%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ROB004-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 : Mon Jul 18 20:56:12 EDT 2022
% Result : Unsatisfiable 0.47s 0.66s
% Output : Refutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 36 RR)
% Number of literals : 36 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(negate(d),c),
file('ROB004-1.p',unknown),
[] ).
cnf(2,axiom,
equal(add(c,d),d),
file('ROB004-1.p',unknown),
[] ).
cnf(3,axiom,
equal(add(c,c),c),
file('ROB004-1.p',unknown),
[] ).
cnf(4,axiom,
~ equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b),
file('ROB004-1.p',unknown),
[] ).
cnf(5,axiom,
equal(add(u,v),add(v,u)),
file('ROB004-1.p',unknown),
[] ).
cnf(6,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('ROB004-1.p',unknown),
[] ).
cnf(7,axiom,
equal(negate(add(negate(add(u,v)),negate(add(u,negate(v))))),u),
file('ROB004-1.p',unknown),
[] ).
cnf(8,plain,
equal(add(d,c),d),
inference(rew,[status(thm),theory(equality)],[5,2]),
[iquote('0:Rew:5.0,2.0')] ).
cnf(22,plain,
equal(add(d,add(c,u)),add(d,u)),
inference(spr,[status(thm),theory(equality)],[8,6]),
[iquote('0:SpR:8.0,6.0')] ).
cnf(23,plain,
equal(add(c,add(c,u)),add(c,u)),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(32,plain,
equal(add(d,add(u,c)),add(d,u)),
inference(spr,[status(thm),theory(equality)],[5,22]),
[iquote('0:SpR:5.0,22.0')] ).
cnf(40,plain,
equal(add(c,add(u,c)),add(u,c)),
inference(spr,[status(thm),theory(equality)],[5,23]),
[iquote('0:SpR:5.0,23.0')] ).
cnf(68,plain,
equal(negate(add(negate(add(u,d)),negate(add(u,c)))),u),
inference(spr,[status(thm),theory(equality)],[1,7]),
[iquote('0:SpR:1.0,7.0')] ).
cnf(69,plain,
equal(negate(add(negate(add(u,v)),negate(add(negate(v),u)))),u),
inference(spr,[status(thm),theory(equality)],[5,7]),
[iquote('0:SpR:5.0,7.0')] ).
cnf(74,plain,
equal(negate(add(negate(add(u,v)),negate(add(v,negate(u))))),v),
inference(spr,[status(thm),theory(equality)],[5,7]),
[iquote('0:SpR:5.0,7.0')] ).
cnf(78,plain,
equal(negate(add(negate(add(c,u)),negate(add(c,negate(add(c,u)))))),c),
inference(spr,[status(thm),theory(equality)],[23,7]),
[iquote('0:SpR:23.0,7.0')] ).
cnf(566,plain,
equal(negate(add(negate(add(d,u)),negate(add(u,c)))),u),
inference(spr,[status(thm),theory(equality)],[5,68]),
[iquote('0:SpR:5.0,68.0')] ).
cnf(639,plain,
equal(negate(add(negate(add(u,v)),negate(add(negate(u),v)))),v),
inference(spr,[status(thm),theory(equality)],[5,69]),
[iquote('0:SpR:5.0,69.0')] ).
cnf(813,plain,
equal(negate(add(negate(add(d,u)),negate(add(add(c,u),negate(d))))),add(c,u)),
inference(spr,[status(thm),theory(equality)],[22,74]),
[iquote('0:SpR:22.0,74.0')] ).
cnf(817,plain,
equal(negate(add(negate(add(d,u)),negate(add(add(u,c),negate(d))))),add(u,c)),
inference(spr,[status(thm),theory(equality)],[32,74]),
[iquote('0:SpR:32.0,74.0')] ).
cnf(935,plain,
equal(negate(add(negate(add(d,u)),negate(add(u,c)))),add(c,u)),
inference(rew,[status(thm),theory(equality)],[40,813,6,1]),
[iquote('0:Rew:40.0,813.0,6.0,813.0,1.0,813.0')] ).
cnf(936,plain,
equal(add(c,u),u),
inference(rew,[status(thm),theory(equality)],[566,935]),
[iquote('0:Rew:566.0,935.0')] ).
