%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN006-5 : 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 13:03:05 EDT 2022
% Result : Unsatisfiable 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 13 RR)
% Number of literals : 13 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 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(u,zero),u),
file('HEN006-5.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(divide(a,b),d),zero),
file('HEN006-5.p',unknown),
[] ).
cnf(3,axiom,
~ equal(divide(divide(a,d),b),zero),
file('HEN006-5.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(divide(u,v),u),zero),
file('HEN006-5.p',unknown),
[] ).
cnf(5,axiom,
equal(divide(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),zero),
file('HEN006-5.p',unknown),
[] ).
cnf(6,axiom,
equal(divide(zero,u),zero),
file('HEN006-5.p',unknown),
[] ).
cnf(59,plain,
equal(divide(divide(divide(a,d),divide(b,d)),zero),zero),
inference(spr,[status(thm),theory(equality)],[2,5]),
[iquote('0:SpR:2.0,5.0')] ).
cnf(66,plain,
equal(divide(divide(divide(u,v),zero),divide(divide(u,divide(v,w)),v)),zero),
inference(spr,[status(thm),theory(equality)],[4,5]),
[iquote('0:SpR:4.0,5.0')] ).
cnf(77,plain,
equal(divide(divide(a,d),divide(b,d)),zero),
inference(rew,[status(thm),theory(equality)],[1,59]),
[iquote('0:Rew:1.0,59.0')] ).
cnf(94,plain,
equal(divide(divide(u,v),divide(divide(u,divide(v,w)),v)),zero),
inference(rew,[status(thm),theory(equality)],[1,66]),
[iquote('0:Rew:1.0,66.0')] ).
cnf(1246,plain,
equal(divide(divide(divide(a,d),b),divide(zero,b)),zero),
inference(spr,[status(thm),theory(equality)],[77,94]),
[iquote('0:SpR:77.0,94.0')] ).
cnf(1315,plain,
equal(divide(divide(a,d),b),zero),
inference(rew,[status(thm),theory(equality)],[1,1246,6]),
[iquote('0:Rew:1.0,1246.0,6.0,1246.0')] ).
cnf(1316,plain,
$false,
inference(mrr,[status(thm)],[1315,3]),
[iquote('0:MRR:1315.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : HEN006-5 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.12 % 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 14:44:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.51
% 0.19/0.51 SPASS V 3.9
% 0.19/0.51 SPASS beiseite: Proof found.
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.51 SPASS derived 940 clauses, backtracked 0 clauses, performed 0 splits and kept 141 clauses.
% 0.19/0.51 SPASS allocated 64372 KBytes.
% 0.19/0.51 SPASS spent 0:00:00.17 on the problem.
% 0.19/0.51 0:00:00.03 for the input.
% 0.19/0.51 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.51 0:00:00.01 for inferences.
% 0.19/0.51 0:00:00.00 for the backtracking.
% 0.19/0.51 0:00:00.10 for the reduction.
% 0.19/0.51
% 0.19/0.51
% 0.19/0.51 Here is a proof with depth 2, length 13 :
% 0.19/0.51 % SZS output start Refutation
% See solution above
% 0.19/0.51 Formulae used in the proof : x_divide_zero_is_x a_divide_b_divide_d_is_zero prove_property_of_divide1 quotient_smaller_than_numerator quotient_property zero_is_smallest
% 0.19/0.51
%------------------------------------------------------------------------------