),theory(equality)],[1557,1264]),
[iquote('0:SpR:1557.0,1264.0')] ).
cnf(1933,plain,
equal(mult(mult(u,v),mult(u,v)),mult(u,mult(v,mult(u,v)))),
inference(rew,[status(thm),theory(equality)],[1401,1911]),
[iquote('0:Rew:1401.0,1911.0')] ).
cnf(1949,plain,
equal(ld(rd(u,rd(v,u)),ld(u,mult(v,u))),mult(rd(v,u),rd(v,u))),
inference(spr,[status(thm),theory(equality)],[1329,1264]),
[iquote('0:SpR:1329.0,1264.0')] ).
cnf(1979,plain,
equal(ld(ld(u,mult(v,v)),ld(v,mult(u,v))),ld(rd(v,u),rd(u,v))),
inference(rew,[status(thm),theory(equality)],[1429,1949,1639,1637]),
[iquote('0:Rew:1429.0,1949.0,1639.0,1949.0,1637.0,1949.0')] ).
cnf(1993,plain,
equal(mult(ld(ld(u,v),ld(v,u)),w),ld(ld(v,u),ld(ld(v,u),w))),
inference(spr,[status(thm),theory(equality)],[1397,1470]),
[iquote('0:SpR:1397.0,1470.0')] ).
cnf(2024,plain,
equal(ld(ld(ld(u,v),ld(v,u)),w),ld(ld(u,v),ld(ld(u,v),w))),
inference(rew,[status(thm),theory(equality)],[1397,1993]),
[iquote('0:Rew:1397.0,1993.0')] ).
cnf(2028,plain,
equal(ld(ld(u,v),ld(ld(u,v),u)),mult(v,ld(u,v))),
inference(rew,[status(thm),theory(equality)],[2024,1063]),
[iquote('0:Rew:2024.0,1063.0')] ).
cnf(2029,plain,
equal(ld(ld(u,v),ld(v,mult(u,u))),mult(v,ld(u,v))),
inference(rew,[status(thm),theory(equality)],[1427,2028]),
[iquote('0:Rew:1427.0,2028.0')] ).
cnf(2121,plain,
equal(ld(ld(u,mult(v,v)),ld(v,w)),mult(u,mult(v,w))),
inference(spr,[status(thm),theory(equality)],[1471,1482]),
[iquote('0:SpR:1471.0,1482.0')] ).
cnf(2152,plain,
equal(mult(u,mult(v,mult(u,v))),ld(rd(v,u),rd(u,v))),
inference(rew,[status(thm),theory(equality)],[2121,1979]),
[iquote('0:Rew:2121.0,1979.0')] ).
cnf(2158,plain,
equal(mult(mult(u,v),mult(u,v)),ld(rd(v,u),rd(u,v))),
inference(rew,[status(thm),theory(equality)],[2152,1933]),
[iquote('0:Rew:2152.0,1933.0')] ).
cnf(2202,plain,
equal(ld(u,mult(rd(u,v),rd(u,v))),ld(v,rd(u,v))),
inference(spr,[status(thm),theory(equality)],[30,1427]),
[iquote('0:SpR:30.0,1427.0')] ).
cnf(2203,plain,
equal(ld(u,mult(mult(u,v),mult(u,v))),ld(ld(v,unit),mult(u,v))),
inference(spr,[status(thm),theory(equality)],[904,1427]),
[iquote('0:SpR:904.0,1427.0')] ).
cnf(2231,plain,
equal(ld(u,ld(rd(v,u),rd(u,v))),ld(v,rd(u,v))),
inference(rew,[status(thm),theory(equality)],[1637,2202]),
[iquote('0:Rew:1637.0,2202.0')] ).
cnf(2234,plain,
equal(ld(u,mult(mult(u,v),mult(u,v))),mult(v,mult(u,v))),
inference(rew,[status(thm),theory(equality)],[1401,2203]),
[iquote('0:Rew:1401.0,2203.0')] ).
