TSTP Solution File: ALG074+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG074+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 1.11s 1.27s
% Output : Refutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of clauses : 60 ( 17 unt; 9 nHn; 60 RR)
% Number of literals : 142 ( 0 equ; 75 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
sorti1(skc3),
file('ALG074+1.p',unknown),
[] ).
cnf(2,axiom,
sorti1(skc2),
file('ALG074+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ sorti1(u)
| sorti2(h(u)) ),
file('ALG074+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ sorti2(u)
| sorti1(j(u)) ),
file('ALG074+1.p',unknown),
[] ).
cnf(5,axiom,
equal(op1(op1(skc2,skc3),skc3),skc2),
file('ALG074+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ sorti2(u)
| equal(h(j(u)),u) ),
file('ALG074+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ sorti1(u)
| equal(j(h(u)),u) ),
file('ALG074+1.p',unknown),
[] ).
cnf(8,axiom,
~ equal(op1(skc3,skc2),op1(skc2,skc3)),
file('ALG074+1.p',unknown),
[] ).
cnf(9,axiom,
~ equal(op1(op1(skc2,skc3),skc2),skc3),
file('ALG074+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sorti1(u)
| ~ sorti1(v)
| sorti1(op1(v,u)) ),
file('ALG074+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ sorti1(u)
| ~ sorti1(v)
| equal(op2(h(v),h(u)),h(op1(v,u))) ),
file('ALG074+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ sorti2(u)
| ~ sorti2(v)
| equal(op1(j(v),j(u)),j(op2(v,u))) ),
file('ALG074+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ sorti2(u)
| ~ sorti2(v)
| ~ equal(op2(op2(v,u),u),v)
| equal(op2(u,v),op2(v,u))
| equal(op2(op2(v,u),v),u) ),
file('ALG074+1.p',unknown),
[] ).
cnf(15,plain,
sorti2(h(skc2)),
inference(res,[status(thm),theory(equality)],[2,3]),
[iquote('0:Res:2.0,3.0')] ).
cnf(16,plain,
sorti2(h(skc3)),
inference(res,[status(thm),theory(equality)],[1,3]),
[iquote('0:Res:1.0,3.0')] ).
cnf(17,plain,
equal(j(h(skc2)),skc2),
inference(res,[status(thm),theory(equality)],[2,7]),
[iquote('0:Res:2.0,7.0')] ).
cnf(18,plain,
equal(j(h(skc3)),skc3),
inference(res,[status(thm),theory(equality)],[1,7]),
[iquote('0:Res:1.0,7.0')] ).
cnf(19,plain,
( ~ sorti1(u)
| equal(op2(h(skc2),h(u)),h(op1(skc2,u))) ),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.0')] ).
cnf(20,plain,
( ~ sorti1(u)
| equal(op2(h(skc3),h(u)),h(op1(skc3,u))) ),
inference(res,[status(thm),theory(equality)],[1,12]),
[iquote('0:Res:1.0,12.0')] ).
cnf(22,plain,
( ~ sorti1(u)
| equal(op2(h(u),h(skc3)),h(op1(u,skc3))) ),
inference(res,[status(thm),theory(equality)],[1,12]),
[iquote('0:Res:1.0,12.1')] ).
cnf(57,plain,
( ~ sorti2(u)
| ~ sorti1(j(u))
| equal(h(op1(skc3,j(u))),op2(h(skc3),u)) ),
inference(spr,[status(thm),theory(equality)],[6,20]),
[iquote('0:SpR:6.1,20.1')] ).
cnf(59,plain,
( ~ sorti2(u)
| equal(h(op1(skc3,j(u))),op2(h(skc3),u)) ),
inference(ssi,[status(thm)],[57,4]),
[iquote('0:SSi:57.1,4.1')] ).
cnf(62,plain,
( ~ sorti2(u)
| ~ sorti1(j(u))
| equal(h(op1(skc2,j(u))),op2(h(skc2),u)) ),
inference(spr,[status(thm),theory(equality)],[6,19]),
[iquote('0:SpR:6.1,19.1')] ).
