TSTP Solution File: PRO003+2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : PRO003+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 17:53:42 EDT 2022
% Result : Theorem 32.05s 32.28s
% Output : Refutation 33.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 28
% Syntax : Number of clauses : 86 ( 22 unt; 9 nHn; 86 RR)
% Number of literals : 237 ( 0 equ; 146 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
atomic(tptp4),
file('PRO003+2.p',unknown),
[] ).
cnf(3,axiom,
atomic(tptp3),
file('PRO003+2.p',unknown),
[] ).
cnf(5,axiom,
atomic(tptp1),
file('PRO003+2.p',unknown),
[] ).
cnf(6,axiom,
occurrence_of(skc1,tptp0),
file('PRO003+2.p',unknown),
[] ).
cnf(10,axiom,
occurrence_of(skf32(u),tptp4),
file('PRO003+2.p',unknown),
[] ).
cnf(11,axiom,
occurrence_of(skf31(u),tptp3),
file('PRO003+2.p',unknown),
[] ).
cnf(15,axiom,
~ equal(tptp1,tptp3),
file('PRO003+2.p',unknown),
[] ).
cnf(18,axiom,
occurrence_of(skf33(u),tptp1),
file('PRO003+2.p',unknown),
[] ).
cnf(24,axiom,
( ~ occurrence_of(u,v)
| activity(v) ),
file('PRO003+2.p',unknown),
[] ).
cnf(25,axiom,
( ~ occurrence_of(u,v)
| activity_occurrence(u) ),
file('PRO003+2.p',unknown),
[] ).
cnf(27,axiom,
( ~ next_subocc(u,v,w)
| arboreal(u) ),
file('PRO003+2.p',unknown),
[] ).
cnf(30,axiom,
( ~ root_occ(u,v)
| subactivity_occurrence(u,v) ),
file('PRO003+2.p',unknown),
[] ).
cnf(31,axiom,
( ~ leaf_occ(u,v)
| subactivity_occurrence(u,v) ),
file('PRO003+2.p',unknown),
[] ).
cnf(32,axiom,
( ~ activity_occurrence(u)
| occurrence_of(u,skf23(u)) ),
file('PRO003+2.p',unknown),
[] ).
cnf(35,axiom,
( ~ occurrence_of(u,tptp0)
| root_occ(skf32(u),u) ),
file('PRO003+2.p',unknown),
[] ).
cnf(36,axiom,
( ~ occurrence_of(u,tptp0)
| leaf_occ(skf31(u),u) ),
file('PRO003+2.p',unknown),
[] ).
cnf(37,axiom,
( ~ next_subocc(u,v,w)
| min_precedes(u,v,w) ),
file('PRO003+2.p',unknown),
[] ).
cnf(44,axiom,
( ~ atomic(u)
| ~ occurrence_of(v,u)
| arboreal(v) ),
file('PRO003+2.p',unknown),
[] ).
cnf(56,axiom,
( ~ occurrence_of(u,tptp0)
| next_subocc(skf32(u),skf31(u),tptp0) ),
file('PRO003+2.p',unknown),
[] ).
cnf(58,axiom,
( ~ occurrence_of(u,v)
| ~ occurrence_of(u,w)
| equal(w,v) ),
file('PRO003+2.p',unknown),
[] ).
cnf(61,axiom,
( ~ min_precedes(u,v,w)
| occurrence_of(skf25(v,u,w),w) ),
file('PRO003+2.p',unknown),
[] ).
cnf(62,axiom,
( ~ min_precedes(u,v,w)
| subactivity_occurrence(u,skf25(v,u,x)) ),
file('PRO003+2.p',unknown),
[] ).
cnf(63,axiom,
( ~ min_precedes(u,v,w)
| subactivity_occurrence(v,skf25(v,x,y)) ),
file('PRO003+2.p',unknown),
[] ).