cnf(2235,plain,
equal(mult(u,mult(v,u)),ld(u,rd(v,u))),
inference(rew,[status(thm),theory(equality)],[2231,2234,2158]),
[iquote('0:Rew:2231.0,2234.0,2158.0,2234.0')] ).
cnf(2236,plain,
~ equal(mult(mult(a,b),a),ld(a,rd(b,a))),
inference(rew,[status(thm),theory(equality)],[2235,10]),
[iquote('0:Rew:2235.0,10.0')] ).
cnf(2267,plain,
equal(ld(u,mult(mult(v,u),mult(v,u))),mult(mult(v,u),v)),
inference(spr,[status(thm),theory(equality)],[4,1429]),
[iquote('0:SpR:4.0,1429.0')] ).
cnf(2268,plain,
equal(ld(u,mult(ld(v,u),ld(v,u))),mult(ld(v,u),ld(v,unit))),
inference(spr,[status(thm),theory(equality)],[1367,1429]),
[iquote('0:SpR:1367.0,1429.0')] ).
cnf(2286,plain,
equal(ld(u,ld(rd(u,v),rd(v,u))),mult(mult(v,u),v)),
inference(rew,[status(thm),theory(equality)],[2158,2267]),
[iquote('0:Rew:2158.0,2267.0')] ).
cnf(2290,plain,
equal(ld(u,ld(ld(u,v),ld(v,u))),ld(ld(u,v),ld(v,unit))),
inference(rew,[status(thm),theory(equality)],[1397,2268]),
[iquote('0:Rew:1397.0,2268.0,1397.0,2268.0')] ).
cnf(2291,plain,
equal(ld(u,ld(ld(u,v),ld(v,u))),rd(ld(v,u),v)),
inference(rew,[status(thm),theory(equality)],[1763,2290]),
[iquote('0:Rew:1763.0,2290.0')] ).
cnf(2417,plain,
equal(ld(mult(u,v),ld(mult(u,v),ld(u,unit))),mult(v,mult(u,v))),
inference(spr,[status(thm),theory(equality)],[1557,1466]),
[iquote('0:SpR:1557.0,1466.0')] ).
cnf(2440,plain,
equal(ld(mult(u,v),ld(v,mult(u,u))),ld(v,rd(u,v))),
inference(rew,[status(thm),theory(equality)],[1811,2417,2235]),
[iquote('0:Rew:1811.0,2417.0,2235.0,2417.0')] ).
cnf(2621,plain,
equal(mult(rd(u,v),rd(u,v)),ld(u,ld(rd(u,v),v))),
inference(spr,[status(thm),theory(equality)],[30,1475]),
[iquote('0:SpR:30.0,1475.0')] ).
cnf(2622,plain,
equal(ld(u,ld(mult(u,v),ld(v,unit))),mult(mult(u,v),mult(u,v))),
inference(spr,[status(thm),theory(equality)],[904,1475]),
[iquote('0:SpR:904.0,1475.0')] ).
cnf(2628,plain,
equal(ld(u,ld(ld(u,v),ld(v,mult(u,u)))),mult(ld(u,v),ld(u,v))),
inference(spr,[status(thm),theory(equality)],[1427,1475]),
[iquote('0:SpR:1427.0,1475.0')] ).
cnf(2659,plain,
equal(ld(rd(u,v),rd(v,u)),ld(v,ld(rd(v,u),u))),
inference(rew,[status(thm),theory(equality)],[1637,2621]),
[iquote('0:Rew:1637.0,2621.0')] ).
cnf(2664,plain,
equal(mult(mult(u,v),mult(u,v)),ld(u,ld(rd(u,v),v))),
inference(rew,[status(thm),theory(equality)],[2659,2158]),
[iquote('0:Rew:2659.0,2158.0')] ).
cnf(2673,plain,
equal(ld(u,ld(v,ld(rd(v,u),u))),mult(mult(v,u),v)),
inference(rew,[status(thm),theory(equality)],[2659,2286]),
[iquote('0:Rew:2659.0,2286.0')] ).
