TSTP Solution File: HEN006-7 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN006-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 2.45s 2.63s
% Output : Refutation 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 33 ( 16 unt; 0 nHn; 33 RR)
% Number of literals : 72 ( 0 equ; 41 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
quotient(zero,u,zero),
file('HEN006-7.p',unknown),
[] ).
cnf(4,axiom,
quotient(u,zero,u),
file('HEN006-7.p',unknown),
[] ).
cnf(5,axiom,
quotient(x__dfg,y__dfg,xQy),
file('HEN006-7.p',unknown),
[] ).
cnf(6,axiom,
less_equal(xQy,z__dfg),
file('HEN006-7.p',unknown),
[] ).
cnf(7,axiom,
quotient(x__dfg,z__dfg,xQz),
file('HEN006-7.p',unknown),
[] ).
cnf(8,axiom,
~ less_equal(xQz,y__dfg),
file('HEN006-7.p',unknown),
[] ).
cnf(9,axiom,
( ~ less_equal(u,v)
| quotient(u,v,zero) ),
file('HEN006-7.p',unknown),
[] ).
cnf(10,axiom,
( ~ quotient(u,v,zero)
| less_equal(u,v) ),
file('HEN006-7.p',unknown),
[] ).
cnf(11,axiom,
( ~ quotient(u,v,w)
| less_equal(w,u) ),
file('HEN006-7.p',unknown),
[] ).
cnf(12,axiom,
( ~ quotient(u,v,w)
| ~ quotient(x,y,z)
| ~ quotient(x1,v,x)
| ~ quotient(x2,v,y)
| ~ quotient(x1,x2,u)
| less_equal(z,w) ),
file('HEN006-7.p',unknown),
[] ).
cnf(13,axiom,
less_equal(zero,u),
file('HEN006-7.p',unknown),
[] ).
cnf(14,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN006-7.p',unknown),
[] ).
cnf(16,axiom,
quotient(u,v,divide(u,v)),
file('HEN006-7.p',unknown),
[] ).
cnf(18,plain,
~ quotient(xQz,y__dfg,zero),
inference(res,[status(thm),theory(equality)],[10,8]),
[iquote('0:Res:10.1,8.0')] ).
cnf(33,plain,
less_equal(divide(u,v),u),
inference(res,[status(thm),theory(equality)],[16,11]),
[iquote('0:Res:16.0,11.0')] ).
cnf(37,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[13,14]),
[iquote('0:Res:13.0,14.0')] ).
cnf(63,plain,
( ~ quotient(u,v,w)
| ~ quotient(x,y,u)
| ~ quotient(z,y,v)
| ~ quotient(x,z,zero)
| less_equal(w,zero) ),
inference(res,[status(thm),theory(equality)],[2,12]),
[iquote('0:Res:2.0,12.0')] ).
cnf(68,plain,
( ~ less_equal(u,v)
| ~ quotient(w,x,y)
| ~ quotient(z,v,w)
| ~ quotient(x1,v,x)
| ~ quotient(z,x1,u)
| less_equal(y,zero) ),
inference(res,[status(thm),theory(equality)],[9,12]),
[iquote('0:Res:9.1,12.0')] ).
cnf(239,plain,
( ~ quotient(u,v,w)
| ~ quotient(x,v,zero)
| ~ quotient(u,x,zero)
| less_equal(w,zero) ),
inference(res,[status(thm),theory(equality)],[4,63]),
[iquote('0:Res:4.0,63.0')] ).
cnf(322,plain,
( ~ less_equal(u,v)
| ~ quotient(w,v,x)
| ~ quotient(y,v,z)
| ~ quotient(w,y,u)
| less_equal(divide(x,z),zero) ),
inference(res,[status(thm),theory(equality)],[16,68]),
[iquote('0:Res:16.0,68.1')] ).
cnf(348,plain,
( ~ quotient(u,v,zero)
| ~ quotient(w,u,zero)
| less_equal(divide(w,v),zero) ),
inference(res,[status(thm),theory(equality)],[16,239]),
[iquote('0:Res:16.0,239.0')] ).
