TSTP Solution File: LCL155-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL155-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 14:34:57 EDT 2022
% Result : Unsatisfiable 0.17s 0.44s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of clauses : 50 ( 50 unt; 0 nHn; 50 RR)
% Number of literals : 50 ( 0 equ; 1 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 : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(xor__dfg(x__dfg,x__dfg),falsehood),
file('LCL155-1.p',unknown),
[] ).
cnf(2,axiom,
equal(implies__dfg(truth,u),u),
file('LCL155-1.p',unknown),
[] ).
cnf(4,axiom,
equal(implies__dfg(implies__dfg(u,v),v),implies__dfg(implies__dfg(v,u),u)),
file('LCL155-1.p',unknown),
[] ).
cnf(5,axiom,
equal(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u)),truth),
file('LCL155-1.p',unknown),
[] ).
cnf(6,axiom,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
file('LCL155-1.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(or__dfg(u,v),w),or__dfg(u,or__dfg(v,w))),
file('LCL155-1.p',unknown),
[] ).
cnf(8,axiom,
equal(or__dfg(u,v),or__dfg(v,u)),
file('LCL155-1.p',unknown),
[] ).
cnf(9,axiom,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)),
file('LCL155-1.p',unknown),
[] ).
cnf(11,axiom,
equal(and__dfg(u,v),and__dfg(v,u)),
file('LCL155-1.p',unknown),
[] ).
cnf(12,axiom,
equal(or__dfg(and__dfg(u,not__dfg(v)),and__dfg(not__dfg(u),v)),xor__dfg(u,v)),
file('LCL155-1.p',unknown),
[] ).
cnf(14,axiom,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and_star(u,v)),
file('LCL155-1.p',unknown),
[] ).
cnf(17,axiom,
equal(not__dfg(truth),falsehood),
file('LCL155-1.p',unknown),
[] ).
cnf(18,plain,
equal(and_star(u,v),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[14,9]),
[iquote('0:Rew:14.0,9.0')] ).
cnf(20,plain,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[18,14]),
[iquote('0:Rew:18.0,14.0')] ).
cnf(23,plain,
equal(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u)),truth),
inference(rew,[status(thm),theory(equality)],[6,5]),
[iquote('0:Rew:6.0,5.0')] ).
cnf(46,plain,
equal(implies__dfg(or__dfg(u,not__dfg(truth)),u),truth),
inference(spr,[status(thm),theory(equality)],[2,23]),
[iquote('0:SpR:2.0,23.0')] ).
cnf(52,plain,
equal(implies__dfg(or__dfg(u,falsehood),u),truth),
inference(rew,[status(thm),theory(equality)],[17,46]),
[iquote('0:Rew:17.0,46.0')] ).
cnf(56,plain,
equal(implies__dfg(or__dfg(falsehood,u),u),truth),
inference(spr,[status(thm),theory(equality)],[8,52]),
[iquote('0:SpR:8.0,52.0')] ).
cnf(79,plain,
equal(not__dfg(or__dfg(not__dfg(u),falsehood)),and__dfg(u,truth)),
inference(spr,[status(thm),theory(equality)],[17,20]),
[iquote('0:SpR:17.0,20.0')] ).
cnf(83,plain,
equal(not__dfg(or__dfg(falsehood,not__dfg(u))),and__dfg(u,truth)),
inference(rew,[status(thm),theory(equality)],[8,79]),
[iquote('0:Rew:8.0,79.0')] ).
cnf(88,plain,
equal(or__dfg(or__dfg(falsehood,not__dfg(u)),v),implies__dfg(and__dfg(u,truth),v)),
inference(spr,[status(thm),theory(equality)],[83,6]),
[iquote('0:SpR:83.0,6.0')] ).
cnf(96,plain,
equal(or__dfg(falsehood,or__dfg(not__dfg(u),v)),implies__dfg(and__dfg(u,truth),v)),
inference(rew,[status(thm),theory(equality)],[7,88]),
[iquote('0:Rew:7.0,88.0')] ).
