%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ROB008-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 20:56:13 EDT 2022
% Result : Unsatisfiable 1.88s 2.10s
% Output : Refutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 9 ( 9 unt; 0 nHn; 9 RR)
% Number of literals : 9 ( 0 equ; 1 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 : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(negate(add(a,add(b,negate(c)))),negate(add(a,negate(add(b,c))))),
file('ROB008-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(add(a,b),a),
file('ROB008-1.p',unknown),
[] ).
cnf(4,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('ROB008-1.p',unknown),
[] ).
cnf(5,axiom,
equal(negate(add(negate(add(u,v)),negate(add(u,negate(v))))),u),
file('ROB008-1.p',unknown),
[] ).
cnf(57,plain,
equal(negate(add(negate(add(add(u,v),w)),negate(add(u,add(v,negate(w)))))),add(u,v)),
inference(spr,[status(thm),theory(equality)],[4,5]),
[iquote('0:SpR:4.0,5.0')] ).
cnf(64,plain,
equal(negate(add(negate(add(u,add(v,w))),negate(add(u,add(v,negate(w)))))),add(u,v)),
inference(rew,[status(thm),theory(equality)],[4,57]),
[iquote('0:Rew:4.0,57.0')] ).
cnf(3782,plain,
equal(negate(add(negate(add(a,add(b,c))),negate(add(a,negate(add(b,c)))))),add(a,b)),
inference(spr,[status(thm),theory(equality)],[1,64]),
[iquote('0:SpR:1.0,64.0')] ).
cnf(3848,plain,
equal(add(a,b),a),
inference(rew,[status(thm),theory(equality)],[5,3782]),
[iquote('0:Rew:5.0,3782.0')] ).
cnf(3849,plain,
$false,
inference(mrr,[status(thm)],[3848,2]),
[iquote('0:MRR:3848.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ROB008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 9 15:43:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.88/2.10
% 1.88/2.10 SPASS V 3.9
% 1.88/2.10 SPASS beiseite: Proof found.
% 1.88/2.10 % SZS status Theorem
% 1.88/2.10 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.88/2.10 SPASS derived 2462 clauses, backtracked 0 clauses, performed 0 splits and kept 547 clauses.
% 1.88/2.10 SPASS allocated 66921 KBytes.
% 1.88/2.10 SPASS spent 0:00:01.73 on the problem.
% 1.88/2.10 0:00:00.03 for the input.
% 1.88/2.10 0:00:00.00 for the FLOTTER CNF translation.
% 1.88/2.10 0:00:00.03 for inferences.
% 1.88/2.10 0:00:00.00 for the backtracking.
% 1.88/2.10 0:00:01.65 for the reduction.
% 1.88/2.10
% 1.88/2.10
% 1.88/2.10 Here is a proof with depth 2, length 9 :
% 1.88/2.10 % SZS output start Refutation
% See solution above
% 1.88/2.10 Formulae used in the proof : condition prove_result associativity_of_add robbins_axiom
% 1.88/2.10
%------------------------------------------------------------------------------