TSTP Solution File: ALG073+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG073+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 : Thu Jul 14 18:02:13 EDT 2022
% Result : Theorem 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of clauses : 52 ( 13 unt; 0 nHn; 52 RR)
% Number of literals : 119 ( 0 equ; 68 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
sorti1(skc1),
file('ALG073+1.p',unknown),
[] ).
cnf(2,axiom,
sorti1(op1(skc1,skc1)),
file('ALG073+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ sorti1(u)
| sorti2(h(u)) ),
file('ALG073+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ sorti2(u)
| sorti1(j(u)) ),
file('ALG073+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ sorti2(u)
| equal(h(j(u)),u) ),
file('ALG073+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ sorti1(u)
| equal(j(h(u)),u) ),
file('ALG073+1.p',unknown),
[] ).
cnf(7,axiom,
~ equal(op1(skc1,op1(skc1,skc1)),skc1),
file('ALG073+1.p',unknown),
[] ).
cnf(8,axiom,
equal(op1(op1(skc1,skc1),op1(skc1,skc1)),skc1),
file('ALG073+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sorti2(u)
| ~ sorti2(v)
| sorti2(op2(v,u)) ),
file('ALG073+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ sorti1(u)
| ~ sorti1(v)
| equal(op2(h(v),h(u)),h(op1(v,u))) ),
file('ALG073+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ sorti2(u)
| ~ sorti2(v)
| equal(op1(j(v),j(u)),j(op2(v,u))) ),
file('ALG073+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ sorti2(u)
| ~ sorti2(op2(u,u))
| ~ equal(op2(op2(u,u),op2(u,u)),u)
| equal(op2(u,op2(u,u)),u) ),
file('ALG073+1.p',unknown),
[] ).
cnf(14,plain,
sorti2(h(skc1)),
inference(res,[status(thm),theory(equality)],[1,3]),
[iquote('0:Res:1.0,3.0')] ).
cnf(16,plain,
equal(j(h(skc1)),skc1),
inference(res,[status(thm),theory(equality)],[1,6]),
[iquote('0:Res:1.0,6.0')] ).
cnf(18,plain,
( ~ sorti1(u)
| equal(op2(h(skc1),h(u)),h(op1(skc1,u))) ),
inference(res,[status(thm),theory(equality)],[1,11]),
[iquote('0:Res:1.0,11.0')] ).
cnf(20,plain,
( ~ sorti1(u)
| equal(op2(h(u),h(skc1)),h(op1(u,skc1))) ),
inference(res,[status(thm),theory(equality)],[1,11]),
[iquote('0:Res:1.0,11.1')] ).
cnf(46,plain,
( ~ sorti1(u)
| ~ sorti2(h(u))
| ~ sorti2(h(skc1))
| sorti2(h(op1(skc1,u))) ),
inference(spr,[status(thm),theory(equality)],[18,10]),
[iquote('0:SpR:18.1,10.2')] ).
cnf(48,plain,
( ~ sorti2(u)
| ~ sorti1(j(u))
| equal(h(op1(skc1,j(u))),op2(h(skc1),u)) ),
inference(spr,[status(thm),theory(equality)],[5,18]),
[iquote('0:SpR:5.1,18.1')] ).
cnf(49,plain,
( ~ sorti1(u)
| sorti2(h(op1(skc1,u))) ),
inference(ssi,[status(thm)],[46,14,3]),
[iquote('0:SSi:46.2,46.1,14.1,3.0')] ).
cnf(50,plain,
( ~ sorti2(u)
| equal(h(op1(skc1,j(u))),op2(h(skc1),u)) ),
inference(ssi,[status(thm)],[48,4]),
[iquote('0:SSi:48.1,4.1')] ).
cnf(53,plain,
( ~ sorti2(h(skc1))
| ~ sorti2(u)
| equal(j(op2(u,h(skc1))),op1(j(u),skc1)) ),
inference(spr,[status(thm),theory(equality)],[16,12]),
[iquote('0:SpR:16.0,12.2')] ).
cnf(56,plain,
( ~ sorti1(u)
| ~ sorti2(v)
| ~ sorti2(h(u))
| equal(j(op2(h(u),v)),op1(u,j(v))) ),
inference(spr,[status(thm),theory(equality)],[6,12]),
[iquote('0:SpR:6.1,12.2')] ).
cnf(57,plain,
( ~ sorti2(u)
| equal(j(op2(u,h(skc1))),op1(j(u),skc1)) ),
inference(ssi,[status(thm)],[53,14]),
[iquote('0:SSi:53.0,14.0')] ).
cnf(60,plain,
( ~ sorti1(u)
| ~ sorti2(v)
| equal(j(op2(h(u),v)),op1(u,j(v))) ),
inference(ssi,[status(thm)],[56,3]),
[iquote('0:SSi:56.2,3.1')] ).
