TSTP Solution File: HEN005-4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN005-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n004.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 13:03:03 EDT 2022
% Result : Unsatisfiable 0.51s 0.67s
% Output : Refutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 9 unt; 0 nHn; 19 RR)
% Number of literals : 31 ( 0 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 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(2,axiom,
equal(divide(zero,u),zero),
file('HEN005-4.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(u,zero),u),
file('HEN005-4.p',unknown),
[] ).
cnf(5,axiom,
less_equal(a,b),
file('HEN005-4.p',unknown),
[] ).
cnf(6,axiom,
less_equal(b,c),
file('HEN005-4.p',unknown),
[] ).
cnf(7,axiom,
~ less_equal(a,c),
file('HEN005-4.p',unknown),
[] ).
cnf(8,axiom,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
file('HEN005-4.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN005-4.p',unknown),
[] ).
cnf(11,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN005-4.p',unknown),
[] ).
cnf(15,plain,
~ equal(divide(a,c),zero),
inference(res,[status(thm),theory(equality)],[9,7]),
[iquote('0:Res:9.1,7.0')] ).
cnf(31,plain,
( ~ less_equal(u,zero)
| equal(zero,u) ),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.1,4.0')] ).
cnf(61,plain,
( ~ less_equal(u,v)
| less_equal(divide(divide(u,w),divide(v,w)),divide(zero,w)) ),
inference(spr,[status(thm),theory(equality)],[8,11]),
[iquote('0:SpR:8.1,11.0')] ).
cnf(91,plain,
( ~ less_equal(u,v)
| less_equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(rew,[status(thm),theory(equality)],[2,61]),
[iquote('0:Rew:2.0,61.1')] ).
cnf(431,plain,
( ~ less_equal(u,v)
| equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(res,[status(thm),theory(equality)],[91,31]),
[iquote('0:Res:91.1,31.0')] ).
cnf(1056,plain,
( ~ less_equal(u,v)
| ~ less_equal(w,u)
| equal(divide(divide(w,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[8,431]),
[iquote('0:SpR:8.1,431.1')] ).
cnf(1090,plain,
( ~ less_equal(u,v)
| ~ less_equal(w,u)
| equal(divide(w,v),zero) ),
inference(rew,[status(thm),theory(equality)],[4,1056]),
[iquote('0:Rew:4.0,1056.2')] ).
cnf(3210,plain,
( ~ less_equal(u,b)
| equal(divide(u,c),zero) ),
inference(res,[status(thm),theory(equality)],[6,1090]),
[iquote('0:Res:6.0,1090.0')] ).
cnf(3290,plain,
( ~ less_equal(a,b)
| ~ equal(zero,zero) ),
inference(spl,[status(thm),theory(equality)],[3210,15]),
[iquote('0:SpL:3210.1,15.0')] ).
cnf(3294,plain,
~ less_equal(a,b),
inference(obv,[status(thm),theory(equality)],[3290]),
[iquote('0:Obv:3290.1')] ).
cnf(3295,plain,
$false,
inference(mrr,[status(thm)],[3294,5]),
[iquote('0:MRR:3294.0,5.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : HEN005-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Fri Jul 1 13:26:23 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.51/0.67
% 0.51/0.67 SPASS V 3.9
% 0.51/0.67 SPASS beiseite: Proof found.
% 0.51/0.67 % SZS status Theorem
% 0.51/0.67 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.51/0.67 SPASS derived 2285 clauses, backtracked 0 clauses, performed 0 splits and kept 353 clauses.
% 0.51/0.67 SPASS allocated 65374 KBytes.
% 0.51/0.67 SPASS spent 0:00:00.29 on the problem.
% 0.51/0.67 0:00:00.04 for the input.
% 0.51/0.67 0:00:00.00 for the FLOTTER CNF translation.
% 0.51/0.67 0:00:00.02 for inferences.
% 0.51/0.67 0:00:00.00 for the backtracking.
% 0.51/0.67 0:00:00.21 for the reduction.
% 0.51/0.67
% 0.51/0.67
% 0.51/0.67 Here is a proof with depth 5, length 19 :
% 0.51/0.67 % SZS output start Refutation
% See solution above
% 0.51/0.67 Formulae used in the proof : zero_divide_anything_is_zero x_divide_zero_is_x a_LE_b b_LE_c prove_a_LE_c quotient_less_equal1 quotient_less_equal2 quotient_property
% 0.51/0.67
%------------------------------------------------------------------------------