cnf(64,plain,
( ~ sorti2(u)
| equal(h(op1(skc2,j(u))),op2(h(skc2),u)) ),
inference(ssi,[status(thm)],[62,4]),
[iquote('0:SSi:62.1,4.1')] ).
cnf(67,plain,
( ~ sorti2(h(skc3))
| ~ sorti2(u)
| equal(j(op2(u,h(skc3))),op1(j(u),skc3)) ),
inference(spr,[status(thm),theory(equality)],[18,13]),
[iquote('0:SpR:18.0,13.2')] ).
cnf(68,plain,
( ~ sorti2(h(skc2))
| ~ sorti2(u)
| equal(j(op2(u,h(skc2))),op1(j(u),skc2)) ),
inference(spr,[status(thm),theory(equality)],[17,13]),
[iquote('0:SpR:17.0,13.2')] ).
cnf(72,plain,
( ~ sorti1(u)
| ~ sorti2(v)
| ~ sorti2(h(u))
| equal(j(op2(h(u),v)),op1(u,j(v))) ),
inference(spr,[status(thm),theory(equality)],[7,13]),
[iquote('0:SpR:7.1,13.2')] ).
cnf(73,plain,
( ~ sorti2(u)
| equal(j(op2(u,h(skc3))),op1(j(u),skc3)) ),
inference(ssi,[status(thm)],[67,16]),
[iquote('0:SSi:67.0,16.0')] ).
cnf(74,plain,
( ~ sorti2(u)
| equal(j(op2(u,h(skc2))),op1(j(u),skc2)) ),
inference(ssi,[status(thm)],[68,15]),
[iquote('0:SSi:68.0,15.0')] ).
cnf(78,plain,
( ~ sorti1(u)
| ~ sorti2(v)
| equal(j(op2(h(u),v)),op1(u,j(v))) ),
inference(ssi,[status(thm)],[72,3]),
[iquote('0:SSi:72.2,3.1')] ).
cnf(91,plain,
( ~ sorti2(u)
| ~ sorti1(j(u))
| equal(h(op1(j(u),skc3)),op2(u,h(skc3))) ),
inference(spr,[status(thm),theory(equality)],[6,22]),
[iquote('0:SpR:6.1,22.1')] ).
cnf(94,plain,
( ~ sorti2(u)
| equal(h(op1(j(u),skc3)),op2(u,h(skc3))) ),
inference(ssi,[status(thm)],[91,4]),
[iquote('0:SSi:91.1,4.1')] ).
cnf(122,plain,
( ~ sorti1(u)
| ~ sorti2(h(skc3))
| ~ sorti2(h(u))
| ~ equal(op2(h(op1(u,skc3)),h(skc3)),h(u))
| equal(op2(h(skc3),h(u)),op2(h(u),h(skc3)))
| equal(op2(op2(h(u),h(skc3)),h(u)),h(skc3)) ),
inference(spl,[status(thm),theory(equality)],[22,14]),
[iquote('0:SpL:22.1,14.2')] ).
cnf(123,plain,
( ~ sorti1(u)
| ~ sorti2(h(skc3))
| ~ sorti2(h(u))
| ~ equal(op2(h(op1(u,skc3)),h(skc3)),h(u))
| equal(h(op1(skc3,u)),h(op1(u,skc3)))
| equal(op2(h(op1(u,skc3)),h(u)),h(skc3)) ),
inference(rew,[status(thm),theory(equality)],[22,122,20]),
[iquote('0:Rew:22.1,122.5,20.1,122.4,22.1,122.4')] ).
cnf(124,plain,
( ~ sorti1(u)
| ~ equal(op2(h(op1(u,skc3)),h(skc3)),h(u))
| equal(h(op1(skc3,u)),h(op1(u,skc3)))
| equal(op2(h(op1(u,skc3)),h(u)),h(skc3)) ),
inference(ssi,[status(thm)],[123,3,16]),
[iquote('0:SSi:123.2,123.1,3.0,16.1')] ).
cnf(182,plain,
( ~ sorti2(h(skc2))
| equal(op2(h(skc3),h(skc2)),h(op1(skc3,skc2))) ),
inference(spr,[status(thm),theory(equality)],[17,59]),
[iquote('0:SpR:17.0,59.1')] ).