cnf(1124,plain,
( ~ less_equal(u,z__dfg)
| ~ quotient(v,z__dfg,w)
| ~ quotient(x__dfg,v,u)
| less_equal(divide(xQz,w),zero) ),
inference(res,[status(thm),theory(equality)],[7,322]),
[iquote('0:Res:7.0,322.1')] ).
cnf(1637,plain,
( ~ less_equal(u,v)
| ~ quotient(w,u,zero)
| less_equal(divide(w,v),zero) ),
inference(res,[status(thm),theory(equality)],[9,348]),
[iquote('0:Res:9.1,348.0')] ).
cnf(3039,plain,
( ~ less_equal(u,z__dfg)
| ~ quotient(x__dfg,v,u)
| less_equal(divide(xQz,divide(v,z__dfg)),zero) ),
inference(res,[status(thm),theory(equality)],[16,1124]),
[iquote('0:Res:16.0,1124.1')] ).
cnf(6875,plain,
( ~ less_equal(xQy,z__dfg)
| less_equal(divide(xQz,divide(y__dfg,z__dfg)),zero) ),
inference(res,[status(thm),theory(equality)],[5,3039]),
[iquote('0:Res:5.0,3039.1')] ).
cnf(6885,plain,
less_equal(divide(xQz,divide(y__dfg,z__dfg)),zero),
inference(mrr,[status(thm)],[6875,6]),
[iquote('0:MRR:6875.0,6.0')] ).
cnf(6906,plain,
equal(divide(xQz,divide(y__dfg,z__dfg)),zero),
inference(res,[status(thm),theory(equality)],[6885,37]),
[iquote('0:Res:6885.0,37.0')] ).
cnf(6972,plain,
quotient(xQz,divide(y__dfg,z__dfg),zero),
inference(spr,[status(thm),theory(equality)],[6906,16]),
[iquote('0:SpR:6906.0,16.0')] ).
cnf(7066,plain,
( ~ less_equal(divide(y__dfg,z__dfg),u)
| less_equal(divide(xQz,u),zero) ),
inference(res,[status(thm),theory(equality)],[6972,1637]),
[iquote('0:Res:6972.0,1637.1')] ).
cnf(9565,plain,
( ~ less_equal(divide(y__dfg,z__dfg),u)
| equal(divide(xQz,u),zero) ),
inference(res,[status(thm),theory(equality)],[7066,37]),
[iquote('0:Res:7066.1,37.0')] ).
cnf(15709,plain,
equal(divide(xQz,y__dfg),zero),
inference(res,[status(thm),theory(equality)],[33,9565]),
[iquote('0:Res:33.0,9565.0')] ).
cnf(15873,plain,
quotient(xQz,y__dfg,zero),
inference(spr,[status(thm),theory(equality)],[15709,16]),
[iquote('0:SpR:15709.0,16.0')] ).
cnf(15984,plain,
$false,
inference(mrr,[status(thm)],[15873,18]),
[iquote('0:MRR:15873.0,18.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : HEN006-7 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 1 13:46:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.45/2.63
% 2.45/2.63 SPASS V 3.9
% 2.45/2.63 SPASS beiseite: Proof found.
% 2.45/2.63 % SZS status Theorem
% 2.45/2.63 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.45/2.63 SPASS derived 13189 clauses, backtracked 0 clauses, performed 0 splits and kept 2560 clauses.
% 2.45/2.63 SPASS allocated 72190 KBytes.
% 2.45/2.63 SPASS spent 0:00:02.21 on the problem.
% 2.45/2.63 0:00:00.04 for the input.
% 2.45/2.63 0:00:00.00 for the FLOTTER CNF translation.
% 2.45/2.63 0:00:00.13 for inferences.
% 2.45/2.63 0:00:00.00 for the backtracking.
% 2.45/2.63 0:00:02.00 for the reduction.
% 2.45/2.63
% 2.45/2.63
% 2.45/2.63 Here is a proof with depth 11, length 33 :
% 2.45/2.63 % SZS output start Refutation
% See solution above
% 2.45/2.64 Formulae used in the proof : zero_divide_anything_is_zero x_divde_zero_is_x xQy xQyLEz xQz prove_xQzLEy quotient_less_equal less_equal_quotient divisor_existence quotient_property zero_is_smallest less_equal_and_equal closure
% 2.45/2.64
%------------------------------------------------------------------------------