TSTP Solution File: SYO620-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SYO620-1 : TPTP v8.1.0. Released v7.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 : Thu Jul 21 19:55:07 EDT 2022
% Result : Unsatisfiable 1.17s 1.34s
% Output : Refutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 8
% Syntax : Number of clauses : 80 ( 15 unt; 14 nHn; 80 RR)
% Number of literals : 185 ( 0 equ; 123 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
le(u,u),
file('SYO620-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ le(max(u,v),w)
| le(u,w) ),
file('SYO620-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ le(max(u,v),w)
| le(v,w) ),
file('SYO620-1.p',unknown),
[] ).
cnf(4,axiom,
( eq(f(u),a3)
| eq(f(u),a2)
| eq(f(u),a1)
| eq(f(u),a0) ),
file('SYO620-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ le(s(u),v)
| ~ eq(f(v),a0)
| ~ eq(f(u),a0) ),
file('SYO620-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ le(s(u),v)
| ~ eq(f(v),a1)
| ~ eq(f(u),a1) ),
file('SYO620-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ le(s(u),v)
| ~ eq(f(v),a2)
| ~ eq(f(u),a2) ),
file('SYO620-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ le(s(u),v)
| ~ eq(f(v),a3)
| ~ eq(f(u),a3) ),
file('SYO620-1.p',unknown),
[] ).
cnf(9,plain,
le(u,max(v,u)),
inference(res,[status(thm),theory(equality)],[1,3]),
[iquote('0:Res:1.0,3.0')] ).
cnf(10,plain,
le(u,max(v,max(w,u))),
inference(res,[status(thm),theory(equality)],[9,3]),
[iquote('0:Res:9.0,3.0')] ).
cnf(12,plain,
le(u,max(u,v)),
inference(res,[status(thm),theory(equality)],[1,2]),
[iquote('0:Res:1.0,2.0')] ).
cnf(13,plain,
le(u,max(v,max(u,w))),
inference(res,[status(thm),theory(equality)],[9,2]),
[iquote('0:Res:9.0,2.0')] ).
cnf(15,plain,
le(u,max(max(u,v),w)),
inference(res,[status(thm),theory(equality)],[12,2]),
[iquote('0:Res:12.0,2.0')] ).
cnf(16,plain,
le(u,max(max(v,u),w)),
inference(res,[status(thm),theory(equality)],[12,3]),
[iquote('0:Res:12.0,3.0')] ).
cnf(19,plain,
le(u,max(max(max(u,v),w),x)),
inference(res,[status(thm),theory(equality)],[15,2]),
[iquote('0:Res:15.0,2.0')] ).
cnf(20,plain,
le(u,max(max(max(v,u),w),x)),
inference(res,[status(thm),theory(equality)],[15,3]),
[iquote('0:Res:15.0,3.0')] ).
cnf(24,plain,
( ~ eq(f(max(u,s(v))),a3)
| ~ eq(f(v),a3) ),
inference(res,[status(thm),theory(equality)],[9,8]),
[iquote('0:Res:9.0,8.0')] ).
cnf(25,plain,
( ~ eq(f(max(u,max(v,s(w)))),a3)
| ~ eq(f(w),a3) ),
inference(res,[status(thm),theory(equality)],[10,8]),
[iquote('0:Res:10.0,8.0')] ).
cnf(27,plain,
( ~ eq(f(max(s(u),v)),a3)
| ~ eq(f(u),a3) ),
inference(res,[status(thm),theory(equality)],[12,8]),
[iquote('0:Res:12.0,8.0')] ).
cnf(28,plain,
( ~ eq(f(max(max(s(u),v),w)),a3)
| ~ eq(f(u),a3) ),
inference(res,[status(thm),theory(equality)],[15,8]),
[iquote('0:Res:15.0,8.0')] ).