cnf(70,axiom,
( ~ root_occ(u,v)
| ~ occurrence_of(v,w)
| ~ min_precedes(x,u,w) ),
file('PRO003+2.p',unknown),
[] ).
cnf(71,axiom,
( ~ leaf_occ(u,v)
| ~ occurrence_of(v,w)
| ~ min_precedes(u,x,w) ),
file('PRO003+2.p',unknown),
[] ).
cnf(72,axiom,
( ~ root_occ(u,v)
| ~ occurrence_of(v,tptp0)
| next_subocc(u,skf33(u),tptp0) ),
file('PRO003+2.p',unknown),
[] ).
cnf(77,axiom,
( ~ next_subocc(u,v,w)
| ~ min_precedes(x,v,w)
| ~ min_precedes(u,x,w) ),
file('PRO003+2.p',unknown),
[] ).
cnf(83,axiom,
( ~ arboreal(u)
| ~ arboreal(v)
| ~ subactivity_occurrence(u,w)
| ~ occurrence_of(w,x)
| ~ subactivity_occurrence(v,w)
| equal(v,u)
| min_precedes(u,v,x)
| min_precedes(v,u,x) ),
file('PRO003+2.p',unknown),
[] ).
cnf(87,plain,
( ~ root_occ(u,skc1)
| ~ min_precedes(v,u,tptp0) ),
inference(res,[status(thm),theory(equality)],[6,70]),
[iquote('0:Res:6.0,70.0')] ).
cnf(96,plain,
root_occ(skf32(skc1),skc1),
inference(res,[status(thm),theory(equality)],[6,35]),
[iquote('0:Res:6.0,35.0')] ).
cnf(100,plain,
( ~ root_occ(u,skc1)
| next_subocc(u,skf33(u),tptp0) ),
inference(res,[status(thm),theory(equality)],[6,72]),
[iquote('0:Res:6.0,72.1')] ).
cnf(112,plain,
activity(tptp1),
inference(res,[status(thm),theory(equality)],[18,24]),
[iquote('0:Res:18.0,24.0')] ).
cnf(113,plain,
activity(tptp3),
inference(res,[status(thm),theory(equality)],[11,24]),
[iquote('0:Res:11.0,24.0')] ).
cnf(114,plain,
activity(tptp4),
inference(res,[status(thm),theory(equality)],[10,24]),
[iquote('0:Res:10.0,24.0')] ).
cnf(119,plain,
activity_occurrence(skf33(u)),
inference(res,[status(thm),theory(equality)],[18,25]),
[iquote('0:Res:18.0,25.0')] ).
cnf(120,plain,
activity_occurrence(skf31(u)),
inference(res,[status(thm),theory(equality)],[11,25]),
[iquote('0:Res:11.0,25.0')] ).
cnf(121,plain,
activity_occurrence(skf32(u)),
inference(res,[status(thm),theory(equality)],[10,25]),
[iquote('0:Res:10.0,25.0')] ).
cnf(145,plain,
( ~ atomic(tptp1)
| arboreal(skf33(u)) ),
inference(res,[status(thm),theory(equality)],[18,44]),
[iquote('0:Res:18.0,44.1')] ).
cnf(146,plain,
( ~ atomic(tptp3)
| arboreal(skf31(u)) ),
inference(res,[status(thm),theory(equality)],[11,44]),
[iquote('0:Res:11.0,44.1')] ).
cnf(147,plain,
( ~ atomic(tptp4)
| arboreal(skf32(u)) ),
inference(res,[status(thm),theory(equality)],[10,44]),
[iquote('0:Res:10.0,44.1')] ).
cnf(149,plain,
arboreal(skf33(u)),
inference(ssi,[status(thm)],[145,5,112]),
[iquote('0:SSi:145.0,5.0,112.0')] ).
cnf(150,plain,
arboreal(skf31(u)),
inference(ssi,[status(thm)],[146,3,113]),
[iquote('0:SSi:146.0,3.0,113.0')] ).