cnf(139,plain,
equal(implies__dfg(u,u),implies__dfg(implies__dfg(u,truth),truth)),
inference(spr,[status(thm),theory(equality)],[2,4]),
[iquote('0:SpR:2.0,4.0')] ).
cnf(148,plain,
equal(implies__dfg(implies__dfg(not__dfg(u),truth),truth),or__dfg(u,not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[139,6]),
[iquote('0:SpR:139.0,6.0')] ).
cnf(165,plain,
equal(implies__dfg(or__dfg(u,truth),truth),or__dfg(u,not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[6,148]),
[iquote('0:Rew:6.0,148.0')] ).
cnf(242,plain,
equal(or__dfg(falsehood,not__dfg(falsehood)),truth),
inference(spr,[status(thm),theory(equality)],[165,56]),
[iquote('0:SpR:165.0,56.0')] ).
cnf(246,plain,
equal(not__dfg(implies__dfg(or__dfg(not__dfg(u),truth),truth)),and__dfg(u,not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[165,20]),
[iquote('0:SpR:165.0,20.0')] ).
cnf(252,plain,
equal(implies__dfg(or__dfg(or__dfg(falsehood,not__dfg(u)),truth),truth),or__dfg(or__dfg(falsehood,not__dfg(u)),and__dfg(u,truth))),
inference(spr,[status(thm),theory(equality)],[83,165]),
[iquote('0:SpR:83.0,165.0')] ).
cnf(253,plain,
equal(not__dfg(implies__dfg(or__dfg(truth,not__dfg(u)),truth)),and__dfg(u,not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[8,246]),
[iquote('0:Rew:8.0,246.0')] ).
cnf(258,plain,
equal(implies__dfg(or__dfg(truth,or__dfg(falsehood,not__dfg(u))),truth),or__dfg(and__dfg(u,truth),or__dfg(falsehood,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[8,252]),
[iquote('0:Rew:8.0,252.0,8.0,252.0')] ).
cnf(260,plain,
equal(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(w,u))),
inference(spr,[status(thm),theory(equality)],[7,8]),
[iquote('0:SpR:7.0,8.0')] ).
cnf(274,plain,
equal(or__dfg(or__dfg(u,v),w),or__dfg(v,or__dfg(u,w))),
inference(spr,[status(thm),theory(equality)],[8,7]),
[iquote('0:SpR:8.0,7.0')] ).
cnf(278,plain,
equal(implies__dfg(or__dfg(truth,or__dfg(falsehood,not__dfg(u))),truth),or__dfg(falsehood,or__dfg(not__dfg(u),and__dfg(u,truth)))),
inference(rew,[status(thm),theory(equality)],[260,258]),
[iquote('0:Rew:260.0,258.0')] ).
cnf(280,plain,
equal(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w))),
inference(rew,[status(thm),theory(equality)],[7,274]),
[iquote('0:Rew:7.0,274.0')] ).
cnf(288,plain,
equal(implies__dfg(or__dfg(falsehood,or__dfg(truth,not__dfg(u))),truth),implies__dfg(and__dfg(u,truth),and__dfg(u,truth))),
inference(rew,[status(thm),theory(equality)],[280,278,96]),
[iquote('0:Rew:280.0,278.0,96.0,278.0')] ).
cnf(290,plain,
equal(implies__dfg(truth,not__dfg(falsehood)),truth),
inference(spr,[status(thm),theory(equality)],[242,56]),
[iquote('0:SpR:242.0,56.0')] ).
cnf(292,plain,
equal(or__dfg(falsehood,or__dfg(not__dfg(falsehood),u)),or__dfg(truth,u)),
inference(spr,[status(thm),theory(equality)],[242,7]),
[iquote('0:SpR:242.0,7.0')] ).
cnf(298,plain,
equal(not__dfg(falsehood),truth),
inference(rew,[status(thm),theory(equality)],[2,290]),
[iquote('0:Rew:2.0,290.0')] ).
