TSTP Solution File: RNG003-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG003-1 : 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 20:41:10 EDT 2022
% Result : Unsatisfiable 0.18s 0.45s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 9 unt; 0 nHn; 17 RR)
% Number of literals : 29 ( 0 equ; 16 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
sum__dfg(a,c,d),
file('RNG003-1.p',unknown),
[] ).
cnf(2,axiom,
sum__dfg(b,c,d),
file('RNG003-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(b,a),
file('RNG003-1.p',unknown),
[] ).
cnf(4,axiom,
sum__dfg(additive_identity,u,u),
file('RNG003-1.p',unknown),
[] ).
cnf(8,axiom,
sum__dfg(additive_inverse(u),u,additive_identity),
file('RNG003-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,v,y)
| ~ sum__dfg(z,x,u)
| sum__dfg(z,y,w) ),
file('RNG003-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('RNG003-1.p',unknown),
[] ).
cnf(19,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(u,v,x)
| equal(x,w) ),
file('RNG003-1.p',unknown),
[] ).
cnf(21,plain,
( ~ sum__dfg(u,v,a)
| ~ sum__dfg(u,v,b) ),
inference(res,[status(thm),theory(equality)],[19,3]),
[iquote('0:Res:19.2,3.0')] ).
cnf(25,plain,
sum__dfg(c,b,d),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.0')] ).
cnf(26,plain,
sum__dfg(c,a,d),
inference(res,[status(thm),theory(equality)],[1,12]),
[iquote('0:Res:1.0,12.0')] ).
cnf(124,plain,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,u,additive_identity)
| sum__dfg(x,w,v) ),
inference(res,[status(thm),theory(equality)],[4,10]),
[iquote('0:Res:4.0,10.0')] ).
cnf(323,plain,
( ~ sum__dfg(u,c,additive_identity)
| sum__dfg(u,d,b) ),
inference(res,[status(thm),theory(equality)],[25,124]),
[iquote('0:Res:25.0,124.0')] ).
cnf(324,plain,
( ~ sum__dfg(u,c,additive_identity)
| sum__dfg(u,d,a) ),
inference(res,[status(thm),theory(equality)],[26,124]),
[iquote('0:Res:26.0,124.0')] ).
cnf(396,plain,
( ~ sum__dfg(u,c,additive_identity)
| ~ sum__dfg(u,d,a) ),
inference(res,[status(thm),theory(equality)],[323,21]),
[iquote('0:Res:323.1,21.1')] ).
cnf(399,plain,
~ sum__dfg(u,c,additive_identity),
inference(mrr,[status(thm)],[396,324]),
[iquote('0:MRR:396.1,324.1')] ).
cnf(400,plain,
$false,
inference(unc,[status(thm)],[399,8]),
[iquote('0:UnC:399.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12 % Command : run_spass %d %s
% 0.11/0.33 % Computer : n017.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon May 30 07:24:10 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.18/0.45
% 0.18/0.45 SPASS V 3.9
% 0.18/0.45 SPASS beiseite: Proof found.
% 0.18/0.45 % SZS status Theorem
% 0.18/0.45 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 SPASS derived 344 clauses, backtracked 0 clauses, performed 0 splits and kept 205 clauses.
% 0.18/0.45 SPASS allocated 63362 KBytes.
% 0.18/0.45 SPASS spent 0:00:00.11 on the problem.
% 0.18/0.45 0:00:00.04 for the input.
% 0.18/0.45 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.45 0:00:00.01 for inferences.
% 0.18/0.45 0:00:00.00 for the backtracking.
% 0.18/0.45 0:00:00.04 for the reduction.
% 0.18/0.45
% 0.18/0.45
% 0.18/0.45 Here is a proof with depth 3, length 17 :
% 0.18/0.45 % SZS output start Refutation
% See solution above
% 0.18/0.45 Formulae used in the proof : a_plus_c_is_d b_plus_c_is_d prove_a_equals_b additive_identity1 left_inverse associativity_of_addition1 commutativity_of_addition addition_is_well_defined
% 0.18/0.45
%------------------------------------------------------------------------------