%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL158-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:06:53 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.38s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of clauses : 92 ( 92 unt; 0 nHn; 92 RR)
% Number of literals : 92 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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(and_star(xor__dfg(truth,x__dfg),x__dfg),falsehood),
file('LCL158-1.p',unknown),
[] ).
cnf(2,axiom,
equal(implies__dfg(truth,u),u),
file('LCL158-1.p',unknown),
[] ).
cnf(3,axiom,
equal(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w))),truth),
file('LCL158-1.p',unknown),
[] ).
cnf(4,axiom,
equal(implies__dfg(implies__dfg(u,v),v),implies__dfg(implies__dfg(v,u),u)),
file('LCL158-1.p',unknown),
[] ).
cnf(5,axiom,
equal(implies__dfg(implies__dfg(not__dfg(u),not__dfg(v)),implies__dfg(v,u)),truth),
file('LCL158-1.p',unknown),
[] ).
cnf(6,axiom,
equal(implies__dfg(not__dfg(u),v),or__dfg(u,v)),
file('LCL158-1.p',unknown),
[] ).
cnf(7,axiom,
equal(or__dfg(or__dfg(u,v),w),or__dfg(u,or__dfg(v,w))),
file('LCL158-1.p',unknown),
[] ).
cnf(8,axiom,
equal(or__dfg(u,v),or__dfg(v,u)),
file('LCL158-1.p',unknown),
[] ).
cnf(9,axiom,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and__dfg(u,v)),
file('LCL158-1.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('LCL158-1.p',unknown),
[] ).
cnf(14,axiom,
equal(not__dfg(or__dfg(not__dfg(u),not__dfg(v))),and_star(u,v)),
file('LCL158-1.p',unknown),
[] ).
cnf(15,axiom,
equal(and_star(and_star(u,v),w),and_star(u,and_star(v,w))),
file('LCL158-1.p',unknown),
[] ).
cnf(16,axiom,
equal(and_star(u,v),and_star(v,u)),
file('LCL158-1.p',unknown),
[] ).
cnf(17,axiom,
equal(not__dfg(truth),falsehood),
file('LCL158-1.p',unknown),
[] ).
cnf(18,plain,
~ equal(and_star(x__dfg,xor__dfg(truth,x__dfg)),falsehood),
inference(rew,[status(thm),theory(equality)],[16,1]),
[iquote('0:Rew:16.0,1.0')] ).
cnf(19,plain,
equal(and__dfg(u,v),and_star(u,v)),
inference(rew,[status(thm),theory(equality)],[14,9]),
[iquote('0:Rew:14.0,9.0')] ).
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(24,plain,
equal(or__dfg(and_star(u,not__dfg(v)),and_star(not__dfg(u),v)),xor__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[19,12]),
[iquote('0:Rew:19.0,12.0,19.0,12.0')] ).
cnf(41,plain,
equal(implies__dfg(falsehood,u),or__dfg(truth,u)),
inference(spr,[status(thm),theory(equality)],[17,6]),
[iquote('0:SpR:17.0,6.0')] ).
cnf(45,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(46,plain,
equal(implies__dfg(or__dfg(u,not__dfg(falsehood)),or__dfg(truth,u)),truth),
inference(spr,[status(thm),theory(equality)],[41,23]),
[iquote('0:SpR:41.0,23.0')] ).
cnf(51,plain,
equal(implies__dfg(or__dfg(u,falsehood),u),truth),
inference(rew,[status(thm),theory(equality)],[17,45]),
[iquote('0:Rew:17.0,45.0')] ).
cnf(55,plain,
equal(implies__dfg(or__dfg(falsehood,u),u),truth),
inference(spr,[status(thm),theory(equality)],[8,51]),
[iquote('0:SpR:8.0,51.0')] ).
cnf(57,plain,
equal(implies__dfg(or__dfg(u,not__dfg(or__dfg(falsehood,u))),truth),truth),
inference(spr,[status(thm),theory(equality)],[55,23]),
[iquote('0:SpR:55.0,23.0')] ).
