TSTP Solution File: LCL145-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL145-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n010.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 : Sun Jul 17 14:34:54 EDT 2022
% Result : Unsatisfiable 65.97s 66.16s
% Output : Refutation 65.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 9
% Syntax : Number of clauses : 72 ( 61 unt; 0 nHn; 72 RR)
% Number of literals : 83 ( 0 equ; 12 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 2 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(big_hat(not__dfg(x__dfg),not__dfg(y__dfg)),not__dfg(big_V(x__dfg,y__dfg))),
file('LCL145-1.p',unknown),
[] ).
cnf(2,axiom,
equal(implies__dfg(truth,u),u),
file('LCL145-1.p',unknown),
[] ).
cnf(3,axiom,
equal(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w))),truth),
file('LCL145-1.p',unknown),
[] ).
cnf(4,axiom,
equal(implies__dfg(implies__dfg(u,v),v),implies__dfg(implies__dfg(v,u),u)),
file('LCL145-1.p',unknown),
[] ).
cnf(5,axiom,
equal(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u)),truth),
file('LCL145-1.p',unknown),
[] ).
cnf(6,axiom,
equal(implies__dfg(implies__dfg(u,v),v),big_V(u,v)),
file('LCL145-1.p',unknown),
[] ).
cnf(7,axiom,
equal(not__dfg(big_V(not__dfg(u),not__dfg(v))),big_hat(u,v)),
file('LCL145-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ ordered(u,v)
| equal(implies__dfg(u,v),truth) ),
file('LCL145-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(implies__dfg(u,v),truth)
| ordered(u,v) ),
file('LCL145-1.p',unknown),
[] ).
cnf(10,plain,
equal(big_V(u,v),big_V(v,u)),
inference(rew,[status(thm),theory(equality)],[6,4]),
[iquote('0:Rew:6.0,4.0,6.0,4.0')] ).
cnf(23,plain,
equal(implies__dfg(big_V(u,v),v),big_V(implies__dfg(u,v),v)),
inference(spr,[status(thm),theory(equality)],[6]),
[iquote('0:SpR:6.0,6.0')] ).
cnf(26,plain,
( ~ ordered(u,v)
| equal(implies__dfg(truth,v),big_V(u,v)) ),
inference(spr,[status(thm),theory(equality)],[8,6]),
[iquote('0:SpR:8.1,6.0')] ).
cnf(28,plain,
equal(implies__dfg(big_V(u,v),v),big_V(v,implies__dfg(u,v))),
inference(rew,[status(thm),theory(equality)],[10,23]),
[iquote('0:Rew:10.0,23.0')] ).
cnf(29,plain,
( ~ ordered(u,v)
| equal(big_V(u,v),v) ),
inference(rew,[status(thm),theory(equality)],[2,26]),
[iquote('0:Rew:2.0,26.1')] ).
cnf(38,plain,
equal(big_hat(big_V(not__dfg(u),not__dfg(v)),w),not__dfg(big_V(big_hat(u,v),not__dfg(w)))),
inference(spr,[status(thm),theory(equality)],[7]),
[iquote('0:SpR:7.0,7.0')] ).
cnf(78,plain,
equal(implies__dfg(implies__dfg(not__dfg(u),not__dfg(truth)),u),truth),
inference(spr,[status(thm),theory(equality)],[2,5]),
[iquote('0:SpR:2.0,5.0')] ).
cnf(85,plain,
( ~ ordered(not__dfg(u),not__dfg(v))
| equal(implies__dfg(truth,implies__dfg(v,u)),truth) ),
inference(spr,[status(thm),theory(equality)],[8,5]),
[iquote('0:SpR:8.1,5.0')] ).
cnf(86,plain,
( ~ equal(truth,truth)
| ordered(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u)) ),
inference(spl,[status(thm),theory(equality)],[5,9]),
[iquote('0:SpL:5.0,9.0')] ).
cnf(89,plain,
( ~ ordered(not__dfg(u),not__dfg(v))
| equal(implies__dfg(v,u),truth) ),
inference(rew,[status(thm),theory(equality)],[2,85]),
[iquote('0:Rew:2.0,85.1')] ).
cnf(90,plain,
ordered(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u)),
inference(obv,[status(thm),theory(equality)],[86]),
[iquote('0:Obv:86.0')] ).
cnf(109,plain,
equal(big_V(implies__dfg(not__dfg(u),not__dfg(truth)),u),implies__dfg(truth,u)),
inference(spr,[status(thm),theory(equality)],[78,6]),
[iquote('0:SpR:78.0,6.0')] ).
