%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ROB022-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 20:56:16 EDT 2022
% Result : Unsatisfiable 0.36s 0.58s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 42 RR)
% Number of literals : 42 ( 0 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(add(c,negate(c)),c),
file('ROB022-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b),
file('ROB022-1.p',unknown),
[] ).
cnf(3,axiom,
equal(add(u,v),add(v,u)),
file('ROB022-1.p',unknown),
[] ).
cnf(4,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('ROB022-1.p',unknown),
[] ).
cnf(5,axiom,
equal(negate(add(negate(add(u,v)),negate(add(u,negate(v))))),u),
file('ROB022-1.p',unknown),
[] ).
cnf(11,plain,
equal(add(u,add(v,w)),add(v,add(w,u))),
inference(spr,[status(thm),theory(equality)],[4,3]),
[iquote('0:SpR:4.0,3.0')] ).
cnf(15,plain,
equal(add(c,add(negate(c),u)),add(c,u)),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(16,plain,
equal(add(add(u,v),w),add(v,add(u,w))),
inference(spr,[status(thm),theory(equality)],[3,4]),
[iquote('0:SpR:3.0,4.0')] ).
cnf(18,plain,
equal(add(u,add(v,w)),add(v,add(u,w))),
inference(rew,[status(thm),theory(equality)],[4,16]),
[iquote('0:Rew:4.0,16.0')] ).
cnf(23,plain,
equal(add(c,add(u,negate(c))),add(c,u)),
inference(spr,[status(thm),theory(equality)],[3,15]),
[iquote('0:SpR:3.0,15.0')] ).
cnf(30,plain,
equal(negate(add(negate(add(c,c)),negate(c))),c),
inference(spr,[status(thm),theory(equality)],[1,5]),
[iquote('0:SpR:1.0,5.0')] ).
cnf(31,plain,
equal(negate(add(negate(add(u,v)),negate(add(negate(v),u)))),u),
inference(spr,[status(thm),theory(equality)],[3,5]),
[iquote('0:SpR:3.0,5.0')] ).
cnf(36,plain,
equal(negate(add(negate(add(u,v)),negate(add(v,negate(u))))),v),
inference(spr,[status(thm),theory(equality)],[3,5]),
[iquote('0:SpR:3.0,5.0')] ).
cnf(39,plain,
equal(negate(add(negate(c),negate(add(c,c)))),c),
inference(rew,[status(thm),theory(equality)],[3,30]),
[iquote('0:Rew:3.0,30.0')] ).
cnf(47,plain,
equal(negate(add(negate(add(negate(c),add(c,c))),c)),negate(c)),
inference(spr,[status(thm),theory(equality)],[39,5]),
[iquote('0:SpR:39.0,5.0')] ).
cnf(52,plain,
equal(negate(add(c,negate(add(negate(c),add(c,c))))),negate(c)),
inference(rew,[status(thm),theory(equality)],[3,47]),
[iquote('0:Rew:3.0,47.0')] ).
cnf(53,plain,
equal(negate(add(c,negate(add(c,c)))),negate(c)),
inference(rew,[status(thm),theory(equality)],[23,52,11,18]),
[iquote('0:Rew:23.0,52.0,11.0,52.0,18.0,52.0')] ).
cnf(499,plain,
equal(negate(add(negate(add(u,add(negate(c),negate(add(c,c))))),negate(add(c,u)))),u),
inference(spr,[status(thm),theory(equality)],[39,31]),
[iquote('0:SpR:39.0,31.0')] ).
cnf(516,plain,
equal(negate(add(negate(add(negate(add(c,c)),c)),c)),negate(add(c,c))),
inference(spr,[status(thm),theory(equality)],[39,31]),
[iquote('0:SpR:39.0,31.0')] ).
cnf(522,plain,
equal(negate(add(negate(add(u,v)),negate(add(negate(u),v)))),v),
inference(spr,[status(thm),theory(equality)],[3,31]),
[iquote('0:SpR:3.0,31.0')] ).
cnf(542,plain,
equal(negate(add(c,c)),negate(c)),
inference(rew,[status(thm),theory(equality)],[1,516,3,53]),
[iquote('0:Rew:1.0,516.0,3.0,516.0,53.0,516.0,3.0,516.0')] ).
cnf(560,plain,
equal(negate(add(negate(add(c,u)),negate(add(u,add(negate(c),negate(add(c,c))))))),u),
inference(rew,[status(thm),theory(equality)],[3,499]),
[iquote('0:Rew:3.0,499.0')] ).
cnf(561,plain,
equal(negate(add(negate(add(c,u)),negate(add(u,add(negate(c),negate(c)))))),u),
inference(rew,[status(thm),theory(equality)],[542,560]),
[iquote('0:Rew:542.0,560.0')] ).
cnf(702,plain,
equal(negate(add(negate(add(c,u)),negate(add(add(negate(c),u),negate(c))))),add(negate(c),u)),
inference(spr,[status(thm),theory(equality)],[15,36]),
[iquote('0:SpR:15.0,36.0')] ).
cnf(703,plain,
equal(negate(add(negate(add(c,u)),negate(add(add(u,negate(c)),negate(c))))),add(u,negate(c))),
inference(spr,[status(thm),theory(equality)],[23,36]),
[iquote('0:SpR:23.0,36.0')] ).