cnf(42,plain,
( ~ eq(f(s(u)),a2)
| ~ eq(f(u),a2) ),
inference(res,[status(thm),theory(equality)],[1,7]),
[iquote('0:Res:1.0,7.0')] ).
cnf(43,plain,
( ~ eq(f(max(u,s(v))),a2)
| ~ eq(f(v),a2) ),
inference(res,[status(thm),theory(equality)],[9,7]),
[iquote('0:Res:9.0,7.0')] ).
cnf(44,plain,
( ~ eq(f(max(u,max(v,s(w)))),a2)
| ~ eq(f(w),a2) ),
inference(res,[status(thm),theory(equality)],[10,7]),
[iquote('0:Res:10.0,7.0')] ).
cnf(47,plain,
( ~ eq(f(max(u,max(s(v),w))),a2)
| ~ eq(f(v),a2) ),
inference(res,[status(thm),theory(equality)],[13,7]),
[iquote('0:Res:13.0,7.0')] ).
cnf(50,plain,
( ~ eq(f(max(s(u),v)),a2)
| ~ eq(f(u),a2) ),
inference(res,[status(thm),theory(equality)],[12,7]),
[iquote('0:Res:12.0,7.0')] ).
cnf(52,plain,
( ~ eq(f(max(max(u,s(v)),w)),a2)
| ~ eq(f(v),a2) ),
inference(res,[status(thm),theory(equality)],[16,7]),
[iquote('0:Res:16.0,7.0')] ).
cnf(54,plain,
le(u,max(max(max(max(v,u),w),x),y)),
inference(res,[status(thm),theory(equality)],[19,3]),
[iquote('0:Res:19.0,3.0')] ).
cnf(59,plain,
( ~ eq(f(max(max(max(u,s(v)),w),x)),a2)
| ~ eq(f(v),a2) ),
inference(res,[status(thm),theory(equality)],[20,7]),
[iquote('0:Res:20.0,7.0')] ).
cnf(69,plain,
( ~ eq(f(s(u)),a1)
| ~ eq(f(u),a1) ),
inference(res,[status(thm),theory(equality)],[1,6]),
[iquote('0:Res:1.0,6.0')] ).
cnf(70,plain,
( ~ eq(f(max(u,s(v))),a1)
| ~ eq(f(v),a1) ),
inference(res,[status(thm),theory(equality)],[9,6]),
[iquote('0:Res:9.0,6.0')] ).
cnf(74,plain,
( ~ eq(f(max(u,max(s(v),w))),a1)
| ~ eq(f(v),a1) ),
inference(res,[status(thm),theory(equality)],[13,6]),
[iquote('0:Res:13.0,6.0')] ).
cnf(77,plain,
( ~ eq(f(max(s(u),v)),a1)
| ~ eq(f(u),a1) ),
inference(res,[status(thm),theory(equality)],[12,6]),
[iquote('0:Res:12.0,6.0')] ).
cnf(79,plain,
( ~ eq(f(max(max(u,s(v)),w)),a1)
| ~ eq(f(v),a1) ),
inference(res,[status(thm),theory(equality)],[16,6]),
[iquote('0:Res:16.0,6.0')] ).
cnf(89,plain,
( ~ eq(f(s(u)),a0)
| ~ eq(f(u),a0) ),
inference(res,[status(thm),theory(equality)],[1,5]),
[iquote('0:Res:1.0,5.0')] ).
cnf(90,plain,
( ~ eq(f(max(u,s(v))),a0)
| ~ eq(f(v),a0) ),
inference(res,[status(thm),theory(equality)],[9,5]),
[iquote('0:Res:9.0,5.0')] ).
cnf(98,plain,
( ~ eq(f(max(s(u),v)),a0)
| ~ eq(f(u),a0) ),
inference(res,[status(thm),theory(equality)],[12,5]),
[iquote('0:Res:12.0,5.0')] ).