cnf(151,plain,
arboreal(skf32(u)),
inference(ssi,[status(thm)],[147,2,114]),
[iquote('0:SSi:147.0,2.0,114.0')] ).
cnf(152,plain,
( ~ root_occ(u,skc1)
| arboreal(u) ),
inference(res,[status(thm),theory(equality)],[100,27]),
[iquote('0:Res:100.1,27.0')] ).
cnf(216,plain,
( ~ root_occ(u,skc1)
| min_precedes(u,skf33(u),tptp0) ),
inference(res,[status(thm),theory(equality)],[100,37]),
[iquote('0:Res:100.1,37.0')] ).
cnf(332,plain,
( ~ occurrence_of(skf33(u),v)
| equal(v,tptp1) ),
inference(res,[status(thm),theory(equality)],[18,58]),
[iquote('0:Res:18.0,58.0')] ).
cnf(333,plain,
( ~ occurrence_of(skf31(u),v)
| equal(v,tptp3) ),
inference(res,[status(thm),theory(equality)],[11,58]),
[iquote('0:Res:11.0,58.0')] ).
cnf(343,plain,
( ~ activity_occurrence(skf33(u))
| equal(skf23(skf33(u)),tptp1) ),
inference(res,[status(thm),theory(equality)],[32,332]),
[iquote('0:Res:32.1,332.0')] ).
cnf(347,plain,
equal(skf23(skf33(u)),tptp1),
inference(ssi,[status(thm)],[343,119,149]),
[iquote('0:SSi:343.0,119.0,149.0')] ).
cnf(353,plain,
( ~ activity_occurrence(skf31(u))
| equal(skf23(skf31(u)),tptp3) ),
inference(res,[status(thm),theory(equality)],[32,333]),
[iquote('0:Res:32.1,333.0')] ).
cnf(357,plain,
equal(skf23(skf31(u)),tptp3),
inference(ssi,[status(thm)],[353,120,150]),
[iquote('0:SSi:353.0,120.0,150.0')] ).
cnf(514,plain,
( ~ root_occ(u,skc1)
| subactivity_occurrence(u,skf25(skf33(u),u,v)) ),
inference(res,[status(thm),theory(equality)],[216,62]),
[iquote('0:Res:216.1,62.0')] ).
cnf(527,plain,
( ~ root_occ(u,skc1)
| subactivity_occurrence(skf33(u),skf25(skf33(u),v,w)) ),
inference(res,[status(thm),theory(equality)],[216,63]),
[iquote('0:Res:216.1,63.0')] ).
cnf(558,plain,
( ~ occurrence_of(u,tptp0)
| ~ occurrence_of(u,tptp0)
| next_subocc(skf32(u),skf33(skf32(u)),tptp0) ),
inference(res,[status(thm),theory(equality)],[35,72]),
[iquote('0:Res:35.1,72.0')] ).
cnf(560,plain,
( ~ occurrence_of(u,tptp0)
| next_subocc(skf32(u),skf33(skf32(u)),tptp0) ),
inference(obv,[status(thm),theory(equality)],[558]),
[iquote('0:Obv:558.0')] ).
cnf(782,plain,
( ~ occurrence_of(u,tptp0)
| ~ min_precedes(v,skf31(u),tptp0)
| ~ min_precedes(skf32(u),v,tptp0) ),
inference(res,[status(thm),theory(equality)],[56,77]),
[iquote('0:Res:56.1,77.0')] ).
cnf(889,plain,
( ~ arboreal(u)
| ~ arboreal(v)
| ~ root_occ(u,w)
| ~ occurrence_of(w,x)
| ~ subactivity_occurrence(v,w)
| equal(v,u)
| min_precedes(u,v,x)
| min_precedes(v,u,x) ),
inference(res,[status(thm),theory(equality)],[30,83]),
[iquote('0:Res:30.1,83.2')] ).