cnf(110,plain,
equal(big_V(not__dfg(not__dfg(truth)),not__dfg(truth)),truth),
inference(spr,[status(thm),theory(equality)],[78,6]),
[iquote('0:SpR:78.0,6.0')] ).
cnf(115,plain,
equal(big_V(not__dfg(truth),not__dfg(not__dfg(truth))),truth),
inference(rew,[status(thm),theory(equality)],[10,110]),
[iquote('0:Rew:10.0,110.0')] ).
cnf(116,plain,
equal(big_V(u,implies__dfg(not__dfg(u),not__dfg(truth))),u),
inference(rew,[status(thm),theory(equality)],[10,109,2]),
[iquote('0:Rew:10.0,109.0,2.0,109.0')] ).
cnf(131,plain,
equal(implies__dfg(implies__dfg(truth,u),implies__dfg(implies__dfg(u,v),v)),truth),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
cnf(137,plain,
equal(implies__dfg(implies__dfg(u,truth),implies__dfg(v,implies__dfg(u,v))),truth),
inference(spr,[status(thm),theory(equality)],[2,3]),
[iquote('0:SpR:2.0,3.0')] ).
cnf(155,plain,
equal(implies__dfg(u,big_V(u,v)),truth),
inference(rew,[status(thm),theory(equality)],[2,131,6]),
[iquote('0:Rew:2.0,131.0,6.0,131.0')] ).
cnf(172,plain,
equal(big_V(truth,u),truth),
inference(spr,[status(thm),theory(equality)],[155,2]),
[iquote('0:SpR:155.0,2.0')] ).
cnf(204,plain,
equal(big_V(u,truth),truth),
inference(spr,[status(thm),theory(equality)],[172,10]),
[iquote('0:SpR:172.0,10.0')] ).
cnf(233,plain,
equal(implies__dfg(u,truth),truth),
inference(spr,[status(thm),theory(equality)],[204,155]),
[iquote('0:SpR:204.0,155.0')] ).
cnf(241,plain,
equal(implies__dfg(truth,implies__dfg(u,implies__dfg(v,u))),truth),
inference(rew,[status(thm),theory(equality)],[233,137]),
[iquote('0:Rew:233.0,137.0')] ).
cnf(242,plain,
equal(implies__dfg(u,implies__dfg(v,u)),truth),
inference(rew,[status(thm),theory(equality)],[2,241]),
[iquote('0:Rew:2.0,241.0')] ).
cnf(271,plain,
equal(implies__dfg(truth,implies__dfg(u,v)),big_V(v,implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[242,6]),
[iquote('0:SpR:242.0,6.0')] ).
cnf(288,plain,
equal(big_V(u,implies__dfg(v,u)),implies__dfg(v,u)),
inference(rew,[status(thm),theory(equality)],[2,271]),
[iquote('0:Rew:2.0,271.0')] ).
cnf(289,plain,
equal(implies__dfg(big_V(u,v),v),implies__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[288,28]),
[iquote('0:Rew:288.0,28.0')] ).
cnf(390,plain,
equal(implies__dfg(not__dfg(truth),not__dfg(not__dfg(truth))),implies__dfg(truth,not__dfg(not__dfg(truth)))),
inference(spr,[status(thm),theory(equality)],[115,289]),
[iquote('0:SpR:115.0,289.0')] ).
cnf(395,plain,
equal(implies__dfg(not__dfg(truth),not__dfg(not__dfg(truth))),not__dfg(not__dfg(truth))),
inference(rew,[status(thm),theory(equality)],[2,390]),
[iquote('0:Rew:2.0,390.0')] ).
cnf(399,plain,
( ~ ordered(u,implies__dfg(not__dfg(u),not__dfg(truth)))
| equal(implies__dfg(not__dfg(u),not__dfg(truth)),u) ),
inference(spr,[status(thm),theory(equality)],[116,29]),
[iquote('0:SpR:116.0,29.1')] ).
cnf(406,plain,
( ~ ordered(not__dfg(u),not__dfg(truth))
| equal(big_V(u,truth),u) ),
inference(spr,[status(thm),theory(equality)],[8,116]),
[iquote('0:SpR:8.1,116.0')] ).
cnf(407,plain,
( ~ ordered(not__dfg(u),not__dfg(truth))
| equal(truth,u) ),
inference(rew,[status(thm),theory(equality)],[204,406]),
[iquote('0:Rew:204.0,406.1')] ).
cnf(458,plain,
equal(implies__dfg(not__dfg(not__dfg(truth)),not__dfg(truth)),not__dfg(truth)),
inference(spr,[status(thm),theory(equality)],[288,116]),
[iquote('0:SpR:288.0,116.0')] ).