cnf(123,plain,
( ~ eq(f(u),a0)
| eq(f(s(u)),a3)
| eq(f(s(u)),a2)
| eq(f(s(u)),a1) ),
inference(res,[status(thm),theory(equality)],[4,89]),
[iquote('0:Res:4.3,89.0')] ).
cnf(159,plain,
( ~ eq(f(max(max(max(max(u,s(v)),w),x),y)),a3)
| ~ eq(f(v),a3) ),
inference(res,[status(thm),theory(equality)],[54,8]),
[iquote('0:Res:54.0,8.0')] ).
cnf(196,plain,
( ~ eq(f(u),a0)
| eq(f(max(v,s(u))),a3)
| eq(f(max(v,s(u))),a2)
| eq(f(max(v,s(u))),a1) ),
inference(res,[status(thm),theory(equality)],[4,90]),
[iquote('0:Res:4.3,90.0')] ).
cnf(197,plain,
( ~ eq(f(u),a0)
| eq(f(max(s(u),v)),a3)
| eq(f(max(s(u),v)),a2)
| eq(f(max(s(u),v)),a1) ),
inference(res,[status(thm),theory(equality)],[4,98]),
[iquote('0:Res:4.3,98.0')] ).
cnf(421,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a1)
| eq(f(max(s(v),s(u))),a3)
| eq(f(max(s(v),s(u))),a2) ),
inference(res,[status(thm),theory(equality)],[196,77]),
[iquote('0:Res:196.3,77.0')] ).
cnf(423,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a1)
| eq(f(max(max(w,s(v)),s(u))),a3)
| eq(f(max(max(w,s(v)),s(u))),a2) ),
inference(res,[status(thm),theory(equality)],[196,79]),
[iquote('0:Res:196.3,79.0')] ).
cnf(450,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a1)
| eq(f(max(s(u),max(s(v),w))),a3)
| eq(f(max(s(u),max(s(v),w))),a2) ),
inference(res,[status(thm),theory(equality)],[197,74]),
[iquote('0:Res:197.3,74.0')] ).
cnf(955,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a1)
| ~ eq(f(w),a2)
| eq(f(max(max(max(x,s(w)),s(v)),s(u))),a3) ),
inference(res,[status(thm),theory(equality)],[423,59]),
[iquote('0:Res:423.3,59.0')] ).
cnf(1009,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a1)
| ~ eq(f(w),a2)
| eq(f(max(s(u),max(s(v),s(w)))),a3) ),
inference(res,[status(thm),theory(equality)],[450,44]),
[iquote('0:Res:450.3,44.0')] ).
cnf(2272,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a1)
| ~ eq(f(w),a2)
| ~ eq(f(x),a3) ),
inference(res,[status(thm),theory(equality)],[955,159]),
[iquote('0:Res:955.3,159.0')] ).
cnf(2273,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a1)
| ~ eq(f(w),a2) ),
inference(mrr,[status(thm)],[1009,2272]),
[iquote('0:MRR:1009.3,2272.3')] ).
cnf(2301,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a1)
| eq(f(max(s(u),max(s(v),w))),a3) ),
inference(mrr,[status(thm)],[450,2273]),
[iquote('0:MRR:450.3,2273.2')] ).
cnf(2303,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a1)
| eq(f(max(s(v),s(u))),a3) ),
inference(mrr,[status(thm)],[421,2273]),
[iquote('0:MRR:421.3,2273.2')] ).
cnf(2450,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a1)
| ~ eq(f(w),a3) ),
inference(res,[status(thm),theory(equality)],[2301,25]),
[iquote('0:Res:2301.2,25.0')] ).
cnf(2459,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a1) ),
inference(mrr,[status(thm)],[2303,2450]),
[iquote('0:MRR:2303.2,2450.2')] ).
cnf(2577,plain,
( ~ eq(f(u),a0)
| eq(f(s(u)),a3)
| eq(f(s(u)),a2) ),
inference(mrr,[status(thm)],[123,2459]),
[iquote('0:MRR:123.3,2459.1')] ).
