TSTP Solution File: HEN004-5 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN004-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n006.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 13:03:01 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 11 unt; 0 nHn; 19 RR)
% Number of literals : 30 ( 0 equ; 12 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(divide(u,u),zero),
file('HEN004-5.p',unknown),
[] ).
cnf(2,axiom,
~ equal(divide(a,zero),a),
file('HEN004-5.p',unknown),
[] ).
cnf(3,axiom,
equal(divide(divide(u,v),u),zero),
file('HEN004-5.p',unknown),
[] ).
cnf(4,axiom,
equal(divide(divide(divide(u,v),divide(w,v)),divide(divide(u,w),v)),zero),
file('HEN004-5.p',unknown),
[] ).
cnf(5,axiom,
equal(divide(zero,u),zero),
file('HEN004-5.p',unknown),
[] ).
cnf(6,axiom,
( ~ equal(divide(u,v),zero)
| ~ equal(divide(v,u),zero)
| equal(v,u) ),
file('HEN004-5.p',unknown),
[] ).
cnf(22,plain,
( ~ equal(zero,zero)
| ~ equal(divide(u,zero),zero)
| equal(u,zero) ),
inference(spl,[status(thm),theory(equality)],[5,6]),
[iquote('0:SpL:5.0,6.0')] ).
cnf(23,plain,
( ~ equal(zero,zero)
| ~ equal(divide(u,divide(u,v)),zero)
| equal(divide(u,v),u) ),
inference(spl,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpL:3.0,6.0')] ).
cnf(26,plain,
( ~ equal(divide(u,zero),zero)
| equal(u,zero) ),
inference(obv,[status(thm),theory(equality)],[22]),
[iquote('0:Obv:22.0')] ).
cnf(28,plain,
( ~ equal(divide(u,divide(u,v)),zero)
| equal(divide(u,v),u) ),
inference(obv,[status(thm),theory(equality)],[23]),
[iquote('0:Obv:23.0')] ).
cnf(57,plain,
equal(divide(divide(divide(u,v),zero),divide(divide(u,zero),v)),zero),
inference(spr,[status(thm),theory(equality)],[5,4]),
[iquote('0:SpR:5.0,4.0')] ).
cnf(154,plain,
equal(divide(divide(divide(u,divide(u,zero)),zero),zero),zero),
inference(spr,[status(thm),theory(equality)],[1,57]),
[iquote('0:SpR:1.0,57.0')] ).
cnf(388,plain,
( ~ equal(zero,zero)
| equal(divide(divide(u,divide(u,zero)),zero),zero) ),
inference(spl,[status(thm),theory(equality)],[154,26]),
[iquote('0:SpL:154.0,26.0')] ).
cnf(395,plain,
equal(divide(divide(u,divide(u,zero)),zero),zero),
inference(obv,[status(thm),theory(equality)],[388]),
[iquote('0:Obv:388.0')] ).
cnf(507,plain,
( ~ equal(zero,zero)
| equal(divide(u,divide(u,zero)),zero) ),
inference(spl,[status(thm),theory(equality)],[395,26]),
[iquote('0:SpL:395.0,26.0')] ).
cnf(511,plain,
equal(divide(u,divide(u,zero)),zero),
inference(obv,[status(thm),theory(equality)],[507]),
[iquote('0:Obv:507.0')] ).
cnf(545,plain,
( ~ equal(zero,zero)
| equal(divide(u,zero),u) ),
inference(spl,[status(thm),theory(equality)],[511,28]),
[iquote('0:SpL:511.0,28.0')] ).
cnf(548,plain,
equal(divide(u,zero),u),
inference(obv,[status(thm),theory(equality)],[545]),
[iquote('0:Obv:545.0')] ).
cnf(549,plain,
$false,
inference(unc,[status(thm)],[548,2]),
[iquote('0:UnC:548.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN004-5 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n006.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 13:51:52 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.44
% 0.19/0.44 SPASS V 3.9
% 0.19/0.44 SPASS beiseite: Proof found.
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 SPASS derived 343 clauses, backtracked 0 clauses, performed 0 splits and kept 56 clauses.
% 0.19/0.44 SPASS allocated 63606 KBytes.
% 0.19/0.44 SPASS spent 0:00:00.10 on the problem.
% 0.19/0.44 0:00:00.04 for the input.
% 0.19/0.44 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.44 0:00:00.00 for inferences.
% 0.19/0.44 0:00:00.00 for the backtracking.
% 0.19/0.44 0:00:00.03 for the reduction.
% 0.19/0.44
% 0.19/0.44
% 0.19/0.44 Here is a proof with depth 5, length 19 :
% 0.19/0.44 % SZS output start Refutation
% See solution above
% 0.19/0.44 Formulae used in the proof : x_divide_x_is_zero prove_x_divide_zero_is_x quotient_smaller_than_numerator quotient_property zero_is_smallest divide_and_equal
% 0.19/0.44
%------------------------------------------------------------------------------