cnf(476,plain,
ordered(implies__dfg(not__dfg(not__dfg(truth)),not__dfg(not__dfg(not__dfg(truth)))),not__dfg(truth)),
inference(spr,[status(thm),theory(equality)],[458,90]),
[iquote('0:SpR:458.0,90.0')] ).
cnf(580,plain,
equal(implies__dfg(implies__dfg(not__dfg(not__dfg(not__dfg(truth))),not__dfg(not__dfg(truth))),not__dfg(not__dfg(truth))),truth),
inference(spr,[status(thm),theory(equality)],[395,5]),
[iquote('0:SpR:395.0,5.0')] ).
cnf(597,plain,
equal(big_V(not__dfg(not__dfg(truth)),not__dfg(not__dfg(not__dfg(truth)))),truth),
inference(rew,[status(thm),theory(equality)],[10,580,6]),
[iquote('0:Rew:10.0,580.0,6.0,580.0')] ).
cnf(608,plain,
equal(implies__dfg(not__dfg(not__dfg(truth)),not__dfg(not__dfg(not__dfg(truth)))),implies__dfg(truth,not__dfg(not__dfg(not__dfg(truth))))),
inference(spr,[status(thm),theory(equality)],[597,289]),
[iquote('0:SpR:597.0,289.0')] ).
cnf(615,plain,
equal(implies__dfg(not__dfg(not__dfg(truth)),not__dfg(not__dfg(not__dfg(truth)))),not__dfg(not__dfg(not__dfg(truth)))),
inference(rew,[status(thm),theory(equality)],[2,608]),
[iquote('0:Rew:2.0,608.0')] ).
cnf(616,plain,
ordered(not__dfg(not__dfg(not__dfg(truth))),not__dfg(truth)),
inference(rew,[status(thm),theory(equality)],[615,476]),
[iquote('0:Rew:615.0,476.0')] ).
cnf(618,plain,
equal(not__dfg(not__dfg(truth)),truth),
inference(res,[status(thm),theory(equality)],[616,407]),
[iquote('0:Res:616.0,407.0')] ).
cnf(646,plain,
equal(implies__dfg(implies__dfg(not__dfg(u),truth),implies__dfg(not__dfg(truth),u)),truth),
inference(spr,[status(thm),theory(equality)],[618,5]),
[iquote('0:SpR:618.0,5.0')] ).
cnf(650,plain,
ordered(implies__dfg(truth,not__dfg(u)),implies__dfg(u,not__dfg(truth))),
inference(spr,[status(thm),theory(equality)],[618,90]),
[iquote('0:SpR:618.0,90.0')] ).
cnf(661,plain,
ordered(not__dfg(u),implies__dfg(u,not__dfg(truth))),
inference(rew,[status(thm),theory(equality)],[2,650]),
[iquote('0:Rew:2.0,650.0')] ).
cnf(666,plain,
equal(implies__dfg(not__dfg(truth),u),truth),
inference(rew,[status(thm),theory(equality)],[2,646,233]),
[iquote('0:Rew:2.0,646.0,233.0,646.0')] ).
cnf(703,plain,
equal(big_V(not__dfg(truth),u),implies__dfg(truth,u)),
inference(spr,[status(thm),theory(equality)],[666,6]),
[iquote('0:SpR:666.0,6.0')] ).
cnf(719,plain,
equal(big_V(not__dfg(truth),u),u),
inference(rew,[status(thm),theory(equality)],[2,703]),
[iquote('0:Rew:2.0,703.0')] ).
cnf(729,plain,
equal(big_V(u,not__dfg(truth)),u),
inference(spr,[status(thm),theory(equality)],[719,10]),
[iquote('0:SpR:719.0,10.0')] ).
cnf(767,plain,
equal(big_hat(u,truth),not__dfg(not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[729,7]),
[iquote('0:SpR:729.0,7.0')] ).
cnf(865,plain,
ordered(not__dfg(implies__dfg(u,not__dfg(truth))),big_V(u,not__dfg(truth))),
inference(spr,[status(thm),theory(equality)],[6,661]),
[iquote('0:SpR:6.0,661.0')] ).
cnf(871,plain,
ordered(not__dfg(implies__dfg(u,not__dfg(truth))),u),
inference(rew,[status(thm),theory(equality)],[729,865]),
[iquote('0:Rew:729.0,865.0')] ).
cnf(982,plain,
equal(implies__dfg(u,implies__dfg(not__dfg(u),not__dfg(truth))),truth),
inference(res,[status(thm),theory(equality)],[871,89]),
[iquote('0:Res:871.0,89.0')] ).