cnf(107,plain,
( ~ sorti1(skc1)
| ~ sorti2(h(skc1))
| ~ sorti2(op2(h(skc1),h(skc1)))
| ~ equal(op2(h(op1(skc1,skc1)),h(op1(skc1,skc1))),h(skc1))
| equal(op2(h(skc1),op2(h(skc1),h(skc1))),h(skc1)) ),
inference(spl,[status(thm),theory(equality)],[20,13]),
[iquote('0:SpL:20.1,13.2')] ).
cnf(108,plain,
( ~ sorti1(skc1)
| ~ sorti2(h(skc1))
| ~ sorti2(h(op1(skc1,skc1)))
| ~ equal(op2(h(op1(skc1,skc1)),h(op1(skc1,skc1))),h(skc1))
| equal(op2(h(skc1),h(op1(skc1,skc1))),h(skc1)) ),
inference(rew,[status(thm),theory(equality)],[20,107]),
[iquote('0:Rew:20.1,107.4,20.1,107.2')] ).
cnf(109,plain,
( ~ sorti2(h(op1(skc1,skc1)))
| ~ equal(op2(h(op1(skc1,skc1)),h(op1(skc1,skc1))),h(skc1))
| equal(op2(h(skc1),h(op1(skc1,skc1))),h(skc1)) ),
inference(ssi,[status(thm)],[108,14,1]),
[iquote('0:SSi:108.1,108.0,14.0,1.0')] ).
cnf(125,plain,
( ~ sorti2(u)
| ~ sorti1(j(u))
| sorti2(op2(h(skc1),u)) ),
inference(spr,[status(thm),theory(equality)],[50,49]),
[iquote('0:SpR:50.1,49.1')] ).
cnf(132,plain,
( ~ sorti2(h(skc1))
| equal(op2(h(skc1),h(skc1)),h(op1(skc1,skc1))) ),
inference(spr,[status(thm),theory(equality)],[16,50]),
[iquote('0:SpR:16.0,50.1')] ).
cnf(134,plain,
( ~ sorti2(u)
| sorti2(op2(h(skc1),u)) ),
inference(ssi,[status(thm)],[125,4]),
[iquote('0:SSi:125.1,4.1')] ).
cnf(138,plain,
equal(op2(h(skc1),h(skc1)),h(op1(skc1,skc1))),
inference(ssi,[status(thm)],[132,14]),
[iquote('0:SSi:132.0,14.0')] ).
cnf(157,plain,
( ~ sorti1(u)
| ~ sorti1(skc1)
| ~ sorti2(h(u))
| equal(op1(skc1,j(h(u))),j(h(op1(skc1,u)))) ),
inference(spr,[status(thm),theory(equality)],[18,60]),
[iquote('0:SpR:18.1,60.2')] ).
cnf(169,plain,
( ~ sorti1(u)
| ~ sorti1(skc1)
| ~ sorti2(h(u))
| equal(j(h(op1(skc1,u))),op1(skc1,u)) ),
inference(rew,[status(thm),theory(equality)],[6,157]),
[iquote('0:Rew:6.1,157.3')] ).
cnf(170,plain,
( ~ sorti1(u)
| equal(j(h(op1(skc1,u))),op1(skc1,u)) ),
inference(ssi,[status(thm)],[169,3,1]),
[iquote('0:SSi:169.2,169.1,3.0,1.1')] ).
cnf(189,plain,
( ~ sorti2(h(skc1))
| sorti2(h(op1(skc1,skc1))) ),
inference(spr,[status(thm),theory(equality)],[138,134]),
[iquote('0:SpR:138.0,134.1')] ).
cnf(196,plain,
sorti2(h(op1(skc1,skc1))),
inference(ssi,[status(thm)],[189,14]),
[iquote('0:SSi:189.0,14.0')] ).
cnf(197,plain,
( ~ equal(op2(h(op1(skc1,skc1)),h(op1(skc1,skc1))),h(skc1))
| equal(op2(h(skc1),h(op1(skc1,skc1))),h(skc1)) ),
inference(mrr,[status(thm)],[109,196]),
[iquote('0:MRR:109.0,196.0')] ).
cnf(435,plain,
( ~ sorti2(h(skc1))
| equal(op1(j(h(skc1)),skc1),j(h(op1(skc1,skc1)))) ),
inference(spr,[status(thm),theory(equality)],[138,57]),
[iquote('0:SpR:138.0,57.1')] ).
cnf(438,plain,
( ~ sorti2(h(skc1))
| equal(j(h(op1(skc1,skc1))),op1(skc1,skc1)) ),
inference(rew,[status(thm),theory(equality)],[16,435]),
[iquote('0:Rew:16.0,435.1')] ).
