TSTP Solution File: LCL146-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL146-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 9
% Syntax : Number of clauses : 65 ( 54 unt; 0 nHn; 65 RR)
% Number of literals : 76 ( 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_V(not__dfg(x__dfg),not__dfg(y__dfg)),not__dfg(big_hat(x__dfg,y__dfg))),
file('LCL146-1.p',unknown),
[] ).
cnf(2,axiom,
equal(implies__dfg(truth,u),u),
file('LCL146-1.p',unknown),
[] ).
cnf(3,axiom,
equal(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w))),truth),
file('LCL146-1.p',unknown),
[] ).
cnf(4,axiom,
equal(implies__dfg(implies__dfg(u,v),v),implies__dfg(implies__dfg(v,u),u)),
file('LCL146-1.p',unknown),
[] ).
cnf(5,axiom,
equal(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u)),truth),
file('LCL146-1.p',unknown),
[] ).
cnf(6,axiom,
equal(implies__dfg(implies__dfg(u,v),v),big_V(u,v)),
file('LCL146-1.p',unknown),
[] ).
cnf(7,axiom,
equal(not__dfg(big_V(not__dfg(u),not__dfg(v))),big_hat(u,v)),
file('LCL146-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ ordered(u,v)
| equal(implies__dfg(u,v),truth) ),
file('LCL146-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(implies__dfg(u,v),truth)
| ordered(u,v) ),
file('LCL146-1.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(80,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(87,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(88,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(91,plain,
( ~ ordered(not__dfg(u),not__dfg(v))
| equal(implies__dfg(v,u),truth) ),
inference(rew,[status(thm),theory(equality)],[2,87]),
[iquote('0:Rew:2.0,87.1')] ).
cnf(92,plain,
ordered(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u)),
inference(obv,[status(thm),theory(equality)],[88]),
[iquote('0:Obv:88.0')] ).
cnf(111,plain,
equal(big_V(implies__dfg(not__dfg(u),not__dfg(truth)),u),implies__dfg(truth,u)),
inference(spr,[status(thm),theory(equality)],[80,6]),
[iquote('0:SpR:80.0,6.0')] ).
cnf(112,plain,
equal(big_V(not__dfg(not__dfg(truth)),not__dfg(truth)),truth),
inference(spr,[status(thm),theory(equality)],[80,6]),
[iquote('0:SpR:80.0,6.0')] ).
cnf(117,plain,
equal(big_V(not__dfg(truth),not__dfg(not__dfg(truth))),truth),
inference(rew,[status(thm),theory(equality)],[10,112]),
[iquote('0:Rew:10.0,112.0')] ).
cnf(118,plain,
equal(big_V(u,implies__dfg(not__dfg(u),not__dfg(truth))),u),
inference(rew,[status(thm),theory(equality)],[10,111,2]),
[iquote('0:Rew:10.0,111.0,2.0,111.0')] ).
cnf(133,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(139,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(157,plain,
equal(implies__dfg(u,big_V(u,v)),truth),
inference(rew,[status(thm),theory(equality)],[2,133,6]),
[iquote('0:Rew:2.0,133.0,6.0,133.0')] ).
cnf(174,plain,
equal(big_V(truth,u),truth),
inference(spr,[status(thm),theory(equality)],[157,2]),
[iquote('0:SpR:157.0,2.0')] ).
cnf(206,plain,
equal(big_V(u,truth),truth),
inference(spr,[status(thm),theory(equality)],[174,10]),
[iquote('0:SpR:174.0,10.0')] ).
cnf(235,plain,
equal(implies__dfg(u,truth),truth),
inference(spr,[status(thm),theory(equality)],[206,157]),
[iquote('0:SpR:206.0,157.0')] ).
cnf(243,plain,
equal(implies__dfg(truth,implies__dfg(u,implies__dfg(v,u))),truth),
inference(rew,[status(thm),theory(equality)],[235,139]),
[iquote('0:Rew:235.0,139.0')] ).