cnf(890,plain,
( ~ arboreal(u)
| ~ arboreal(v)
| ~ leaf_occ(u,w)
| ~ occurrence_of(w,x)
| ~ subactivity_occurrence(v,w)
| equal(v,u)
| min_precedes(u,v,x)
| min_precedes(v,u,x) ),
inference(res,[status(thm),theory(equality)],[31,83]),
[iquote('0:Res:31.1,83.2')] ).
cnf(895,plain,
( ~ arboreal(u)
| ~ arboreal(v)
| ~ leaf_occ(u,w)
| ~ occurrence_of(w,x)
| ~ subactivity_occurrence(v,w)
| equal(v,u)
| min_precedes(v,u,x) ),
inference(mrr,[status(thm)],[890,71]),
[iquote('0:MRR:890.6,71.2')] ).
cnf(896,plain,
( ~ arboreal(u)
| ~ arboreal(v)
| ~ root_occ(u,w)
| ~ occurrence_of(w,x)
| ~ subactivity_occurrence(v,w)
| equal(v,u)
| min_precedes(u,v,x) ),
inference(mrr,[status(thm)],[889,70]),
[iquote('0:MRR:889.7,70.2')] ).
cnf(902,plain,
( ~ occurrence_of(u,tptp0)
| min_precedes(skf32(u),skf33(skf32(u)),tptp0) ),
inference(res,[status(thm),theory(equality)],[560,37]),
[iquote('0:Res:560.1,37.0')] ).
cnf(2482,plain,
( ~ arboreal(skf31(u))
| ~ arboreal(v)
| ~ occurrence_of(u,tptp0)
| ~ occurrence_of(u,w)
| ~ subactivity_occurrence(v,u)
| equal(v,skf31(u))
| min_precedes(v,skf31(u),w) ),
inference(res,[status(thm),theory(equality)],[36,895]),
[iquote('0:Res:36.1,895.2')] ).
cnf(2486,plain,
( ~ arboreal(u)
| ~ occurrence_of(v,tptp0)
| ~ occurrence_of(v,w)
| ~ subactivity_occurrence(u,v)
| equal(u,skf31(v))
| min_precedes(u,skf31(v),w) ),
inference(ssi,[status(thm)],[2482,120,150]),
[iquote('0:SSi:2482.0,120.0,150.0')] ).
cnf(2510,plain,
( ~ arboreal(skf32(u))
| ~ arboreal(v)
| ~ occurrence_of(u,tptp0)
| ~ occurrence_of(u,w)
| ~ subactivity_occurrence(v,u)
| equal(v,skf32(u))
| min_precedes(skf32(u),v,w) ),
inference(res,[status(thm),theory(equality)],[35,896]),
[iquote('0:Res:35.1,896.2')] ).
cnf(2512,plain,
( ~ arboreal(u)
| ~ occurrence_of(v,tptp0)
| ~ occurrence_of(v,w)
| ~ subactivity_occurrence(u,v)
| equal(u,skf32(v))
| min_precedes(skf32(v),u,w) ),
inference(ssi,[status(thm)],[2510,121,151]),
[iquote('0:SSi:2510.0,121.0,151.0')] ).
cnf(5185,plain,
( ~ arboreal(u)
| ~ occurrence_of(v,tptp0)
| ~ occurrence_of(v,tptp0)
| ~ subactivity_occurrence(u,v)
| ~ occurrence_of(v,tptp0)
| ~ min_precedes(skf32(v),u,tptp0)
| equal(u,skf31(v)) ),
inference(res,[status(thm),theory(equality)],[2486,782]),
[iquote('0:Res:2486.5,782.1')] ).
cnf(5199,plain,
( ~ arboreal(u)
| ~ subactivity_occurrence(u,v)
| ~ occurrence_of(v,tptp0)
| ~ min_precedes(skf32(v),u,tptp0)
| equal(u,skf31(v)) ),
inference(obv,[status(thm),theory(equality)],[5185]),
[iquote('0:Obv:5185.2')] ).
