TSTP Solution File: HEN007-5 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN007-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 13:03:07 EDT 2022
% Result : Unsatisfiable 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of clauses : 32 ( 18 unt; 0 nHn; 32 RR)
% Number of literals : 51 ( 0 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 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(u,v),zero)
| ~ equal(divide(w,u),zero)
| equal(divide(w,v),zero) ),
file('HEN007-5.p',unknown),
[] ).
cnf(2,axiom,
equal(divide(a,b),zero),
file('HEN007-5.p',unknown),
[] ).
cnf(3,axiom,
~ equal(divide(divide(c,b),divide(c,a)),zero),
file('HEN007-5.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(divide(u,v),u),zero),
file('HEN007-5.p',unknown),
[] ).
cnf(5,axiom,
equal(divide(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),zero),
file('HEN007-5.p',unknown),
[] ).
cnf(6,axiom,
equal(divide(zero,u),zero),
file('HEN007-5.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(divide(u,v),zero)
| ~ equal(divide(v,u),zero)
| equal(v,u) ),
file('HEN007-5.p',unknown),
[] ).
cnf(23,plain,
( ~ equal(zero,zero)
| ~ equal(divide(u,zero),zero)
| equal(u,zero) ),
inference(spl,[status(thm),theory(equality)],[6,7]),
[iquote('0:SpL:6.0,7.0')] ).
cnf(24,plain,
( ~ equal(zero,zero)
| ~ equal(divide(u,divide(u,v)),zero)
| equal(divide(u,v),u) ),
inference(spl,[status(thm),theory(equality)],[4,7]),
[iquote('0:SpL:4.0,7.0')] ).
cnf(27,plain,
( ~ equal(divide(u,zero),zero)
| equal(u,zero) ),
inference(obv,[status(thm),theory(equality)],[23]),
[iquote('0:Obv:23.0')] ).
cnf(29,plain,
( ~ equal(divide(u,divide(u,v)),zero)
| equal(divide(u,v),u) ),
inference(obv,[status(thm),theory(equality)],[24]),
[iquote('0:Obv:24.0')] ).
cnf(44,plain,
equal(divide(divide(divide(u,u),divide(v,u)),zero),zero),
inference(spr,[status(thm),theory(equality)],[4,5]),
[iquote('0:SpR:4.0,5.0')] ).
cnf(46,plain,
equal(divide(divide(divide(u,b),zero),divide(divide(u,a),b)),zero),
inference(spr,[status(thm),theory(equality)],[2,5]),
[iquote('0:SpR:2.0,5.0')] ).
cnf(47,plain,
equal(divide(divide(divide(u,v),zero),divide(divide(u,zero),v)),zero),
inference(spr,[status(thm),theory(equality)],[6,5]),
[iquote('0:SpR:6.0,5.0')] ).
cnf(152,plain,
( ~ equal(zero,zero)
| ~ equal(divide(u,divide(v,w)),zero)
| equal(divide(u,v),zero) ),
inference(spl,[status(thm),theory(equality)],[4,1]),
[iquote('0:SpL:4.0,1.0')] ).
cnf(160,plain,
( ~ equal(divide(u,divide(v,w)),zero)
| equal(divide(u,v),zero) ),
inference(obv,[status(thm),theory(equality)],[152]),
[iquote('0:Obv:152.0')] ).
cnf(203,plain,
equal(divide(divide(divide(u,u),zero),zero),zero),
inference(spr,[status(thm),theory(equality)],[6,44]),
[iquote('0:SpR:6.0,44.0')] ).
cnf(248,plain,
( ~ equal(zero,zero)
| equal(divide(divide(u,u),zero),zero) ),
inference(spl,[status(thm),theory(equality)],[203,27]),
[iquote('0:SpL:203.0,27.0')] ).
cnf(249,plain,
equal(divide(divide(u,u),zero),zero),
inference(obv,[status(thm),theory(equality)],[248]),
[iquote('0:Obv:248.0')] ).