cnf(189,plain,
equal(op2(h(skc3),h(skc2)),h(op1(skc3,skc2))),
inference(ssi,[status(thm)],[182,15]),
[iquote('0:SSi:182.0,15.0')] ).
cnf(210,plain,
( ~ sorti1(u)
| ~ sorti1(u)
| ~ sorti2(h(skc3))
| equal(op1(u,j(h(skc3))),j(h(op1(u,skc3)))) ),
inference(spr,[status(thm),theory(equality)],[22,78]),
[iquote('0:SpR:22.1,78.2')] ).
cnf(221,plain,
( ~ sorti1(u)
| ~ sorti2(h(skc3))
| equal(op1(u,j(h(skc3))),j(h(op1(u,skc3)))) ),
inference(obv,[status(thm),theory(equality)],[210]),
[iquote('0:Obv:210.0')] ).
cnf(222,plain,
( ~ sorti1(u)
| ~ sorti2(h(skc3))
| equal(j(h(op1(u,skc3))),op1(u,skc3)) ),
inference(rew,[status(thm),theory(equality)],[18,221]),
[iquote('0:Rew:18.0,221.2')] ).
cnf(223,plain,
( ~ sorti1(u)
| equal(j(h(op1(u,skc3))),op1(u,skc3)) ),
inference(ssi,[status(thm)],[222,16]),
[iquote('0:SSi:222.1,16.0')] ).
cnf(607,plain,
( ~ sorti2(h(skc3))
| equal(op2(h(skc2),h(skc3)),h(op1(skc2,skc3))) ),
inference(spr,[status(thm),theory(equality)],[18,64]),
[iquote('0:SpR:18.0,64.1')] ).
cnf(618,plain,
equal(op2(h(skc2),h(skc3)),h(op1(skc2,skc3))),
inference(ssi,[status(thm)],[607,16]),
[iquote('0:SSi:607.0,16.0')] ).
cnf(699,plain,
( ~ sorti2(h(skc2))
| equal(op1(j(h(skc2)),skc3),j(h(op1(skc2,skc3)))) ),
inference(spr,[status(thm),theory(equality)],[618,73]),
[iquote('0:SpR:618.0,73.1')] ).
cnf(705,plain,
( ~ sorti2(h(skc2))
| equal(j(h(op1(skc2,skc3))),op1(skc2,skc3)) ),
inference(rew,[status(thm),theory(equality)],[17,699]),
[iquote('0:Rew:17.0,699.1')] ).
cnf(706,plain,
equal(j(h(op1(skc2,skc3))),op1(skc2,skc3)),
inference(ssi,[status(thm)],[705,15]),
[iquote('0:SSi:705.0,15.0')] ).
cnf(762,plain,
( ~ sorti2(h(skc3))
| equal(op1(j(h(skc3)),skc2),j(h(op1(skc3,skc2)))) ),
inference(spr,[status(thm),theory(equality)],[189,74]),
[iquote('0:SpR:189.0,74.1')] ).
cnf(766,plain,
( ~ sorti2(h(skc3))
| equal(j(h(op1(skc3,skc2))),op1(skc3,skc2)) ),
inference(rew,[status(thm),theory(equality)],[18,762]),
[iquote('0:Rew:18.0,762.1')] ).
cnf(767,plain,
equal(j(h(op1(skc3,skc2))),op1(skc3,skc2)),
inference(ssi,[status(thm)],[766,16]),
[iquote('0:SSi:766.0,16.0')] ).
cnf(995,plain,
( ~ sorti1(u)
| ~ sorti2(h(op1(u,skc3)))
| equal(op2(h(op1(u,skc3)),h(skc3)),h(op1(op1(u,skc3),skc3))) ),
inference(spr,[status(thm),theory(equality)],[223,94]),
[iquote('0:SpR:223.1,94.1')] ).
cnf(1013,plain,
( ~ sorti1(u)
| equal(op2(h(op1(u,skc3)),h(skc3)),h(op1(op1(u,skc3),skc3))) ),
inference(ssi,[status(thm)],[995,3,10,1]),
[iquote('0:SSi:995.1,3.0,10.2,1.1')] ).