cnf(5289,plain,
( ~ arboreal(u)
| ~ occurrence_of(v,tptp0)
| ~ occurrence_of(v,tptp0)
| ~ subactivity_occurrence(u,v)
| ~ root_occ(u,skc1)
| equal(u,skf32(v)) ),
inference(res,[status(thm),theory(equality)],[2512,87]),
[iquote('0:Res:2512.5,87.1')] ).
cnf(5319,plain,
( ~ arboreal(u)
| ~ occurrence_of(v,tptp0)
| ~ subactivity_occurrence(u,v)
| ~ root_occ(u,skc1)
| equal(u,skf32(v)) ),
inference(obv,[status(thm),theory(equality)],[5289]),
[iquote('0:Obv:5289.1')] ).
cnf(5320,plain,
( ~ occurrence_of(u,tptp0)
| ~ subactivity_occurrence(v,u)
| ~ root_occ(v,skc1)
| equal(v,skf32(u)) ),
inference(mrr,[status(thm)],[5319,152]),
[iquote('0:MRR:5319.0,152.1')] ).
cnf(5459,plain,
( ~ root_occ(u,skc1)
| ~ occurrence_of(skf25(skf33(u),u,v),tptp0)
| ~ root_occ(u,skc1)
| equal(skf32(skf25(skf33(u),u,v)),u) ),
inference(res,[status(thm),theory(equality)],[514,5320]),
[iquote('0:Res:514.1,5320.1')] ).
cnf(5470,plain,
( ~ occurrence_of(skf25(skf33(u),u,v),tptp0)
| ~ root_occ(u,skc1)
| equal(skf32(skf25(skf33(u),u,v)),u) ),
inference(obv,[status(thm),theory(equality)],[5459]),
[iquote('0:Obv:5459.0')] ).
cnf(16001,plain,
( ~ arboreal(skf33(skf32(u)))
| ~ occurrence_of(u,tptp0)
| ~ subactivity_occurrence(skf33(skf32(u)),u)
| ~ occurrence_of(u,tptp0)
| equal(skf33(skf32(u)),skf31(u)) ),
inference(res,[status(thm),theory(equality)],[902,5199]),
[iquote('0:Res:902.1,5199.3')] ).
cnf(16018,plain,
( ~ arboreal(skf33(skf32(u)))
| ~ subactivity_occurrence(skf33(skf32(u)),u)
| ~ occurrence_of(u,tptp0)
| equal(skf33(skf32(u)),skf31(u)) ),
inference(obv,[status(thm),theory(equality)],[16001]),
[iquote('0:Obv:16001.1')] ).
cnf(16019,plain,
( ~ subactivity_occurrence(skf33(skf32(u)),u)
| ~ occurrence_of(u,tptp0)
| equal(skf33(skf32(u)),skf31(u)) ),
inference(ssi,[status(thm)],[16018,119,121,151,149]),
[iquote('0:SSi:16018.0,119.0,121.0,151.0,149.0,121.0,151.0')] ).
cnf(35228,plain,
( ~ min_precedes(u,skf33(u),tptp0)
| ~ root_occ(u,skc1)
| equal(skf32(skf25(skf33(u),u,tptp0)),u) ),
inference(res,[status(thm),theory(equality)],[61,5470]),
[iquote('0:Res:61.1,5470.0')] ).
cnf(35229,plain,
( ~ root_occ(u,skc1)
| equal(skf32(skf25(skf33(u),u,tptp0)),u) ),
inference(mrr,[status(thm)],[35228,216]),
[iquote('0:MRR:35228.0,216.1')] ).
cnf(35349,plain,
( ~ root_occ(u,skc1)
| ~ subactivity_occurrence(skf33(u),skf25(skf33(u),u,tptp0))
| ~ occurrence_of(skf25(skf33(u),u,tptp0),tptp0)
| equal(skf33(skf32(skf25(skf33(u),u,tptp0))),skf31(skf25(skf33(u),u,tptp0))) ),
inference(spl,[status(thm),theory(equality)],[35229,16019]),
[iquote('0:SpL:35229.1,16019.0')] ).
