TSTP Solution File: HEN008-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN008-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 13:03:08 EDT 2022
% Result : Unsatisfiable 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 8 unt; 0 nHn; 17 RR)
% Number of literals : 28 ( 0 equ; 13 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(1,axiom,
less_equal(a,b),
file('HEN008-3.p',unknown),
[] ).
cnf(2,axiom,
~ less_equal(divide(a,c),divide(b,c)),
file('HEN008-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ less_equal(u,v)
| equal(divide(u,v),zero) ),
file('HEN008-3.p',unknown),
[] ).
cnf(4,axiom,
( ~ equal(divide(u,v),zero)
| less_equal(u,v) ),
file('HEN008-3.p',unknown),
[] ).
cnf(5,axiom,
less_equal(divide(u,v),u),
file('HEN008-3.p',unknown),
[] ).
cnf(6,axiom,
less_equal(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),
file('HEN008-3.p',unknown),
[] ).
cnf(7,axiom,
less_equal(zero,u),
file('HEN008-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN008-3.p',unknown),
[] ).
cnf(19,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[7,8]),
[iquote('0:Res:7.0,8.0')] ).
cnf(23,plain,
equal(divide(zero,u),zero),
inference(res,[status(thm),theory(equality)],[5,19]),
[iquote('0:Res:5.0,19.0')] ).
cnf(30,plain,
( ~ less_equal(u,v)
| less_equal(divide(divide(u,w),divide(v,w)),divide(zero,w)) ),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.1,6.0')] ).
cnf(40,plain,
( ~ less_equal(u,v)
| less_equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(rew,[status(thm),theory(equality)],[23,30]),
[iquote('0:Rew:23.0,30.1')] ).
cnf(138,plain,
( ~ less_equal(u,v)
| equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(res,[status(thm),theory(equality)],[40,19]),
[iquote('0:Res:40.1,19.0')] ).
cnf(657,plain,
( ~ less_equal(u,v)
| ~ equal(zero,zero)
| less_equal(divide(u,w),divide(v,w)) ),
inference(spl,[status(thm),theory(equality)],[138,4]),
[iquote('0:SpL:138.1,4.0')] ).
cnf(673,plain,
( ~ less_equal(u,v)
| less_equal(divide(u,w),divide(v,w)) ),
inference(obv,[status(thm),theory(equality)],[657]),
[iquote('0:Obv:657.1')] ).
cnf(1067,plain,
~ less_equal(a,b),
inference(res,[status(thm),theory(equality)],[673,2]),
[iquote('0:Res:673.1,2.0')] ).
cnf(1069,plain,
$false,
inference(mrr,[status(thm)],[1067,1]),
[iquote('0:MRR:1067.0,1.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN008-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.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 13:14:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.49
% 0.19/0.49 SPASS V 3.9
% 0.19/0.49 SPASS beiseite: Proof found.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49 SPASS derived 745 clauses, backtracked 0 clauses, performed 0 splits and kept 190 clauses.
% 0.19/0.49 SPASS allocated 63875 KBytes.
% 0.19/0.49 SPASS spent 0:00:00.14 on the problem.
% 0.19/0.49 0:00:00.03 for the input.
% 0.19/0.49 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.49 0:00:00.01 for inferences.
% 0.19/0.49 0:00:00.00 for the backtracking.
% 0.19/0.49 0:00:00.07 for the reduction.
% 0.19/0.49
% 0.19/0.49
% 0.19/0.49 Here is a proof with depth 4, length 17 :
% 0.19/0.49 % SZS output start Refutation
% See solution above
% 0.19/0.49 Formulae used in the proof : a_LE_b prove_a_divide_c_LE_b_divide_c quotient_less_equal1 quotient_less_equal2 quotient_smaller_than_numerator quotient_property zero_is_smallest less_equal_and_equal
% 0.19/0.49
%------------------------------------------------------------------------------