cnf(78,plain,
equal(not__dfg(or__dfg(not__dfg(u),falsehood)),and_star(u,truth)),
inference(spr,[status(thm),theory(equality)],[17,14]),
[iquote('0:SpR:17.0,14.0')] ).
cnf(82,plain,
equal(not__dfg(or__dfg(falsehood,not__dfg(u))),and_star(u,truth)),
inference(rew,[status(thm),theory(equality)],[8,78]),
[iquote('0:Rew:8.0,78.0')] ).
cnf(87,plain,
equal(or__dfg(or__dfg(falsehood,not__dfg(u)),v),implies__dfg(and_star(u,truth),v)),
inference(spr,[status(thm),theory(equality)],[82,6]),
[iquote('0:SpR:82.0,6.0')] ).
cnf(89,plain,
equal(not__dfg(or__dfg(falsehood,and_star(u,truth))),and_star(or__dfg(falsehood,not__dfg(u)),truth)),
inference(spr,[status(thm),theory(equality)],[82]),
[iquote('0:SpR:82.0,82.0')] ).
cnf(95,plain,
equal(or__dfg(falsehood,or__dfg(not__dfg(u),v)),implies__dfg(and_star(u,truth),v)),
inference(rew,[status(thm),theory(equality)],[7,87]),
[iquote('0:Rew:7.0,87.0')] ).
cnf(96,plain,
equal(not__dfg(or__dfg(falsehood,and_star(u,truth))),and_star(truth,or__dfg(falsehood,not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[16,89]),
[iquote('0:Rew:16.0,89.0')] ).
cnf(131,plain,
equal(implies__dfg(or__dfg(not__dfg(u),and_star(u,truth)),truth),truth),
inference(spr,[status(thm),theory(equality)],[82,57]),
[iquote('0:SpR:82.0,57.0')] ).
cnf(138,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(147,plain,
equal(implies__dfg(implies__dfg(not__dfg(u),truth),truth),or__dfg(u,not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[138,6]),
[iquote('0:SpR:138.0,6.0')] ).
cnf(164,plain,
equal(implies__dfg(or__dfg(u,truth),truth),or__dfg(u,not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[6,147]),
[iquote('0:Rew:6.0,147.0')] ).
cnf(196,plain,
equal(and_star(u,and_star(v,w)),and_star(w,and_star(u,v))),
inference(spr,[status(thm),theory(equality)],[15,16]),
[iquote('0:SpR:15.0,16.0')] ).
cnf(242,plain,
equal(or__dfg(falsehood,not__dfg(falsehood)),truth),
inference(spr,[status(thm),theory(equality)],[164,55]),
[iquote('0:SpR:164.0,55.0')] ).
cnf(246,plain,
equal(not__dfg(implies__dfg(or__dfg(not__dfg(u),truth),truth)),and_star(u,not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[164,14]),
[iquote('0:SpR:164.0,14.0')] ).
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_star(u,truth))),
inference(spr,[status(thm),theory(equality)],[82,164]),
[iquote('0:SpR:82.0,164.0')] ).
cnf(253,plain,
equal(not__dfg(implies__dfg(or__dfg(truth,not__dfg(u)),truth)),and_star(u,not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[8,246]),
[iquote('0:Rew:8.0,246.0')] ).
cnf(255,plain,
equal(implies__dfg(or__dfg(truth,or__dfg(falsehood,not__dfg(u))),truth),or__dfg(and_star(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(257,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(271,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(275,plain,
equal(implies__dfg(or__dfg(truth,or__dfg(falsehood,not__dfg(u))),truth),or__dfg(falsehood,or__dfg(not__dfg(u),and_star(u,truth)))),
inference(rew,[status(thm),theory(equality)],[257,255]),
[iquote('0:Rew:257.0,255.0')] ).
cnf(277,plain,
equal(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w))),
inference(rew,[status(thm),theory(equality)],[7,271]),
[iquote('0:Rew:7.0,271.0')] ).
cnf(285,plain,
equal(implies__dfg(or__dfg(truth,or__dfg(falsehood,not__dfg(u))),truth),implies__dfg(and_star(u,truth),and_star(u,truth))),
inference(rew,[status(thm),theory(equality)],[95,275]),
[iquote('0:Rew:95.0,275.0')] ).