cnf(2578,plain,
( ~ eq(f(u),a0)
| eq(f(max(s(u),v)),a3)
| eq(f(max(s(u),v)),a2) ),
inference(mrr,[status(thm)],[197,2459]),
[iquote('0:MRR:197.3,2459.1')] ).
cnf(2612,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a2)
| eq(f(max(s(u),s(v))),a3) ),
inference(res,[status(thm),theory(equality)],[2578,43]),
[iquote('0:Res:2578.2,43.0')] ).
cnf(2620,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a2)
| eq(f(max(s(u),max(s(v),w))),a3) ),
inference(res,[status(thm),theory(equality)],[2578,47]),
[iquote('0:Res:2578.2,47.0')] ).
cnf(2675,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a2)
| ~ eq(f(w),a3) ),
inference(res,[status(thm),theory(equality)],[2620,25]),
[iquote('0:Res:2620.2,25.0')] ).
cnf(2684,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a2) ),
inference(mrr,[status(thm)],[2612,2675]),
[iquote('0:MRR:2612.2,2675.2')] ).
cnf(2714,plain,
( ~ eq(f(u),a0)
| eq(f(s(u)),a3) ),
inference(mrr,[status(thm)],[2577,2684]),
[iquote('0:MRR:2577.2,2684.1')] ).
cnf(2715,plain,
( ~ eq(f(u),a0)
| eq(f(max(s(u),v)),a3) ),
inference(mrr,[status(thm)],[2578,2684]),
[iquote('0:MRR:2578.2,2684.1')] ).
cnf(2748,plain,
( ~ eq(f(u),a0)
| ~ eq(f(v),a3) ),
inference(res,[status(thm),theory(equality)],[2715,24]),
[iquote('0:Res:2715.1,24.0')] ).
cnf(2764,plain,
~ eq(f(u),a0),
inference(mrr,[status(thm)],[2714,2748]),
[iquote('0:MRR:2714.1,2748.1')] ).
cnf(2795,plain,
( eq(f(u),a3)
| eq(f(u),a2)
| eq(f(u),a1) ),
inference(mrr,[status(thm)],[4,2764]),
[iquote('0:MRR:4.3,2764.0')] ).
cnf(2796,plain,
( ~ eq(f(u),a1)
| eq(f(s(u)),a3)
| eq(f(s(u)),a2) ),
inference(res,[status(thm),theory(equality)],[2795,69]),
[iquote('0:Res:2795.2,69.0')] ).
cnf(2797,plain,
( ~ eq(f(u),a1)
| eq(f(max(v,s(u))),a3)
| eq(f(max(v,s(u))),a2) ),
inference(res,[status(thm),theory(equality)],[2795,70]),
[iquote('0:Res:2795.2,70.0')] ).
cnf(2812,plain,
( ~ eq(f(u),a1)
| eq(f(max(s(u),v)),a3)
| eq(f(max(s(u),v)),a2) ),
inference(res,[status(thm),theory(equality)],[2795,77]),
[iquote('0:Res:2795.2,77.0')] ).
cnf(2831,plain,
( ~ eq(f(u),a1)
| ~ eq(f(v),a2)
| eq(f(max(s(v),s(u))),a3) ),
inference(res,[status(thm),theory(equality)],[2797,50]),
[iquote('0:Res:2797.2,50.0')] ).
cnf(2833,plain,
( ~ eq(f(u),a1)
| ~ eq(f(v),a2)
| eq(f(max(max(w,s(v)),s(u))),a3) ),
inference(res,[status(thm),theory(equality)],[2797,52]),
[iquote('0:Res:2797.2,52.0')] ).
cnf(2896,plain,
( ~ eq(f(u),a1)
| ~ eq(f(v),a2)
| ~ eq(f(w),a3) ),
inference(res,[status(thm),theory(equality)],[2833,28]),
[iquote('0:Res:2833.2,28.0')] ).