cnf(439,plain,
equal(j(h(op1(skc1,skc1))),op1(skc1,skc1)),
inference(ssi,[status(thm)],[438,14]),
[iquote('0:SSi:438.0,14.0')] ).
cnf(473,plain,
( ~ sorti2(h(op1(skc1,skc1)))
| equal(op2(h(skc1),h(op1(skc1,skc1))),h(op1(skc1,op1(skc1,skc1)))) ),
inference(spr,[status(thm),theory(equality)],[439,50]),
[iquote('0:SpR:439.0,50.1')] ).
cnf(485,plain,
equal(op2(h(skc1),h(op1(skc1,skc1))),h(op1(skc1,op1(skc1,skc1)))),
inference(ssi,[status(thm)],[473,3,2]),
[iquote('0:SSi:473.0,3.0,2.1')] ).
cnf(486,plain,
( ~ equal(op2(h(op1(skc1,skc1)),h(op1(skc1,skc1))),h(skc1))
| equal(h(op1(skc1,op1(skc1,skc1))),h(skc1)) ),
inference(rew,[status(thm),theory(equality)],[485,197]),
[iquote('0:Rew:485.0,197.1')] ).
cnf(829,plain,
( ~ sorti1(op1(skc1,skc1))
| ~ sorti1(op1(skc1,skc1))
| ~ equal(h(op1(op1(skc1,skc1),op1(skc1,skc1))),h(skc1))
| equal(h(op1(skc1,op1(skc1,skc1))),h(skc1)) ),
inference(spl,[status(thm),theory(equality)],[11,486]),
[iquote('0:SpL:11.2,486.0')] ).
cnf(830,plain,
( ~ sorti1(op1(skc1,skc1))
| ~ equal(h(op1(op1(skc1,skc1),op1(skc1,skc1))),h(skc1))
| equal(h(op1(skc1,op1(skc1,skc1))),h(skc1)) ),
inference(obv,[status(thm),theory(equality)],[829]),
[iquote('0:Obv:829.0')] ).
cnf(831,plain,
( ~ sorti1(op1(skc1,skc1))
| ~ equal(h(skc1),h(skc1))
| equal(h(op1(skc1,op1(skc1,skc1))),h(skc1)) ),
inference(rew,[status(thm),theory(equality)],[8,830]),
[iquote('0:Rew:8.0,830.1')] ).
cnf(832,plain,
( ~ sorti1(op1(skc1,skc1))
| equal(h(op1(skc1,op1(skc1,skc1))),h(skc1)) ),
inference(obv,[status(thm),theory(equality)],[831]),
[iquote('0:Obv:831.1')] ).
cnf(833,plain,
equal(h(op1(skc1,op1(skc1,skc1))),h(skc1)),
inference(ssi,[status(thm)],[832,2]),
[iquote('0:SSi:832.0,2.0')] ).
cnf(843,plain,
( ~ sorti1(op1(skc1,skc1))
| equal(op1(skc1,op1(skc1,skc1)),j(h(skc1))) ),
inference(spr,[status(thm),theory(equality)],[833,170]),
[iquote('0:SpR:833.0,170.1')] ).
cnf(852,plain,
( ~ sorti1(op1(skc1,skc1))
| equal(op1(skc1,op1(skc1,skc1)),skc1) ),
inference(rew,[status(thm),theory(equality)],[16,843]),
[iquote('0:Rew:16.0,843.1')] ).
cnf(853,plain,
equal(op1(skc1,op1(skc1,skc1)),skc1),
inference(ssi,[status(thm)],[852,2]),
[iquote('0:SSi:852.0,2.0')] ).
cnf(854,plain,
$false,
inference(mrr,[status(thm)],[853,7]),
[iquote('0:MRR:853.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG073+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n017.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 : Wed Jun 8 05:28:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.53
% 0.19/0.53 SPASS V 3.9
% 0.19/0.53 SPASS beiseite: Proof found.
% 0.19/0.53 % SZS status Theorem
% 0.19/0.53 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.53 SPASS derived 491 clauses, backtracked 0 clauses, performed 0 splits and kept 236 clauses.
% 0.19/0.53 SPASS allocated 104936 KBytes.
% 0.19/0.53 SPASS spent 0:00:00.17 on the problem.
% 0.19/0.53 0:00:00.03 for the input.
% 0.19/0.53 0:00:00.02 for the FLOTTER CNF translation.
% 0.19/0.53 0:00:00.01 for inferences.
% 0.19/0.53 0:00:00.00 for the backtracking.
% 0.19/0.53 0:00:00.08 for the reduction.
% 0.19/0.53
% 0.19/0.53
% 0.19/0.53 Here is a proof with depth 5, length 52 :
% 0.19/0.53 % SZS output start Refutation
% See solution above
% 0.19/0.53 Formulae used in the proof : ax3 co1 ax2 ax4
% 0.19/0.53
%------------------------------------------------------------------------------