cnf(287,plain,
equal(implies__dfg(truth,not__dfg(falsehood)),truth),
inference(spr,[status(thm),theory(equality)],[242,55]),
[iquote('0:SpR:242.0,55.0')] ).
cnf(289,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(295,plain,
equal(not__dfg(falsehood),truth),
inference(rew,[status(thm),theory(equality)],[2,287]),
[iquote('0:Rew:2.0,287.0')] ).
cnf(296,plain,
equal(implies__dfg(or__dfg(u,truth),or__dfg(truth,u)),truth),
inference(rew,[status(thm),theory(equality)],[295,46]),
[iquote('0:Rew:295.0,46.0')] ).
cnf(320,plain,
equal(or__dfg(truth,or__dfg(falsehood,u)),or__dfg(truth,u)),
inference(rew,[status(thm),theory(equality)],[277,289,295]),
[iquote('0:Rew:277.0,289.0,295.0,289.0')] ).
cnf(321,plain,
equal(implies__dfg(and_star(u,truth),and_star(u,truth)),implies__dfg(or__dfg(truth,not__dfg(u)),truth)),
inference(rew,[status(thm),theory(equality)],[320,285]),
[iquote('0:Rew:320.0,285.0')] ).
cnf(327,plain,
equal(implies__dfg(truth,u),or__dfg(falsehood,u)),
inference(spr,[status(thm),theory(equality)],[295,6]),
[iquote('0:SpR:295.0,6.0')] ).
cnf(328,plain,
equal(not__dfg(or__dfg(truth,not__dfg(u))),and_star(falsehood,u)),
inference(spr,[status(thm),theory(equality)],[295,14]),
[iquote('0:SpR:295.0,14.0')] ).
cnf(335,plain,
equal(or__dfg(falsehood,u),u),
inference(rew,[status(thm),theory(equality)],[2,327]),
[iquote('0:Rew:2.0,327.0')] ).
cnf(338,plain,
equal(not__dfg(not__dfg(u)),and_star(u,truth)),
inference(rew,[status(thm),theory(equality)],[335,82]),
[iquote('0:Rew:335.0,82.0')] ).
cnf(339,plain,
equal(implies__dfg(u,u),truth),
inference(rew,[status(thm),theory(equality)],[335,55]),
[iquote('0:Rew:335.0,55.0')] ).
cnf(346,plain,
equal(and_star(truth,or__dfg(falsehood,not__dfg(u))),not__dfg(and_star(u,truth))),
inference(rew,[status(thm),theory(equality)],[335,96]),
[iquote('0:Rew:335.0,96.0')] ).
cnf(355,plain,
equal(implies__dfg(implies__dfg(u,truth),truth),truth),
inference(rew,[status(thm),theory(equality)],[339,138]),
[iquote('0:Rew:339.0,138.0')] ).
cnf(356,plain,
equal(implies__dfg(or__dfg(truth,not__dfg(u)),truth),truth),
inference(rew,[status(thm),theory(equality)],[339,321]),
[iquote('0:Rew:339.0,321.0')] ).
cnf(370,plain,
equal(and_star(u,not__dfg(u)),not__dfg(truth)),
inference(rew,[status(thm),theory(equality)],[356,253]),
[iquote('0:Rew:356.0,253.0')] ).
cnf(371,plain,
equal(and_star(u,not__dfg(u)),falsehood),
inference(rew,[status(thm),theory(equality)],[17,370]),
[iquote('0:Rew:17.0,370.0')] ).
cnf(384,plain,
equal(not__dfg(and_star(u,truth)),and_star(truth,not__dfg(u))),
inference(rew,[status(thm),theory(equality)],[335,346]),
[iquote('0:Rew:335.0,346.0')] ).
cnf(400,plain,
equal(or__dfg(and_star(truth,not__dfg(u)),and_star(falsehood,u)),xor__dfg(truth,u)),
inference(spr,[status(thm),theory(equality)],[17,24]),
[iquote('0:SpR:17.0,24.0')] ).