cnf(2676,plain,
equal(ld(u,mult(v,ld(u,v))),ld(u,ld(rd(u,v),v))),
inference(rew,[status(thm),theory(equality)],[1507,2622,2664]),
[iquote('0:Rew:1507.0,2622.0,2664.0,2622.0')] ).
cnf(2685,plain,
equal(ld(u,ld(ld(u,v),ld(v,mult(u,u)))),ld(ld(v,u),ld(u,v))),
inference(rew,[status(thm),theory(equality)],[1397,2628]),
[iquote('0:Rew:1397.0,2628.0')] ).
cnf(2686,plain,
equal(ld(ld(u,v),ld(v,u)),ld(v,ld(rd(v,u),u))),
inference(rew,[status(thm),theory(equality)],[2676,2685,2029]),
[iquote('0:Rew:2676.0,2685.0,2029.0,2685.0')] ).
cnf(2699,plain,
equal(ld(u,ld(v,ld(rd(v,u),u))),rd(ld(v,u),v)),
inference(rew,[status(thm),theory(equality)],[2686,2291]),
[iquote('0:Rew:2686.0,2291.0')] ).
cnf(2702,plain,
equal(rd(ld(u,v),u),mult(mult(u,v),u)),
inference(rew,[status(thm),theory(equality)],[2673,2699]),
[iquote('0:Rew:2673.0,2699.0')] ).
cnf(5928,plain,
equal(ld(mult(u,v),ld(w,mult(u,u))),ld(mult(w,ld(u,v)),unit)),
inference(spr,[status(thm),theory(equality)],[1668,907]),
[iquote('0:SpR:1668.0,907.0')] ).
cnf(6016,plain,
equal(ld(mult(u,v),ld(w,mult(u,u))),ld(ld(u,v),ld(w,unit))),
inference(rew,[status(thm),theory(equality)],[1572,5928]),
[iquote('0:Rew:1572.0,5928.0')] ).
cnf(6017,plain,
equal(ld(mult(u,v),ld(w,mult(u,u))),rd(ld(v,u),w)),
inference(rew,[status(thm),theory(equality)],[1763,6016]),
[iquote('0:Rew:1763.0,6016.0')] ).
cnf(6018,plain,
equal(rd(ld(u,v),u),ld(u,rd(v,u))),
inference(rew,[status(thm),theory(equality)],[6017,2440]),
[iquote('0:Rew:6017.0,2440.0')] ).
cnf(6019,plain,
equal(mult(mult(u,v),u),ld(u,rd(v,u))),
inference(rew,[status(thm),theory(equality)],[2702,6018]),
[iquote('0:Rew:2702.0,6018.0')] ).
cnf(6020,plain,
$false,
inference(unc,[status(thm)],[6019,2236]),
[iquote('0:UnC:6019.0,2236.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP707-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 07:30:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.87/1.13
% 0.87/1.13 SPASS V 3.9
% 0.87/1.13 SPASS beiseite: Proof found.
% 0.87/1.13 % SZS status Theorem
% 0.87/1.13 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.87/1.13 SPASS derived 3013 clauses, backtracked 0 clauses, performed 0 splits and kept 704 clauses.
% 0.87/1.13 SPASS allocated 69634 KBytes.
% 0.87/1.13 SPASS spent 0:00:00.78 on the problem.
% 0.87/1.13 0:00:00.03 for the input.
% 0.87/1.13 0:00:00.00 for the FLOTTER CNF translation.
% 0.87/1.13 0:00:00.02 for inferences.
% 0.87/1.13 0:00:00.00 for the backtracking.
% 0.87/1.13 0:00:00.70 for the reduction.
% 0.87/1.13
% 0.87/1.13
% 0.87/1.13 Here is a proof with depth 7, length 156 :
% 0.87/1.13 % SZS output start Refutation
% See solution above
% 0.97/1.16 Formulae used in the proof : c01 c02 c03 c04 c05 c06 c07 c08 c09 goals
% 0.97/1.16
%------------------------------------------------------------------------------