%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN008-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 : Sat Jul 16 13:03:09 EDT 2022
% Result : Unsatisfiable 0.18s 0.40s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 12 ( 8 unt; 0 nHn; 12 RR)
% Number of literals : 18 ( 0 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(a,b),zero),
file('HEN008-5.p',unknown),
[] ).
cnf(2,axiom,
~ equal(divide(divide(a,c),divide(b,c)),zero),
file('HEN008-5.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),zero),
file('HEN008-5.p',unknown),
[] ).
cnf(5,axiom,
equal(divide(zero,u),zero),
file('HEN008-5.p',unknown),
[] ).
cnf(6,axiom,
( ~ equal(divide(u,v),zero)
| ~ equal(divide(v,u),zero)
| equal(v,u) ),
file('HEN008-5.p',unknown),
[] ).
cnf(21,plain,
( ~ equal(zero,zero)
| ~ equal(divide(u,zero),zero)
| equal(u,zero) ),
inference(spl,[status(thm),theory(equality)],[5,6]),
[iquote('0:SpL:5.0,6.0')] ).
cnf(25,plain,
( ~ equal(divide(u,zero),zero)
| equal(u,zero) ),
inference(obv,[status(thm),theory(equality)],[21]),
[iquote('0:Obv:21.0')] ).
cnf(38,plain,
equal(divide(divide(divide(a,u),divide(b,u)),divide(zero,u)),zero),
inference(spr,[status(thm),theory(equality)],[1,4]),
[iquote('0:SpR:1.0,4.0')] ).
cnf(55,plain,
equal(divide(divide(divide(a,u),divide(b,u)),zero),zero),
inference(rew,[status(thm),theory(equality)],[5,38]),
[iquote('0:Rew:5.0,38.0')] ).
cnf(76,plain,
( ~ equal(zero,zero)
| equal(divide(divide(a,u),divide(b,u)),zero) ),
inference(spl,[status(thm),theory(equality)],[55,25]),
[iquote('0:SpL:55.0,25.0')] ).
cnf(78,plain,
equal(divide(divide(a,u),divide(b,u)),zero),
inference(obv,[status(thm),theory(equality)],[76]),
[iquote('0:Obv:76.0')] ).
cnf(79,plain,
$false,
inference(unc,[status(thm)],[78,2]),
[iquote('0:UnC:78.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN008-5 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Fri Jul 1 14:45:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.40
% 0.18/0.40 SPASS V 3.9
% 0.18/0.40 SPASS beiseite: Proof found.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.40 SPASS derived 50 clauses, backtracked 0 clauses, performed 0 splits and kept 27 clauses.
% 0.18/0.40 SPASS allocated 63216 KBytes.
% 0.18/0.40 SPASS spent 0:00:00.06 on the problem.
% 0.18/0.40 0:00:00.03 for the input.
% 0.18/0.40 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.40 0:00:00.00 for inferences.
% 0.18/0.40 0:00:00.00 for the backtracking.
% 0.18/0.40 0:00:00.00 for the reduction.
% 0.18/0.40
% 0.18/0.40
% 0.18/0.40 Here is a proof with depth 2, length 12 :
% 0.18/0.40 % SZS output start Refutation
% See solution above
% 0.18/0.41 Formulae used in the proof : a_divide_b_is_zero prove_property_of_divide3 quotient_property zero_is_smallest divide_and_equal
% 0.18/0.41
%------------------------------------------------------------------------------