cnf(320,plain,
equal(or__dfg(falsehood,or__dfg(truth,u)),or__dfg(truth,u)),
inference(rew,[status(thm),theory(equality)],[298,292]),
[iquote('0:Rew:298.0,292.0')] ).
cnf(321,plain,
equal(implies__dfg(and__dfg(u,truth),and__dfg(u,truth)),implies__dfg(or__dfg(truth,not__dfg(u)),truth)),
inference(rew,[status(thm),theory(equality)],[320,288]),
[iquote('0:Rew:320.0,288.0')] ).
cnf(330,plain,
equal(implies__dfg(truth,u),or__dfg(falsehood,u)),
inference(spr,[status(thm),theory(equality)],[298,6]),
[iquote('0:SpR:298.0,6.0')] ).
cnf(338,plain,
equal(or__dfg(falsehood,u),u),
inference(rew,[status(thm),theory(equality)],[2,330]),
[iquote('0:Rew:2.0,330.0')] ).
cnf(342,plain,
equal(implies__dfg(u,u),truth),
inference(rew,[status(thm),theory(equality)],[338,56]),
[iquote('0:Rew:338.0,56.0')] ).
cnf(358,plain,
equal(implies__dfg(or__dfg(truth,not__dfg(u)),truth),truth),
inference(rew,[status(thm),theory(equality)],[342,321]),
[iquote('0:Rew:342.0,321.0')] ).
cnf(371,plain,
equal(and__dfg(u,not__dfg(u)),not__dfg(truth)),
inference(rew,[status(thm),theory(equality)],[358,253]),
[iquote('0:Rew:358.0,253.0')] ).
cnf(372,plain,
equal(and__dfg(u,not__dfg(u)),falsehood),
inference(rew,[status(thm),theory(equality)],[17,371]),
[iquote('0:Rew:17.0,371.0')] ).
cnf(422,plain,
equal(or__dfg(u,falsehood),u),
inference(spr,[status(thm),theory(equality)],[338,8]),
[iquote('0:SpR:338.0,8.0')] ).
cnf(463,plain,
equal(or__dfg(falsehood,and__dfg(not__dfg(u),u)),xor__dfg(u,u)),
inference(spr,[status(thm),theory(equality)],[372,12]),
[iquote('0:SpR:372.0,12.0')] ).
cnf(473,plain,
equal(xor__dfg(u,u),falsehood),
inference(rew,[status(thm),theory(equality)],[422,463,372,11]),
[iquote('0:Rew:422.0,463.0,372.0,463.0,11.0,463.0')] ).
cnf(474,plain,
$false,
inference(unc,[status(thm)],[473,1]),
[iquote('0:UnC:473.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LCL155-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sun Jul 3 23:22:08 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.17/0.44
% 0.17/0.44 SPASS V 3.9
% 0.17/0.44 SPASS beiseite: Proof found.
% 0.17/0.44 % SZS status Theorem
% 0.17/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 SPASS derived 321 clauses, backtracked 0 clauses, performed 0 splits and kept 147 clauses.
% 0.17/0.44 SPASS allocated 63625 KBytes.
% 0.17/0.44 SPASS spent 0:00:00.10 on the problem.
% 0.17/0.44 0:00:00.03 for the input.
% 0.17/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.17/0.44 0:00:00.00 for inferences.
% 0.17/0.44 0:00:00.00 for the backtracking.
% 0.17/0.44 0:00:00.04 for the reduction.
% 0.17/0.44
% 0.17/0.44
% 0.17/0.44 Here is a proof with depth 6, length 50 :
% 0.17/0.44 % SZS output start Refutation
% See solution above
% 0.17/0.44 Formulae used in the proof : prove_alternative_wajsberg_axiom wajsberg_1 wajsberg_3 wajsberg_4 or_definition or_associativity or_commutativity and_definition and_commutativity xor_definition and_star_definition false_definition
% 0.17/0.44
%------------------------------------------------------------------------------