cnf(1014,plain,
( ~ sorti1(u)
| ~ equal(h(op1(op1(u,skc3),skc3)),h(u))
| equal(h(op1(skc3,u)),h(op1(u,skc3)))
| equal(op2(h(op1(u,skc3)),h(u)),h(skc3)) ),
inference(rew,[status(thm),theory(equality)],[1013,124]),
[iquote('0:Rew:1013.1,124.1')] ).
cnf(3228,plain,
( ~ sorti1(skc2)
| ~ sorti2(h(op1(skc2,skc3)))
| ~ equal(h(op1(op1(skc2,skc3),skc3)),h(skc2))
| equal(h(op1(skc3,skc2)),h(op1(skc2,skc3)))
| equal(op1(j(h(op1(skc2,skc3))),skc2),j(h(skc3))) ),
inference(spr,[status(thm),theory(equality)],[1014,74]),
[iquote('0:SpR:1014.3,74.1')] ).
cnf(3247,plain,
( ~ sorti1(skc2)
| ~ sorti2(h(op1(skc2,skc3)))
| ~ equal(h(skc2),h(skc2))
| equal(h(op1(skc3,skc2)),h(op1(skc2,skc3)))
| equal(op1(op1(skc2,skc3),skc2),skc3) ),
inference(rew,[status(thm),theory(equality)],[706,3228,18,5]),
[iquote('0:Rew:706.0,3228.4,18.0,3228.4,5.0,3228.2')] ).
cnf(3248,plain,
( ~ sorti1(skc2)
| ~ sorti2(h(op1(skc2,skc3)))
| equal(h(op1(skc3,skc2)),h(op1(skc2,skc3)))
| equal(op1(op1(skc2,skc3),skc2),skc3) ),
inference(obv,[status(thm),theory(equality)],[3247]),
[iquote('0:Obv:3247.2')] ).
cnf(3249,plain,
( equal(h(op1(skc3,skc2)),h(op1(skc2,skc3)))
| equal(op1(op1(skc2,skc3),skc2),skc3) ),
inference(ssi,[status(thm)],[3248,3,10,2,1]),
[iquote('0:SSi:3248.1,3248.0,3.0,10.0,2.0,1.2,2.1')] ).
cnf(3250,plain,
equal(h(op1(skc3,skc2)),h(op1(skc2,skc3))),
inference(mrr,[status(thm)],[3249,9]),
[iquote('0:MRR:3249.1,9.0')] ).
cnf(3253,plain,
equal(j(h(op1(skc2,skc3))),op1(skc3,skc2)),
inference(rew,[status(thm),theory(equality)],[3250,767]),
[iquote('0:Rew:3250.0,767.0')] ).
cnf(3266,plain,
equal(op1(skc3,skc2),op1(skc2,skc3)),
inference(rew,[status(thm),theory(equality)],[706,3253]),
[iquote('0:Rew:706.0,3253.0')] ).
cnf(3267,plain,
$false,
inference(mrr,[status(thm)],[3266,8]),
[iquote('0:MRR:3266.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ALG074+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 04:23:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.11/1.27
% 1.11/1.27 SPASS V 3.9
% 1.11/1.27 SPASS beiseite: Proof found.
% 1.11/1.27 % SZS status Theorem
% 1.11/1.27 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.11/1.27 SPASS derived 1695 clauses, backtracked 0 clauses, performed 1 splits and kept 885 clauses.
% 1.11/1.27 SPASS allocated 108716 KBytes.
% 1.11/1.27 SPASS spent 0:00:00.90 on the problem.
% 1.11/1.27 0:00:00.04 for the input.
% 1.11/1.27 0:00:00.03 for the FLOTTER CNF translation.
% 1.11/1.27 0:00:00.03 for inferences.
% 1.11/1.27 0:00:00.00 for the backtracking.
% 1.11/1.27 0:00:00.79 for the reduction.
% 1.11/1.27
% 1.11/1.27
% 1.11/1.27 Here is a proof with depth 4, length 60 :
% 1.11/1.27 % SZS output start Refutation
% See solution above
% 1.11/1.27 Formulae used in the proof : ax3 co1 ax1 ax4
% 1.11/1.27
%------------------------------------------------------------------------------