cnf(2904,plain,
( ~ eq(f(u),a1)
| ~ eq(f(v),a2) ),
inference(mrr,[status(thm)],[2831,2896]),
[iquote('0:MRR:2831.2,2896.2')] ).
cnf(2934,plain,
( ~ eq(f(u),a1)
| eq(f(s(u)),a3) ),
inference(mrr,[status(thm)],[2796,2904]),
[iquote('0:MRR:2796.2,2904.1')] ).
cnf(2935,plain,
( ~ eq(f(u),a1)
| eq(f(max(s(u),v)),a3) ),
inference(mrr,[status(thm)],[2812,2904]),
[iquote('0:MRR:2812.2,2904.1')] ).
cnf(2968,plain,
( ~ eq(f(u),a1)
| ~ eq(f(v),a3) ),
inference(res,[status(thm),theory(equality)],[2935,24]),
[iquote('0:Res:2935.1,24.0')] ).
cnf(2984,plain,
~ eq(f(u),a1),
inference(mrr,[status(thm)],[2934,2968]),
[iquote('0:MRR:2934.1,2968.1')] ).
cnf(3015,plain,
( eq(f(u),a3)
| eq(f(u),a2) ),
inference(mrr,[status(thm)],[2795,2984]),
[iquote('0:MRR:2795.2,2984.0')] ).
cnf(3016,plain,
( ~ eq(f(u),a2)
| eq(f(s(u)),a3) ),
inference(res,[status(thm),theory(equality)],[3015,42]),
[iquote('0:Res:3015.1,42.0')] ).
cnf(3017,plain,
( ~ eq(f(u),a2)
| eq(f(max(v,s(u))),a3) ),
inference(res,[status(thm),theory(equality)],[3015,43]),
[iquote('0:Res:3015.1,43.0')] ).
cnf(3050,plain,
( ~ eq(f(u),a2)
| ~ eq(f(v),a3) ),
inference(res,[status(thm),theory(equality)],[3017,27]),
[iquote('0:Res:3017.1,27.0')] ).
cnf(3065,plain,
~ eq(f(u),a2),
inference(mrr,[status(thm)],[3016,3050]),
[iquote('0:MRR:3016.1,3050.1')] ).
cnf(3096,plain,
eq(f(u),a3),
inference(mrr,[status(thm)],[3015,3065]),
[iquote('0:MRR:3015.1,3065.0')] ).
cnf(3098,plain,
$false,
inference(mrr,[status(thm)],[24,3096]),
[iquote('0:MRR:24.0,24.1,3096.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO620-1 : TPTP v8.1.0. Released v7.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n018.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 : Sat Jul 9 05:49:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.17/1.34
% 1.17/1.34 SPASS V 3.9
% 1.17/1.34 SPASS beiseite: Proof found.
% 1.17/1.34 % SZS status Theorem
% 1.17/1.34 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.17/1.34 SPASS derived 3408 clauses, backtracked 0 clauses, performed 0 splits and kept 2556 clauses.
% 1.17/1.34 SPASS allocated 68147 KBytes.
% 1.17/1.34 SPASS spent 0:00:00.97 on the problem.
% 1.17/1.34 0:00:00.04 for the input.
% 1.17/1.34 0:00:00.00 for the FLOTTER CNF translation.
% 1.17/1.34 0:00:00.06 for inferences.
% 1.17/1.34 0:00:00.00 for the backtracking.
% 1.17/1.34 0:00:00.78 for the reduction.
% 1.17/1.34
% 1.17/1.34
% 1.17/1.34 Here is a proof with depth 6, length 80 :
% 1.17/1.34 % SZS output start Refutation
% See solution above
% 1.17/1.34 Formulae used in the proof : sos_01 sos_02 sos_03 sos_04 sos_05 sos_06 sos_07 sos_08
% 1.17/1.34
%------------------------------------------------------------------------------