cnf(941,plain,
equal(negate(add(negate(u),negate(add(c,negate(u))))),c),
inference(rew,[status(thm),theory(equality)],[936,78]),
[iquote('0:Rew:936.0,78.0')] ).
cnf(953,plain,
equal(negate(add(negate(u),negate(negate(u)))),c),
inference(rew,[status(thm),theory(equality)],[936,941]),
[iquote('0:Rew:936.0,941.0')] ).
cnf(959,plain,
equal(negate(add(negate(add(d,u)),negate(add(u,add(c,c))))),add(u,c)),
inference(rew,[status(thm),theory(equality)],[6,817,1]),
[iquote('0:Rew:6.0,817.0,1.0,817.0')] ).
cnf(960,plain,
equal(add(u,c),u),
inference(rew,[status(thm),theory(equality)],[566,959,936]),
[iquote('0:Rew:566.0,959.0,936.0,959.0')] ).
cnf(1329,plain,
equal(negate(add(negate(add(negate(negate(u)),u)),c)),negate(negate(u))),
inference(spr,[status(thm),theory(equality)],[953,69]),
[iquote('0:SpR:953.0,69.0')] ).
cnf(1333,plain,
equal(negate(add(u,negate(u))),c),
inference(spr,[status(thm),theory(equality)],[7,953]),
[iquote('0:SpR:7.0,953.0')] ).
cnf(1348,plain,
equal(negate(negate(add(u,negate(negate(u))))),negate(negate(u))),
inference(rew,[status(thm),theory(equality)],[960,1329,5]),
[iquote('0:Rew:960.0,1329.0,5.0,1329.0')] ).
cnf(1364,plain,
equal(negate(add(c,negate(add(u,negate(negate(u)))))),u),
inference(spr,[status(thm),theory(equality)],[1333,7]),
[iquote('0:SpR:1333.0,7.0')] ).
cnf(1387,plain,
equal(negate(negate(add(u,negate(negate(u))))),u),
inference(rew,[status(thm),theory(equality)],[936,1364]),
[iquote('0:Rew:936.0,1364.0')] ).
cnf(1388,plain,
equal(negate(negate(u)),u),
inference(rew,[status(thm),theory(equality)],[1348,1387]),
[iquote('0:Rew:1348.0,1387.0')] ).
cnf(1991,plain,
equal(add(negate(add(u,v)),negate(add(negate(u),v))),negate(v)),
inference(spr,[status(thm),theory(equality)],[639,1388]),
[iquote('0:SpR:639.0,1388.0')] ).
cnf(2046,plain,
~ equal(negate(negate(b)),b),
inference(rew,[status(thm),theory(equality)],[1991,4]),
[iquote('0:Rew:1991.0,4.0')] ).
cnf(2047,plain,
~ equal(b,b),
inference(rew,[status(thm),theory(equality)],[1388,2046]),
[iquote('0:Rew:1388.0,2046.0')] ).
cnf(2048,plain,
$false,
inference(obv,[status(thm),theory(equality)],[2047]),
[iquote('0:Obv:2047.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ROB004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 9 14:48:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.47/0.66
% 0.47/0.66 SPASS V 3.9
% 0.47/0.66 SPASS beiseite: Proof found.
% 0.47/0.66 % SZS status Theorem
% 0.47/0.66 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.66 SPASS derived 1234 clauses, backtracked 0 clauses, performed 0 splits and kept 282 clauses.
% 0.47/0.66 SPASS allocated 65384 KBytes.
% 0.47/0.66 SPASS spent 0:00:00.30 on the problem.
% 0.47/0.66 0:00:00.03 for the input.
% 0.47/0.66 0:00:00.00 for the FLOTTER CNF translation.
% 0.47/0.66 0:00:00.01 for inferences.
% 0.47/0.66 0:00:00.00 for the backtracking.
% 0.47/0.66 0:00:00.23 for the reduction.
% 0.47/0.66
% 0.47/0.66
% 0.47/0.66 Here is a proof with depth 5, length 36 :
% 0.47/0.66 % SZS output start Refutation
% See solution above
% 0.47/0.66 Formulae used in the proof : negate_d_is_c c_plus_d_is_d c_plus_c_is_c prove_huntingtons_axiom commutativity_of_add associativity_of_add robbins_axiom
% 0.47/0.66
%------------------------------------------------------------------------------