%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL164-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n009.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 01:06:54 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.47s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 30 RR)
% Number of literals : 30 ( 0 equ; 6 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(xor__dfg(u,v),xor__dfg(v,u)),
file('LCL164-1.p',unknown),
[] ).
cnf(3,axiom,
equal(and_star(u,v),and_star(v,u)),
file('LCL164-1.p',unknown),
[] ).
cnf(4,axiom,
equal(not__dfg(truth),falsehood),
file('LCL164-1.p',unknown),
[] ).
cnf(5,axiom,
equal(xor__dfg(truth,and_star(u,xor__dfg(truth,v))),implies__dfg(u,v)),
file('LCL164-1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(implies__dfg(implies__dfg(not__dfg(x__dfg),not__dfg(y__dfg)),implies__dfg(y__dfg,x__dfg)),truth),
file('LCL164-1.p',unknown),
[] ).
cnf(7,axiom,
equal(xor__dfg(u,truth),not__dfg(u)),
file('LCL164-1.p',unknown),
[] ).
cnf(8,axiom,
equal(xor__dfg(u,falsehood),u),
file('LCL164-1.p',unknown),
[] ).
cnf(12,axiom,
equal(and_star(xor__dfg(truth,u),u),falsehood),
file('LCL164-1.p',unknown),
[] ).
cnf(13,axiom,
equal(xor__dfg(xor__dfg(u,truth),v),xor__dfg(u,xor__dfg(truth,v))),
file('LCL164-1.p',unknown),
[] ).
cnf(15,plain,
equal(and_star(u,xor__dfg(truth,u)),falsehood),
inference(rew,[status(thm),theory(equality)],[3,12]),
[iquote('0:Rew:3.0,12.0')] ).
cnf(16,plain,
equal(xor__dfg(u,xor__dfg(truth,v)),xor__dfg(not__dfg(u),v)),
inference(rew,[status(thm),theory(equality)],[7,13]),
[iquote('0:Rew:7.0,13.0')] ).
cnf(45,plain,
equal(xor__dfg(falsehood,u),u),
inference(spr,[status(thm),theory(equality)],[1,8]),
[iquote('0:SpR:1.0,8.0')] ).
cnf(47,plain,
equal(xor__dfg(truth,u),not__dfg(u)),
inference(spr,[status(thm),theory(equality)],[1,7]),
[iquote('0:SpR:1.0,7.0')] ).
cnf(57,plain,
equal(and_star(u,not__dfg(u)),falsehood),
inference(rew,[status(thm),theory(equality)],[47,15]),
[iquote('0:Rew:47.0,15.0')] ).
cnf(59,plain,
equal(not__dfg(and_star(u,xor__dfg(truth,v))),implies__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[47,5]),
[iquote('0:Rew:47.0,5.0')] ).
cnf(60,plain,
equal(xor__dfg(not__dfg(u),v),xor__dfg(u,not__dfg(v))),
inference(rew,[status(thm),theory(equality)],[47,16]),
[iquote('0:Rew:47.0,16.0')] ).
cnf(63,plain,
equal(not__dfg(and_star(u,not__dfg(v))),implies__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[47,59]),
[iquote('0:Rew:47.0,59.0')] ).
cnf(72,plain,
equal(not__dfg(falsehood),truth),
inference(spr,[status(thm),theory(equality)],[45,7]),
[iquote('0:SpR:45.0,7.0')] ).
cnf(90,plain,
equal(xor__dfg(u,not__dfg(truth)),not__dfg(not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[60,7]),
[iquote('0:SpR:60.0,7.0')] ).
cnf(97,plain,
equal(not__dfg(not__dfg(u)),u),
inference(rew,[status(thm),theory(equality)],[8,90,4]),
[iquote('0:Rew:8.0,90.0,4.0,90.0')] ).
cnf(111,plain,
equal(and_star(u,not__dfg(v)),not__dfg(implies__dfg(u,v))),
inference(spr,[status(thm),theory(equality)],[63,97]),
[iquote('0:SpR:63.0,97.0')] ).
cnf(116,plain,
equal(implies__dfg(u,not__dfg(v)),not__dfg(and_star(u,v))),
inference(spr,[status(thm),theory(equality)],[97,63]),
[iquote('0:SpR:97.0,63.0')] ).
cnf(118,plain,
equal(implies__dfg(u,u),not__dfg(falsehood)),
inference(spr,[status(thm),theory(equality)],[57,63]),
[iquote('0:SpR:57.0,63.0')] ).
cnf(122,plain,
equal(implies__dfg(u,u),truth),
inference(rew,[status(thm),theory(equality)],[72,118]),
[iquote('0:Rew:72.0,118.0')] ).
cnf(131,plain,
~ equal(implies__dfg(not__dfg(and_star(not__dfg(x__dfg),y__dfg)),implies__dfg(y__dfg,x__dfg)),truth),
inference(rew,[status(thm),theory(equality)],[116,6]),
[iquote('0:Rew:116.0,6.0')] ).
cnf(134,plain,
~ equal(implies__dfg(not__dfg(and_star(y__dfg,not__dfg(x__dfg))),implies__dfg(y__dfg,x__dfg)),truth),
inference(rew,[status(thm),theory(equality)],[3,131]),
[iquote('0:Rew:3.0,131.0')] ).
cnf(135,plain,
~ equal(implies__dfg(not__dfg(not__dfg(implies__dfg(y__dfg,x__dfg))),implies__dfg(y__dfg,x__dfg)),truth),
inference(rew,[status(thm),theory(equality)],[111,134]),
[iquote('0:Rew:111.0,134.0')] ).
cnf(136,plain,
~ equal(implies__dfg(implies__dfg(y__dfg,x__dfg),implies__dfg(y__dfg,x__dfg)),truth),
inference(rew,[status(thm),theory(equality)],[97,135]),
[iquote('0:Rew:97.0,135.0')] ).
cnf(137,plain,
~ equal(truth,truth),
inference(rew,[status(thm),theory(equality)],[122,136]),
[iquote('0:Rew:122.0,136.0')] ).
cnf(138,plain,
$false,
inference(obv,[status(thm),theory(equality)],[137]),
[iquote('0:Obv:137.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL164-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_spass %d %s
% 0.08/0.34 % Computer : n009.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 5 06:42:21 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.21/0.47
% 0.21/0.47 SPASS V 3.9
% 0.21/0.47 SPASS beiseite: Proof found.
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.47 SPASS derived 98 clauses, backtracked 0 clauses, performed 0 splits and kept 37 clauses.
% 0.21/0.47 SPASS allocated 63207 KBytes.
% 0.21/0.47 SPASS spent 0:00:00.11 on the problem.
% 0.21/0.47 0:00:00.06 for the input.
% 0.21/0.47 0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.47 0:00:00.00 for inferences.
% 0.21/0.47 0:00:00.00 for the backtracking.
% 0.21/0.47 0:00:00.00 for the reduction.
% 0.21/0.47
% 0.21/0.47
% 0.21/0.47 Here is a proof with depth 2, length 30 :
% 0.21/0.47 % SZS output start Refutation
% See solution above
% 0.21/0.47 Formulae used in the proof : xor_commutativity and_star_commutativity false_definition implies_definition prove_wajsberg_axiom axiom_1 axiom_2 axiom_6 axiom_7
% 0.21/0.47
%------------------------------------------------------------------------------