cnf(244,plain,
equal(implies__dfg(u,implies__dfg(v,u)),truth),
inference(rew,[status(thm),theory(equality)],[2,243]),
[iquote('0:Rew:2.0,243.0')] ).
cnf(273,plain,
equal(implies__dfg(truth,implies__dfg(u,v)),big_V(v,implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[244,6]),
[iquote('0:SpR:244.0,6.0')] ).
cnf(290,plain,
equal(big_V(u,implies__dfg(v,u)),implies__dfg(v,u)),
inference(rew,[status(thm),theory(equality)],[2,273]),
[iquote('0:Rew:2.0,273.0')] ).
cnf(291,plain,
equal(implies__dfg(big_V(u,v),v),implies__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[290,28]),
[iquote('0:Rew:290.0,28.0')] ).
cnf(392,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)],[117,291]),
[iquote('0:SpR:117.0,291.0')] ).
cnf(397,plain,
equal(implies__dfg(not__dfg(truth),not__dfg(not__dfg(truth))),not__dfg(not__dfg(truth))),
inference(rew,[status(thm),theory(equality)],[2,392]),
[iquote('0:Rew:2.0,392.0')] ).
cnf(401,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)],[118,29]),
[iquote('0:SpR:118.0,29.1')] ).
cnf(408,plain,
( ~ ordered(not__dfg(u),not__dfg(truth))
| equal(big_V(u,truth),u) ),
inference(spr,[status(thm),theory(equality)],[8,118]),
[iquote('0:SpR:8.1,118.0')] ).
cnf(409,plain,
( ~ ordered(not__dfg(u),not__dfg(truth))
| equal(truth,u) ),
inference(rew,[status(thm),theory(equality)],[206,408]),
[iquote('0:Rew:206.0,408.1')] ).
cnf(462,plain,
equal(implies__dfg(not__dfg(not__dfg(truth)),not__dfg(truth)),not__dfg(truth)),
inference(spr,[status(thm),theory(equality)],[290,118]),
[iquote('0:SpR:290.0,118.0')] ).
cnf(480,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)],[462,92]),
[iquote('0:SpR:462.0,92.0')] ).
cnf(584,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)],[397,5]),
[iquote('0:SpR:397.0,5.0')] ).
cnf(601,plain,
equal(big_V(not__dfg(not__dfg(truth)),not__dfg(not__dfg(not__dfg(truth)))),truth),
inference(rew,[status(thm),theory(equality)],[10,584,6]),
[iquote('0:Rew:10.0,584.0,6.0,584.0')] ).
cnf(612,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)],[601,291]),
[iquote('0:SpR:601.0,291.0')] ).
cnf(619,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)],[2,612]),
[iquote('0:Rew:2.0,612.0')] ).
cnf(620,plain,
ordered(not__dfg(not__dfg(not__dfg(truth))),not__dfg(truth)),
inference(rew,[status(thm),theory(equality)],[619,480]),
[iquote('0:Rew:619.0,480.0')] ).
cnf(622,plain,
equal(not__dfg(not__dfg(truth)),truth),
inference(res,[status(thm),theory(equality)],[620,409]),
[iquote('0:Res:620.0,409.0')] ).
cnf(650,plain,
equal(implies__dfg(implies__dfg(not__dfg(u),truth),implies__dfg(not__dfg(truth),u)),truth),
inference(spr,[status(thm),theory(equality)],[622,5]),
[iquote('0:SpR:622.0,5.0')] ).
cnf(654,plain,
ordered(implies__dfg(truth,not__dfg(u)),implies__dfg(u,not__dfg(truth))),
inference(spr,[status(thm),theory(equality)],[622,92]),
[iquote('0:SpR:622.0,92.0')] ).
cnf(665,plain,
ordered(not__dfg(u),implies__dfg(u,not__dfg(truth))),
inference(rew,[status(thm),theory(equality)],[2,654]),
[iquote('0:Rew:2.0,654.0')] ).
cnf(670,plain,
equal(implies__dfg(not__dfg(truth),u),truth),
inference(rew,[status(thm),theory(equality)],[2,650,235]),
[iquote('0:Rew:2.0,650.0,235.0,650.0')] ).