cnf(754,plain,
equal(negate(add(negate(add(c,u)),negate(add(negate(c),add(u,negate(c)))))),add(negate(c),u)),
inference(rew,[status(thm),theory(equality)],[4,702]),
[iquote('0:Rew:4.0,702.0')] ).
cnf(755,plain,
equal(negate(add(negate(add(c,u)),negate(add(u,add(negate(c),negate(c)))))),add(u,negate(c))),
inference(rew,[status(thm),theory(equality)],[4,703]),
[iquote('0:Rew:4.0,703.0')] ).
cnf(756,plain,
equal(add(u,negate(c)),u),
inference(rew,[status(thm),theory(equality)],[561,755]),
[iquote('0:Rew:561.0,755.0')] ).
cnf(766,plain,
equal(negate(add(negate(add(c,u)),negate(add(negate(c),u)))),add(negate(c),u)),
inference(rew,[status(thm),theory(equality)],[756,754]),
[iquote('0:Rew:756.0,754.0')] ).
cnf(789,plain,
equal(add(negate(c),u),u),
inference(rew,[status(thm),theory(equality)],[522,766]),
[iquote('0:Rew:522.0,766.0')] ).
cnf(863,plain,
equal(negate(add(negate(u),negate(add(negate(c),negate(u))))),negate(c)),
inference(spr,[status(thm),theory(equality)],[756,36]),
[iquote('0:SpR:756.0,36.0')] ).
cnf(884,plain,
equal(negate(add(negate(u),negate(negate(u)))),negate(c)),
inference(rew,[status(thm),theory(equality)],[789,863]),
[iquote('0:Rew:789.0,863.0')] ).
cnf(1103,plain,
equal(negate(add(negate(c),negate(add(negate(u),negate(negate(negate(u))))))),negate(u)),
inference(spr,[status(thm),theory(equality)],[884,5]),
[iquote('0:SpR:884.0,5.0')] ).
cnf(1109,plain,
equal(negate(add(negate(add(negate(negate(u)),u)),negate(c))),negate(negate(u))),
inference(spr,[status(thm),theory(equality)],[884,31]),
[iquote('0:SpR:884.0,31.0')] ).
cnf(1128,plain,
equal(negate(negate(add(u,negate(negate(u))))),negate(negate(u))),
inference(rew,[status(thm),theory(equality)],[756,1109,3]),
[iquote('0:Rew:756.0,1109.0,3.0,1109.0')] ).
cnf(1129,plain,
equal(negate(negate(add(negate(u),negate(negate(negate(u)))))),negate(u)),
inference(rew,[status(thm),theory(equality)],[789,1103]),
[iquote('0:Rew:789.0,1103.0')] ).
cnf(1130,plain,
equal(negate(negate(negate(u))),negate(u)),
inference(rew,[status(thm),theory(equality)],[1128,1129]),
[iquote('0:Rew:1128.0,1129.0')] ).
cnf(1147,plain,
equal(negate(negate(u)),u),
inference(spr,[status(thm),theory(equality)],[5,1130]),
[iquote('0:SpR:5.0,1130.0')] ).
cnf(1439,plain,
equal(add(negate(add(u,v)),negate(add(negate(u),v))),negate(v)),
inference(spr,[status(thm),theory(equality)],[522,1147]),
[iquote('0:SpR:522.0,1147.0')] ).
cnf(1476,plain,
~ equal(negate(negate(b)),b),
inference(rew,[status(thm),theory(equality)],[1439,2]),
[iquote('0:Rew:1439.0,2.0')] ).
cnf(1477,plain,
~ equal(b,b),
inference(rew,[status(thm),theory(equality)],[1147,1476]),
[iquote('0:Rew:1147.0,1476.0')] ).
cnf(1478,plain,
$false,
inference(obv,[status(thm),theory(equality)],[1477]),
[iquote('0:Obv:1477.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : ROB022-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.09 % Command : run_spass %d %s
% 0.08/0.28 % Computer : n021.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Thu Jun 9 13:57:38 EDT 2022
% 0.08/0.29 % CPUTime :
% 0.36/0.58
% 0.36/0.58 SPASS V 3.9
% 0.36/0.58 SPASS beiseite: Proof found.
% 0.36/0.58 % SZS status Theorem
% 0.36/0.58 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.36/0.58 SPASS derived 938 clauses, backtracked 0 clauses, performed 0 splits and kept 232 clauses.
% 0.36/0.58 SPASS allocated 64892 KBytes.
% 0.36/0.58 SPASS spent 0:00:00.27 on the problem.
% 0.36/0.58 0:00:00.03 for the input.
% 0.36/0.58 0:00:00.00 for the FLOTTER CNF translation.
% 0.36/0.58 0:00:00.01 for inferences.
% 0.36/0.58 0:00:00.00 for the backtracking.
% 0.36/0.58 0:00:00.21 for the reduction.
% 0.36/0.58
% 0.36/0.58
% 0.36/0.58 Here is a proof with depth 7, length 42 :
% 0.36/0.58 % SZS output start Refutation
% See solution above
% 0.36/0.58 Formulae used in the proof : condition prove_huntingtons_axiom commutativity_of_add associativity_of_add robbins_axiom
% 0.36/0.58
%------------------------------------------------------------------------------