cnf(402,plain,
equal(or__dfg(and_star(falsehood,not__dfg(u)),and_star(truth,u)),xor__dfg(falsehood,u)),
inference(spr,[status(thm),theory(equality)],[295,24]),
[iquote('0:SpR:295.0,24.0')] ).
cnf(411,plain,
equal(or__dfg(and_star(falsehood,u),and_star(truth,not__dfg(u))),xor__dfg(truth,u)),
inference(rew,[status(thm),theory(equality)],[8,400]),
[iquote('0:Rew:8.0,400.0')] ).
cnf(412,plain,
equal(or__dfg(and_star(truth,u),and_star(falsehood,not__dfg(u))),xor__dfg(falsehood,u)),
inference(rew,[status(thm),theory(equality)],[8,402]),
[iquote('0:Rew:8.0,402.0')] ).
cnf(424,plain,
equal(or__dfg(u,falsehood),u),
inference(spr,[status(thm),theory(equality)],[335,8]),
[iquote('0:SpR:335.0,8.0')] ).
cnf(446,plain,
equal(or__dfg(u,not__dfg(u)),truth),
inference(spr,[status(thm),theory(equality)],[339,6]),
[iquote('0:SpR:339.0,6.0')] ).
cnf(479,plain,
equal(implies__dfg(implies__dfg(or__dfg(not__dfg(u),and_star(u,truth)),v),implies__dfg(implies__dfg(v,truth),truth)),truth),
inference(spr,[status(thm),theory(equality)],[131,3]),
[iquote('0:SpR:131.0,3.0')] ).
cnf(510,plain,
equal(implies__dfg(implies__dfg(or__dfg(not__dfg(u),and_star(u,truth)),v),truth),truth),
inference(rew,[status(thm),theory(equality)],[355,479]),
[iquote('0:Rew:355.0,479.0')] ).
cnf(527,plain,
equal(or__dfg(and_star(u,not__dfg(not__dfg(not__dfg(u)))),falsehood),xor__dfg(u,not__dfg(not__dfg(u)))),
inference(spr,[status(thm),theory(equality)],[371,24]),
[iquote('0:SpR:371.0,24.0')] ).
cnf(535,plain,
equal(and_star(u,not__dfg(not__dfg(not__dfg(u)))),xor__dfg(u,not__dfg(not__dfg(u)))),
inference(rew,[status(thm),theory(equality)],[424,527]),
[iquote('0:Rew:424.0,527.0')] ).
cnf(536,plain,
equal(and_star(u,and_star(truth,not__dfg(u))),xor__dfg(u,and_star(u,truth))),
inference(rew,[status(thm),theory(equality)],[384,535,338]),
[iquote('0:Rew:384.0,535.0,338.0,535.0')] ).
cnf(583,plain,
equal(and_star(not__dfg(u),and_star(u,truth)),falsehood),
inference(spr,[status(thm),theory(equality)],[338,371]),
[iquote('0:SpR:338.0,371.0')] ).
cnf(584,plain,
equal(or__dfg(not__dfg(u),and_star(u,truth)),truth),
inference(spr,[status(thm),theory(equality)],[338,446]),
[iquote('0:SpR:338.0,446.0')] ).
cnf(595,plain,
equal(xor__dfg(u,and_star(u,truth)),falsehood),
inference(rew,[status(thm),theory(equality)],[536,583,196]),
[iquote('0:Rew:536.0,583.0,196.0,583.0')] ).
cnf(596,plain,
equal(and_star(u,and_star(truth,not__dfg(u))),falsehood),
inference(rew,[status(thm),theory(equality)],[595,536]),
[iquote('0:Rew:595.0,536.0')] ).
cnf(600,plain,
equal(implies__dfg(implies__dfg(truth,u),truth),truth),
inference(rew,[status(thm),theory(equality)],[584,510]),
[iquote('0:Rew:584.0,510.0')] ).
cnf(602,plain,
equal(implies__dfg(u,truth),truth),
inference(rew,[status(thm),theory(equality)],[2,600]),
[iquote('0:Rew:2.0,600.0')] ).
