%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL161-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 0.22s 0.50s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 20 RR)
% Number of literals : 20 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(xor__dfg(u,v),xor__dfg(v,u)),
file('LCL161-1.p',unknown),
[] ).
cnf(3,axiom,
equal(and_star(u,v),and_star(v,u)),
file('LCL161-1.p',unknown),
[] ).
cnf(4,axiom,
equal(not__dfg(truth),falsehood),
file('LCL161-1.p',unknown),
[] ).
cnf(5,axiom,
equal(xor__dfg(truth,and_star(u,xor__dfg(truth,v))),implies__dfg(u,v)),
file('LCL161-1.p',unknown),
[] ).
cnf(6,axiom,
~ equal(implies__dfg(truth,x__dfg),x__dfg),
file('LCL161-1.p',unknown),
[] ).
cnf(7,axiom,
equal(xor__dfg(u,truth),not__dfg(u)),
file('LCL161-1.p',unknown),
[] ).
cnf(8,axiom,
equal(xor__dfg(u,falsehood),u),
file('LCL161-1.p',unknown),
[] ).
cnf(10,axiom,
equal(and_star(u,truth),u),
file('LCL161-1.p',unknown),
[] ).
cnf(13,axiom,
equal(xor__dfg(xor__dfg(u,truth),v),xor__dfg(u,xor__dfg(truth,v))),
file('LCL161-1.p',unknown),
[] ).
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(32,plain,
equal(and_star(truth,u),u),
inference(spr,[status(thm),theory(equality)],[3,10]),
[iquote('0:SpR:3.0,10.0')] ).
cnf(41,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(53,plain,
equal(not__dfg(and_star(u,xor__dfg(truth,v))),implies__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[41,5]),
[iquote('0:Rew:41.0,5.0')] ).
cnf(54,plain,
equal(xor__dfg(not__dfg(u),v),xor__dfg(u,not__dfg(v))),
inference(rew,[status(thm),theory(equality)],[41,16]),
[iquote('0:Rew:41.0,16.0')] ).
cnf(57,plain,
equal(not__dfg(and_star(u,not__dfg(v))),implies__dfg(u,v)),
inference(rew,[status(thm),theory(equality)],[41,53]),
[iquote('0:Rew:41.0,53.0')] ).
cnf(89,plain,
equal(xor__dfg(u,not__dfg(truth)),not__dfg(not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[54,7]),
[iquote('0:SpR:54.0,7.0')] ).
cnf(96,plain,
equal(not__dfg(not__dfg(u)),u),
inference(rew,[status(thm),theory(equality)],[8,89,4]),
[iquote('0:Rew:8.0,89.0,4.0,89.0')] ).
cnf(120,plain,
equal(implies__dfg(truth,u),not__dfg(not__dfg(u))),
inference(spr,[status(thm),theory(equality)],[32,57]),
[iquote('0:SpR:32.0,57.0')] ).
cnf(123,plain,
equal(implies__dfg(truth,u),u),
inference(rew,[status(thm),theory(equality)],[96,120]),
[iquote('0:Rew:96.0,120.0')] ).
cnf(124,plain,
$false,
inference(unc,[status(thm)],[123,6]),
[iquote('0:UnC:123.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL161-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 5 08:55:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.22/0.50
% 0.22/0.50 SPASS V 3.9
% 0.22/0.50 SPASS beiseite: Proof found.
% 0.22/0.50 % SZS status Theorem
% 0.22/0.50 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.50 SPASS derived 96 clauses, backtracked 0 clauses, performed 0 splits and kept 36 clauses.
% 0.22/0.50 SPASS allocated 63197 KBytes.
% 0.22/0.50 SPASS spent 0:00:00.11 on the problem.
% 0.22/0.50 0:00:00.06 for the input.
% 0.22/0.50 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.50 0:00:00.00 for inferences.
% 0.22/0.50 0:00:00.00 for the backtracking.
% 0.22/0.50 0:00:00.00 for the reduction.
% 0.22/0.50
% 0.22/0.50
% 0.22/0.50 Here is a proof with depth 2, length 20 :
% 0.22/0.50 % SZS output start Refutation
% See solution above
% 0.22/0.50 Formulae used in the proof : xor_commutativity and_star_commutativity false_definition implies_definition prove_wajsberg_axiom axiom_1 axiom_2 axiom_4 axiom_7
% 0.22/0.50
%------------------------------------------------------------------------------