cnf(707,plain,
equal(big_V(not__dfg(truth),u),implies__dfg(truth,u)),
inference(spr,[status(thm),theory(equality)],[670,6]),
[iquote('0:SpR:670.0,6.0')] ).
cnf(723,plain,
equal(big_V(not__dfg(truth),u),u),
inference(rew,[status(thm),theory(equality)],[2,707]),
[iquote('0:Rew:2.0,707.0')] ).
cnf(733,plain,
equal(big_V(u,not__dfg(truth)),u),
inference(spr,[status(thm),theory(equality)],[723,10]),
[iquote('0:SpR:723.0,10.0')] ).
cnf(869,plain,
ordered(not__dfg(implies__dfg(u,not__dfg(truth))),big_V(u,not__dfg(truth))),
inference(spr,[status(thm),theory(equality)],[6,665]),
[iquote('0:SpR:6.0,665.0')] ).
cnf(875,plain,
ordered(not__dfg(implies__dfg(u,not__dfg(truth))),u),
inference(rew,[status(thm),theory(equality)],[733,869]),
[iquote('0:Rew:733.0,869.0')] ).
cnf(986,plain,
equal(implies__dfg(u,implies__dfg(not__dfg(u),not__dfg(truth))),truth),
inference(res,[status(thm),theory(equality)],[875,91]),
[iquote('0:Res:875.0,91.0')] ).
cnf(1349,plain,
( ~ equal(truth,truth)
| ordered(u,implies__dfg(not__dfg(u),not__dfg(truth))) ),
inference(spl,[status(thm),theory(equality)],[986,9]),
[iquote('0:SpL:986.0,9.0')] ).
cnf(1351,plain,
ordered(u,implies__dfg(not__dfg(u),not__dfg(truth))),
inference(obv,[status(thm),theory(equality)],[1349]),
[iquote('0:Obv:1349.0')] ).
cnf(1352,plain,
equal(implies__dfg(not__dfg(u),not__dfg(truth)),u),
inference(mrr,[status(thm)],[401,1351]),
[iquote('0:MRR:401.0,1351.0')] ).
cnf(1393,plain,
equal(big_V(not__dfg(u),not__dfg(truth)),implies__dfg(u,not__dfg(truth))),
inference(spr,[status(thm),theory(equality)],[1352,6]),
[iquote('0:SpR:1352.0,6.0')] ).
cnf(1415,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)],[7,1352]),
[iquote('0:SpR:7.0,1352.0')] ).
cnf(1422,plain,
equal(implies__dfg(u,not__dfg(truth)),not__dfg(u)),
inference(rew,[status(thm),theory(equality)],[733,1393]),
[iquote('0:Rew:733.0,1393.0')] ).
cnf(1475,plain,
equal(big_V(not__dfg(u),not__dfg(v)),not__dfg(big_hat(u,v))),
inference(rew,[status(thm),theory(equality)],[1422,1415]),
[iquote('0:Rew:1422.0,1415.0')] ).
cnf(1476,plain,
$false,
inference(unc,[status(thm)],[1475,1]),
[iquote('0:UnC:1475.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL146-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 18:46:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.51
% 0.18/0.51 SPASS V 3.9
% 0.18/0.51 SPASS beiseite: Proof found.
% 0.18/0.51 % SZS status Theorem
% 0.18/0.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.51 SPASS derived 1097 clauses, backtracked 0 clauses, performed 0 splits and kept 292 clauses.
% 0.18/0.51 SPASS allocated 64264 KBytes.
% 0.18/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.18/0.51 0:00:00.03 for the input.
% 0.18/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.51 0:00:00.01 for inferences.
% 0.18/0.51 0:00:00.00 for the backtracking.
% 0.18/0.51 0:00:00.09 for the reduction.
% 0.18/0.51
% 0.18/0.51
% 0.18/0.51 Here is a proof with depth 9, length 65 :
% 0.18/0.51 % SZS output start Refutation
% See solution above
% 0.18/0.51 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
% 0.18/0.51
%------------------------------------------------------------------------------