cnf(626,plain,
equal(or__dfg(u,truth),truth),
inference(spr,[status(thm),theory(equality)],[602,6]),
[iquote('0:SpR:602.0,6.0')] ).
cnf(633,plain,
equal(implies__dfg(truth,or__dfg(truth,u)),truth),
inference(rew,[status(thm),theory(equality)],[626,296]),
[iquote('0:Rew:626.0,296.0')] ).
cnf(639,plain,
equal(or__dfg(truth,u),truth),
inference(rew,[status(thm),theory(equality)],[2,633]),
[iquote('0:Rew:2.0,633.0')] ).
cnf(643,plain,
equal(and_star(falsehood,u),not__dfg(truth)),
inference(rew,[status(thm),theory(equality)],[639,328]),
[iquote('0:Rew:639.0,328.0')] ).
cnf(645,plain,
equal(and_star(falsehood,u),falsehood),
inference(rew,[status(thm),theory(equality)],[17,643]),
[iquote('0:Rew:17.0,643.0')] ).
cnf(647,plain,
equal(or__dfg(and_star(truth,u),falsehood),xor__dfg(falsehood,u)),
inference(rew,[status(thm),theory(equality)],[645,412]),
[iquote('0:Rew:645.0,412.0')] ).
cnf(650,plain,
equal(or__dfg(falsehood,and_star(truth,not__dfg(u))),xor__dfg(truth,u)),
inference(rew,[status(thm),theory(equality)],[645,411]),
[iquote('0:Rew:645.0,411.0')] ).
cnf(654,plain,
equal(and_star(truth,u),xor__dfg(falsehood,u)),
inference(rew,[status(thm),theory(equality)],[424,647]),
[iquote('0:Rew:424.0,647.0')] ).
cnf(662,plain,
equal(and_star(u,xor__dfg(falsehood,not__dfg(u))),falsehood),
inference(rew,[status(thm),theory(equality)],[654,596]),
[iquote('0:Rew:654.0,596.0')] ).
cnf(673,plain,
equal(and_star(truth,not__dfg(u)),xor__dfg(truth,u)),
inference(rew,[status(thm),theory(equality)],[335,650]),
[iquote('0:Rew:335.0,650.0')] ).
cnf(674,plain,
equal(xor__dfg(falsehood,not__dfg(u)),xor__dfg(truth,u)),
inference(rew,[status(thm),theory(equality)],[654,673]),
[iquote('0:Rew:654.0,673.0')] ).
cnf(675,plain,
equal(and_star(u,xor__dfg(truth,u)),falsehood),
inference(rew,[status(thm),theory(equality)],[674,662]),
[iquote('0:Rew:674.0,662.0')] ).
cnf(677,plain,
$false,
inference(unc,[status(thm)],[675,18]),
[iquote('0:UnC:675.0,18.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL158-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_spass %d %s
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 5 06:14:12 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.08/0.38
% 0.08/0.38 SPASS V 3.9
% 0.08/0.38 SPASS beiseite: Proof found.
% 0.08/0.38 % SZS status Theorem
% 0.08/0.38 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.38 SPASS derived 458 clauses, backtracked 0 clauses, performed 0 splits and kept 210 clauses.
% 0.08/0.38 SPASS allocated 63843 KBytes.
% 0.08/0.38 SPASS spent 0:00:00.08 on the problem.
% 0.08/0.38 0:00:00.03 for the input.
% 0.08/0.38 0:00:00.00 for the FLOTTER CNF translation.
% 0.08/0.38 0:00:00.00 for inferences.
% 0.08/0.38 0:00:00.00 for the backtracking.
% 0.08/0.38 0:00:00.03 for the reduction.
% 0.08/0.38
% 0.08/0.38
% 0.08/0.38 Here is a proof with depth 6, length 92 :
% 0.08/0.38 % SZS output start Refutation
% See solution above
% 0.08/0.39 Formulae used in the proof : prove_alternative_wajsberg_axiom wajsberg_1 wajsberg_2 wajsberg_3 wajsberg_4 or_definition or_associativity or_commutativity and_definition xor_definition and_star_definition and_star_associativity and_star_commutativity false_definition
% 0.08/0.39
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