cnf(1345,plain,
( ~ equal(truth,truth)
| ordered(u,implies__dfg(not__dfg(u),not__dfg(truth))) ),
inference(spl,[status(thm),theory(equality)],[982,9]),
[iquote('0:SpL:982.0,9.0')] ).
cnf(1347,plain,
ordered(u,implies__dfg(not__dfg(u),not__dfg(truth))),
inference(obv,[status(thm),theory(equality)],[1345]),
[iquote('0:Obv:1345.0')] ).
cnf(1348,plain,
equal(implies__dfg(not__dfg(u),not__dfg(truth)),u),
inference(mrr,[status(thm)],[399,1347]),
[iquote('0:MRR:399.0,1347.0')] ).
cnf(1389,plain,
equal(big_V(not__dfg(u),not__dfg(truth)),implies__dfg(u,not__dfg(truth))),
inference(spr,[status(thm),theory(equality)],[1348,6]),
[iquote('0:SpR:1348.0,6.0')] ).
cnf(1411,plain,
equal(implies__dfg(big_hat(u,v),not__dfg(truth)),big_V(not__dfg(u),not__dfg(v))),
inference(spr,[status(thm),theory(equality)],[7,1348]),
[iquote('0:SpR:7.0,1348.0')] ).
cnf(1418,plain,
equal(implies__dfg(u,not__dfg(truth)),not__dfg(u)),
inference(rew,[status(thm),theory(equality)],[729,1389]),
[iquote('0:Rew:729.0,1389.0')] ).
cnf(1424,plain,
equal(not__dfg(not__dfg(u)),u),
inference(rew,[status(thm),theory(equality)],[1418,1348]),
[iquote('0:Rew:1418.0,1348.0')] ).
cnf(1449,plain,
equal(big_hat(u,truth),u),
inference(rew,[status(thm),theory(equality)],[1424,767]),
[iquote('0:Rew:1424.0,767.0')] ).
cnf(1469,plain,
equal(big_V(not__dfg(u),not__dfg(v)),not__dfg(big_hat(u,v))),
inference(rew,[status(thm),theory(equality)],[1418,1411]),
[iquote('0:Rew:1418.0,1411.0')] ).
cnf(1471,plain,
equal(not__dfg(big_V(big_hat(u,v),not__dfg(w))),big_hat(not__dfg(big_hat(u,v)),w)),
inference(rew,[status(thm),theory(equality)],[1469,38]),
[iquote('0:Rew:1469.0,38.0')] ).
cnf(1624,plain,
equal(not__dfg(big_V(u,not__dfg(v))),big_hat(not__dfg(u),v)),
inference(spr,[status(thm),theory(equality)],[1449,1471]),
[iquote('0:SpR:1449.0,1471.0')] ).
cnf(94641,plain,
equal(big_hat(not__dfg(u),not__dfg(v)),not__dfg(big_V(u,v))),
inference(spr,[status(thm),theory(equality)],[1424,1624]),
[iquote('0:SpR:1424.0,1624.0')] ).
cnf(94684,plain,
$false,
inference(unc,[status(thm)],[94641,1]),
[iquote('0:UnC:94641.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL145-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n010.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 : Sun Jul 3 06:27:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 65.97/66.16
% 65.97/66.16 SPASS V 3.9
% 65.97/66.16 SPASS beiseite: Proof found.
% 65.97/66.16 % SZS status Theorem
% 65.97/66.16 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 65.97/66.16 SPASS derived 61495 clauses, backtracked 0 clauses, performed 0 splits and kept 10205 clauses.
% 65.97/66.16 SPASS allocated 142218 KBytes.
% 65.97/66.16 SPASS spent 0:01:02.78 on the problem.
% 65.97/66.16 0:00:00.04 for the input.
% 65.97/66.16 0:00:00.00 for the FLOTTER CNF translation.
% 65.97/66.16 0:00:00.38 for inferences.
% 65.97/66.16 0:00:00.00 for the backtracking.
% 65.97/66.16 0:01:02.29 for the reduction.
% 65.97/66.16
% 65.97/66.16
% 65.97/66.16 Here is a proof with depth 11, length 72 :
% 65.97/66.16 % SZS output start Refutation
% See solution above
% 65.97/66.16 Formulae used in the proof : prove_wajsberg_theorem wajsberg_1 wajsberg_2 wajsberg_3 wajsberg_4 big_V_definition big_hat_definition partial_order_definition1 partial_order_definition2
% 65.97/66.16
%------------------------------------------------------------------------------