TSTP Solution File: HEN012-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : HEN012-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n007.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 13:03:16 EDT 2022
% Result : Unsatisfiable 0.46s 0.68s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 10 unt; 0 nHn; 25 RR)
% Number of literals : 55 ( 0 equ; 32 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 : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ less_equal(x__dfg,x__dfg),
file('HEN012-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ less_equal(u,v)
| quotient(u,v,zero) ),
file('HEN012-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ quotient(u,v,zero)
| less_equal(u,v) ),
file('HEN012-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ quotient(u,v,w)
| less_equal(w,u) ),
file('HEN012-1.p',unknown),
[] ).
cnf(5,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('HEN012-1.p',unknown),
[] ).
cnf(6,axiom,
less_equal(zero,u),
file('HEN012-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ less_equal(u,v)
| ~ less_equal(v,u)
| equal(v,u) ),
file('HEN012-1.p',unknown),
[] ).
cnf(9,axiom,
quotient(u,v,divide(u,v)),
file('HEN012-1.p',unknown),
[] ).
cnf(11,plain,
~ quotient(x__dfg,x__dfg,zero),
inference(res,[status(thm),theory(equality)],[3,1]),
[iquote('0:Res:3.1,1.0')] ).
cnf(16,plain,
less_equal(divide(u,v),u),
inference(res,[status(thm),theory(equality)],[9,4]),
[iquote('0:Res:9.0,4.0')] ).
cnf(18,plain,
( ~ less_equal(u,zero)
| equal(u,zero) ),
inference(res,[status(thm),theory(equality)],[6,7]),
[iquote('0:Res:6.0,7.0')] ).
cnf(22,plain,
equal(divide(zero,u),zero),
inference(res,[status(thm),theory(equality)],[16,18]),
[iquote('0:Res:16.0,18.0')] ).
cnf(43,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)],[2,5]),
[iquote('0:Res:2.1,5.0')] ).
cnf(135,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)],[9,43]),
[iquote('0:Res:9.0,43.1')] ).
cnf(311,plain,
( ~ less_equal(u,v)
| ~ quotient(w,v,x)
| ~ quotient(y,w,u)
| less_equal(divide(divide(y,v),x),zero) ),
inference(res,[status(thm),theory(equality)],[9,135]),
[iquote('0:Res:9.0,135.1')] ).
cnf(499,plain,
( ~ less_equal(u,v)
| ~ quotient(w,x,u)
| less_equal(divide(divide(w,v),divide(x,v)),zero) ),
inference(res,[status(thm),theory(equality)],[9,311]),
[iquote('0:Res:9.0,311.1')] ).
cnf(826,plain,
( ~ less_equal(divide(u,v),w)
| less_equal(divide(divide(u,w),divide(v,w)),zero) ),
inference(res,[status(thm),theory(equality)],[9,499]),
[iquote('0:Res:9.0,499.1')] ).
cnf(2096,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(divide(u,v),zero),zero) ),
inference(spr,[status(thm),theory(equality)],[22,826]),
[iquote('0:SpR:22.0,826.1')] ).
cnf(2187,plain,
( ~ less_equal(divide(u,zero),v)
| equal(divide(divide(u,v),zero),zero) ),
inference(res,[status(thm),theory(equality)],[2096,18]),
[iquote('0:Res:2096.1,18.0')] ).
cnf(2199,plain,
( ~ less_equal(divide(u,zero),v)
| quotient(divide(u,v),zero,zero) ),
inference(spr,[status(thm),theory(equality)],[2187,9]),
[iquote('0:SpR:2187.1,9.0')] ).
cnf(2294,plain,
( ~ less_equal(divide(u,zero),v)
| less_equal(divide(u,v),zero) ),
inference(res,[status(thm),theory(equality)],[2199,3]),
[iquote('0:Res:2199.1,3.0')] ).
cnf(2355,plain,
less_equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[16,2294]),
[iquote('0:Res:16.0,2294.0')] ).
cnf(2391,plain,
equal(divide(u,u),zero),
inference(res,[status(thm),theory(equality)],[2355,18]),
[iquote('0:Res:2355.0,18.0')] ).
cnf(2406,plain,
quotient(u,u,zero),
inference(spr,[status(thm),theory(equality)],[2391,9]),
[iquote('0:SpR:2391.0,9.0')] ).
cnf(2476,plain,
$false,
inference(unc,[status(thm)],[2406,11]),
[iquote('0:UnC:2406.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN012-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n007.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 12:40:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.46/0.68
% 0.46/0.68 SPASS V 3.9
% 0.46/0.68 SPASS beiseite: Proof found.
% 0.46/0.68 % SZS status Theorem
% 0.46/0.68 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.46/0.68 SPASS derived 1975 clauses, backtracked 0 clauses, performed 0 splits and kept 448 clauses.
% 0.46/0.68 SPASS allocated 64866 KBytes.
% 0.46/0.68 SPASS spent 0:00:00.32 on the problem.
% 0.46/0.68 0:00:00.03 for the input.
% 0.46/0.68 0:00:00.00 for the FLOTTER CNF translation.
% 0.46/0.68 0:00:00.03 for inferences.
% 0.46/0.68 0:00:00.00 for the backtracking.
% 0.46/0.68 0:00:00.24 for the reduction.
% 0.46/0.68
% 0.46/0.68
% 0.46/0.68 Here is a proof with depth 12, length 25 :
% 0.46/0.68 % SZS output start Refutation
% See solution above
% 0.46/0.68 Formulae used in the proof : prove_X_less_than_or_equal_to_X quotient_less_equal less_equal_quotient divisor_existence quotient_property zero_is_smallest less_equal_and_equal closure
% 0.46/0.68
%------------------------------------------------------------------------------