cnf(279,plain,
( ~ equal(zero,zero)
| equal(divide(u,u),zero) ),
inference(spl,[status(thm),theory(equality)],[249,27]),
[iquote('0:SpL:249.0,27.0')] ).
cnf(280,plain,
equal(divide(u,u),zero),
inference(obv,[status(thm),theory(equality)],[279]),
[iquote('0:Obv:279.0')] ).
cnf(485,plain,
equal(divide(divide(divide(u,divide(u,zero)),zero),zero),zero),
inference(spr,[status(thm),theory(equality)],[280,47]),
[iquote('0:SpR:280.0,47.0')] ).
cnf(879,plain,
( ~ equal(zero,zero)
| equal(divide(divide(divide(u,b),zero),divide(u,a)),zero) ),
inference(spl,[status(thm),theory(equality)],[46,160]),
[iquote('0:SpL:46.0,160.0')] ).
cnf(890,plain,
equal(divide(divide(divide(u,b),zero),divide(u,a)),zero),
inference(obv,[status(thm),theory(equality)],[879]),
[iquote('0:Obv:879.0')] ).
cnf(999,plain,
( ~ equal(zero,zero)
| equal(divide(divide(u,divide(u,zero)),zero),zero) ),
inference(spl,[status(thm),theory(equality)],[485,27]),
[iquote('0:SpL:485.0,27.0')] ).
cnf(1005,plain,
equal(divide(divide(u,divide(u,zero)),zero),zero),
inference(obv,[status(thm),theory(equality)],[999]),
[iquote('0:Obv:999.0')] ).
cnf(1046,plain,
( ~ equal(zero,zero)
| equal(divide(u,divide(u,zero)),zero) ),
inference(spl,[status(thm),theory(equality)],[1005,27]),
[iquote('0:SpL:1005.0,27.0')] ).
cnf(1051,plain,
equal(divide(u,divide(u,zero)),zero),
inference(obv,[status(thm),theory(equality)],[1046]),
[iquote('0:Obv:1046.0')] ).
cnf(1124,plain,
( ~ equal(zero,zero)
| equal(divide(u,zero),u) ),
inference(spl,[status(thm),theory(equality)],[1051,29]),
[iquote('0:SpL:1051.0,29.0')] ).
cnf(1131,plain,
equal(divide(u,zero),u),
inference(obv,[status(thm),theory(equality)],[1124]),
[iquote('0:Obv:1124.0')] ).
cnf(1157,plain,
equal(divide(divide(u,b),divide(u,a)),zero),
inference(rew,[status(thm),theory(equality)],[1131,890]),
[iquote('0:Rew:1131.0,890.0')] ).
cnf(1185,plain,
$false,
inference(unc,[status(thm)],[1157,3]),
[iquote('0:UnC:1157.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN007-5 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n018.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 : Fri Jul 1 14:43:02 EDT 2022
% 0.13/0.34 % 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/sandbox/benchmark/theBenchmark.p
% 0.19/0.51 SPASS derived 764 clauses, backtracked 0 clauses, performed 0 splits and kept 154 clauses.
% 0.19/0.51 SPASS allocated 64161 KBytes.
% 0.19/0.51 SPASS spent 0:00:00.16 on the problem.
% 0.19/0.51 0:00:00.04 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 0:00:00.09 for the reduction.
% 0.19/0.51
% 0.19/0.51
% 0.19/0.51 Here is a proof with depth 8, length 32 :
% 0.19/0.51 % SZS output start Refutation
% See solution above
% 0.19/0.51 Formulae used in the proof : transitivity_of_divide_to_zero a_divide_b_is_zero prove_property_of_divide2 quotient_smaller_than_numerator quotient_property zero_is_smallest divide_and_equal
% 0.19/0.51
%------------------------------------------------------------------------------