%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM836+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 : Mon Jul 18 14:30:53 EDT 2022
% Result : Theorem 0.51s 0.70s
% Output : Refutation 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 26 ( 13 unt; 0 nHn; 26 RR)
% Number of literals : 40 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
greater(vd203,vd204),
file('NUM836+2.p',unknown),
[] ).
cnf(2,axiom,
less(vd203,vd204),
file('NUM836+2.p',unknown),
[] ).
cnf(4,axiom,
~ equal(vplus(u,v),u),
file('NUM836+2.p',unknown),
[] ).
cnf(7,axiom,
( ~ equal(u,vplus(v,w))
| less(v,u) ),
file('NUM836+2.p',unknown),
[] ).
cnf(8,axiom,
( ~ equal(u,vplus(v,w))
| greater(u,v) ),
file('NUM836+2.p',unknown),
[] ).
cnf(10,axiom,
( ~ less(u,v)
| equal(vplus(u,skf4(u,v)),v) ),
file('NUM836+2.p',unknown),
[] ).
cnf(11,axiom,
( ~ greater(u,v)
| equal(vplus(v,skf5(v,u)),u) ),
file('NUM836+2.p',unknown),
[] ).
cnf(12,axiom,
( ~ equal(vplus(u,v),vplus(u,w))
| equal(v,w) ),
file('NUM836+2.p',unknown),
[] ).
cnf(13,axiom,
equal(vplus(vplus(u,v),w),vplus(u,vplus(v,w))),
file('NUM836+2.p',unknown),
[] ).
cnf(18,plain,
equal(vplus(vd204,skf5(vd204,vd203)),vd203),
inference(res,[status(thm),theory(equality)],[1,11]),
[iquote('0:Res:1.0,11.0')] ).
cnf(35,plain,
greater(vplus(u,v),u),
inference(eqr,[status(thm),theory(equality)],[8]),
[iquote('0:EqR:8.0')] ).
cnf(48,plain,
less(u,vplus(u,v)),
inference(eqr,[status(thm),theory(equality)],[7]),
[iquote('0:EqR:7.0')] ).
cnf(59,plain,
( ~ greater(u,v)
| less(v,u) ),
inference(spr,[status(thm),theory(equality)],[11,48]),
[iquote('0:SpR:11.1,48.0')] ).
cnf(77,plain,
( ~ less(u,v)
| ~ equal(v,u) ),
inference(spl,[status(thm),theory(equality)],[10,4]),
[iquote('0:SpL:10.1,4.0')] ).
cnf(93,plain,
( ~ less(u,v)
| equal(vplus(u,vplus(skf4(u,v),w)),vplus(v,w)) ),
inference(spr,[status(thm),theory(equality)],[10,13]),
[iquote('0:SpR:10.1,13.0')] ).
cnf(116,plain,
( ~ less(u,v)
| ~ equal(v,vplus(u,w))
| equal(skf4(u,v),w) ),
inference(spl,[status(thm),theory(equality)],[10,12]),
[iquote('0:SpL:10.1,12.0')] ).
cnf(128,plain,
( ~ equal(u,vplus(v,w))
| equal(skf4(v,u),w) ),
inference(mrr,[status(thm)],[116,7]),
[iquote('0:MRR:116.0,7.1')] ).
cnf(748,plain,
equal(skf4(u,vplus(u,v)),v),
inference(eqr,[status(thm),theory(equality)],[128]),
[iquote('0:EqR:128.0')] ).
cnf(772,plain,
equal(skf5(vd204,vd203),skf4(vd204,vd203)),
inference(spr,[status(thm),theory(equality)],[18,748]),
[iquote('0:SpR:18.0,748.0')] ).
cnf(777,plain,
equal(vplus(vd204,skf4(vd204,vd203)),vd203),
inference(rew,[status(thm),theory(equality)],[772,18]),
[iquote('0:Rew:772.0,18.0')] ).
cnf(2092,plain,
( ~ less(u,v)
| greater(vplus(v,w),u) ),
inference(spr,[status(thm),theory(equality)],[93,35]),
[iquote('0:SpR:93.1,35.0')] ).
cnf(2237,plain,
( ~ less(u,vd204)
| greater(vd203,u) ),
inference(spr,[status(thm),theory(equality)],[777,2092]),
[iquote('0:SpR:777.0,2092.1')] ).
cnf(2268,plain,
( ~ less(u,vd204)
| less(u,vd203) ),
inference(res,[status(thm),theory(equality)],[2237,59]),
[iquote('0:Res:2237.1,59.0')] ).
cnf(2334,plain,
less(vd203,vd203),
inference(res,[status(thm),theory(equality)],[2,2268]),
[iquote('0:Res:2.0,2268.0')] ).
cnf(2345,plain,
~ equal(vd203,vd203),
inference(res,[status(thm),theory(equality)],[2334,77]),
[iquote('0:Res:2334.0,77.0')] ).
cnf(2346,plain,
$false,
inference(obv,[status(thm),theory(equality)],[2345]),
[iquote('0:Obv:2345.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM836+2 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n021.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 : Thu Jul 7 12:27:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.51/0.70
% 0.51/0.70 SPASS V 3.9
% 0.51/0.70 SPASS beiseite: Proof found.
% 0.51/0.70 % SZS status Theorem
% 0.51/0.70 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.51/0.70 SPASS derived 2147 clauses, backtracked 0 clauses, performed 0 splits and kept 820 clauses.
% 0.51/0.70 SPASS allocated 86721 KBytes.
% 0.51/0.70 SPASS spent 0:00:00.35 on the problem.
% 0.51/0.70 0:00:00.03 for the input.
% 0.51/0.70 0:00:00.03 for the FLOTTER CNF translation.
% 0.51/0.70 0:00:00.03 for inferences.
% 0.51/0.70 0:00:00.00 for the backtracking.
% 0.51/0.70 0:00:00.24 for the reduction.
% 0.51/0.70
% 0.51/0.70
% 0.51/0.70 Here is a proof with depth 6, length 26 :
% 0.51/0.70 % SZS output start Refutation
% See solution above
% 0.51/0.70 Formulae used in the proof : dis_a40_ex_a40_cond_a40_conseq_a40_131_a41__a44__a32_0_a41__a44__a32_1_a41__a41_ ass_a40_cond_a40_goal_a40_88_a41__a44__a32_0_a41__a44__a32_3_a41_ def_a40_cond_a40_conseq_a40_axiom_a40_3_a41__a41__a44__a32_12_a41__a44__a32_1_a41_ def_a40_cond_a40_conseq_a40_axiom_a40_3_a41__a41__a44__a32_11_a41__a44__a32_1_a41_ ass_a40_cond_a40_81_a44__a32_0_a41__a44__a32_0_a41_ ass_a40_cond_a40_33_a44__a32_0_a41__a44__a32_0_a41_
% 0.51/0.70
%------------------------------------------------------------------------------