cnf(35558,plain,
( ~ root_occ(u,skc1)
| ~ subactivity_occurrence(skf33(u),skf25(skf33(u),u,tptp0))
| ~ occurrence_of(skf25(skf33(u),u,tptp0),tptp0)
| equal(skf31(skf25(skf33(u),u,tptp0)),skf33(u)) ),
inference(rew,[status(thm),theory(equality)],[35229,35349]),
[iquote('0:Rew:35229.1,35349.3')] ).
cnf(35559,plain,
( ~ root_occ(u,skc1)
| ~ occurrence_of(skf25(skf33(u),u,tptp0),tptp0)
| equal(skf31(skf25(skf33(u),u,tptp0)),skf33(u)) ),
inference(mrr,[status(thm)],[35558,527]),
[iquote('0:MRR:35558.1,527.1')] ).
cnf(41446,plain,
( ~ min_precedes(u,skf33(u),tptp0)
| ~ root_occ(u,skc1)
| equal(skf31(skf25(skf33(u),u,tptp0)),skf33(u)) ),
inference(res,[status(thm),theory(equality)],[61,35559]),
[iquote('0:Res:61.1,35559.1')] ).
cnf(41447,plain,
( ~ root_occ(u,skc1)
| equal(skf31(skf25(skf33(u),u,tptp0)),skf33(u)) ),
inference(mrr,[status(thm)],[41446,216]),
[iquote('0:MRR:41446.0,216.1')] ).
cnf(41484,plain,
( ~ root_occ(u,skc1)
| equal(skf23(skf33(u)),tptp3) ),
inference(spr,[status(thm),theory(equality)],[41447,357]),
[iquote('0:SpR:41447.1,357.0')] ).
cnf(41606,plain,
( ~ root_occ(u,skc1)
| equal(tptp1,tptp3) ),
inference(rew,[status(thm),theory(equality)],[347,41484]),
[iquote('0:Rew:347.0,41484.1')] ).
cnf(41607,plain,
~ root_occ(u,skc1),
inference(mrr,[status(thm)],[41606,15]),
[iquote('0:MRR:41606.1,15.0')] ).
cnf(41608,plain,
$false,
inference(unc,[status(thm)],[41607,96]),
[iquote('0:UnC:41607.0,96.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PRO003+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n027.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 : Mon Jun 13 03:36:31 EDT 2022
% 0.12/0.34 % CPUTime :
% 32.05/32.28
% 32.05/32.28 SPASS V 3.9
% 32.05/32.28 SPASS beiseite: Proof found.
% 32.05/32.28 % SZS status Theorem
% 32.05/32.28 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.05/32.28 SPASS derived 33283 clauses, backtracked 3342 clauses, performed 48 splits and kept 14192 clauses.
% 32.05/32.28 SPASS allocated 138742 KBytes.
% 32.05/32.28 SPASS spent 0:0:31.89 on the problem.
% 32.05/32.28 0:00:00.03 for the input.
% 32.05/32.28 0:00:00.08 for the FLOTTER CNF translation.
% 32.05/32.28 0:00:00.76 for inferences.
% 32.05/32.28 0:00:01.11 for the backtracking.
% 32.05/32.28 0:0:29.46 for the reduction.
% 32.05/32.28
% 32.05/32.28
% 32.05/32.28 Here is a proof with depth 8, length 86 :
% 32.05/32.28 % SZS output start Refutation
% See solution above
% 33.11/33.33 Formulae used in the proof : sos_35 sos_36 sos_38 goals sos_32 sos_42 sos_45 sos_29 sos_05 sos_10 sos_11 sos_18 sos_04 sos_13 sos_22 sos_24 sos_20 sos_21 sos_28
% 33.11/33.33
%------------------------------------------------------------------------------