TSTP Solution File: COL092-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL092-1 : TPTP v8.1.0. Released v2.7.0.
% 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 : Fri Jul 15 00:42:37 EDT 2022
% Result : Unsatisfiable 0.55s 0.75s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of clauses : 48 ( 16 unt; 7 nHn; 48 RR)
% Number of literals : 93 ( 0 equ; 45 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ equal(comb_app(u,v),combK),
file('COL092-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ member(comb_app(u,v),comb)
| member(v,comb) ),
file('COL092-1.p',unknown),
[] ).
cnf(32,axiom,
( ~ member(u,comb)
| member(pair(u,u),parcontract) ),
file('COL092-1.p',unknown),
[] ).
cnf(37,axiom,
( ~ member(pair(combK,u),parcontract)
| equal(u,combK) ),
file('COL092-1.p',unknown),
[] ).
cnf(40,axiom,
( ~ member(pair(comb_app(u,v),w),parcontract)
| ap_parcontractE_c4(u,v,w)
| ap_parcontractE_c3(u,v,w)
| ap_parcontractE_c2(u,v,w)
| ap_parcontractE_c1(u,v,w) ),
file('COL092-1.p',unknown),
[] ).
cnf(41,axiom,
( ~ ap_parcontractE_c1(u,v,w)
| member(comb_app(u,v),comb) ),
file('COL092-1.p',unknown),
[] ).
cnf(42,axiom,
( ~ ap_parcontractE_c1(u,v,w)
| equal(w,comb_app(u,v)) ),
file('COL092-1.p',unknown),
[] ).
cnf(45,axiom,
( ~ ap_parcontractE_c2(u,v,w)
| equal(u,comb_app(combK,w)) ),
file('COL092-1.p',unknown),
[] ).
cnf(49,axiom,
( ~ ap_parcontractE_c3(u,v,w)
| equal(comb_app(comb_app(ap_parcontractE_sk1p(u,v,w),v),comb_app(ap_parcontractE_sk1q(u,v,w),v)),w) ),
file('COL092-1.p',unknown),
[] ).
cnf(50,axiom,
( ~ ap_parcontractE_c3(u,v,w)
| equal(comb_app(comb_app(combS,ap_parcontractE_sk1p(u,v,w)),ap_parcontractE_sk1q(u,v,w)),u) ),
file('COL092-1.p',unknown),
[] ).
cnf(51,axiom,
( ~ ap_parcontractE_c4(u,v,w)
| member(pair(u,ap_parcontractE_sk2q(u,v,w)),parcontract) ),
file('COL092-1.p',unknown),
[] ).
cnf(52,axiom,
( ~ ap_parcontractE_c4(u,v,w)
| member(pair(v,ap_parcontractE_sk2s(u,v,w)),parcontract) ),
file('COL092-1.p',unknown),
[] ).
cnf(53,axiom,
( ~ ap_parcontractE_c4(u,v,w)
| equal(comb_app(ap_parcontractE_sk2q(u,v,w),ap_parcontractE_sk2s(u,v,w)),w) ),
file('COL092-1.p',unknown),
[] ).
cnf(54,axiom,
member(pair(comb_app(combK,p),r),parcontract),
file('COL092-1.p',unknown),
[] ).
cnf(55,axiom,
( ~ member(pair(p,u),parcontract)
| ~ equal(comb_app(combK,u),r) ),
file('COL092-1.p',unknown),
[] ).
cnf(60,plain,
( ~ member(p,comb)
| ~ equal(comb_app(combK,p),r) ),
inference(res,[status(thm),theory(equality)],[32,55]),
[iquote('0:Res:32.1,55.0')] ).
cnf(65,plain,
( ~ ap_parcontractE_c4(u,p,v)
| ~ equal(comb_app(combK,ap_parcontractE_sk2s(u,p,v)),r) ),
inference(res,[status(thm),theory(equality)],[52,55]),
[iquote('0:Res:52.1,55.0')] ).
cnf(73,plain,
( ~ ap_parcontractE_c4(combK,u,v)
| equal(ap_parcontractE_sk2q(combK,u,v),combK) ),
inference(res,[status(thm),theory(equality)],[51,37]),
[iquote('0:Res:51.1,37.0')] ).
cnf(187,plain,
( ~ ap_parcontractE_c4(combK,u,v)
| ~ ap_parcontractE_c4(combK,u,v)
| equal(comb_app(combK,ap_parcontractE_sk2s(combK,u,v)),v) ),
inference(spr,[status(thm),theory(equality)],[73,53]),
[iquote('0:SpR:73.1,53.1')] ).
cnf(189,plain,
( ~ ap_parcontractE_c4(u,v,w)
| ~ equal(w,combK) ),
inference(spl,[status(thm),theory(equality)],[53,2]),
[iquote('0:SpL:53.1,2.0')] ).
cnf(200,plain,
( ~ ap_parcontractE_c4(combK,u,v)
| equal(comb_app(combK,ap_parcontractE_sk2s(combK,u,v)),v) ),
inference(obv,[status(thm),theory(equality)],[187]),
[iquote('0:Obv:187.0')] ).
cnf(290,plain,
( ~ ap_parcontractE_c3(u,v,w)
| ~ equal(u,combK) ),
inference(spl,[status(thm),theory(equality)],[50,2]),
[iquote('0:SpL:50.1,2.0')] ).
cnf(315,plain,
( ~ ap_parcontractE_c4(combK,p,u)
| ~ ap_parcontractE_c4(combK,p,u)
| ~ equal(u,r) ),
inference(spl,[status(thm),theory(equality)],[200,65]),
[iquote('0:SpL:200.1,65.1')] ).
cnf(319,plain,
( ~ ap_parcontractE_c4(combK,p,u)
| ~ equal(u,r) ),
inference(obv,[status(thm),theory(equality)],[315]),
[iquote('0:Obv:315.0')] ).
cnf(378,plain,
( ~ ap_parcontractE_c3(u,v,w)
| ~ equal(w,combK) ),
inference(spl,[status(thm),theory(equality)],[49,2]),
[iquote('0:SpL:49.1,2.0')] ).
cnf(487,plain,
( ap_parcontractE_c4(combK,p,r)
| ap_parcontractE_c3(combK,p,r)
| ap_parcontractE_c2(combK,p,r)
| ap_parcontractE_c1(combK,p,r) ),
inference(res,[status(thm),theory(equality)],[54,40]),
[iquote('0:Res:54.0,40.0')] ).
cnf(1112,plain,
( ~ equal(r,combK)
| ap_parcontractE_c3(combK,p,r)
| ap_parcontractE_c2(combK,p,r)
| ap_parcontractE_c1(combK,p,r) ),
inference(res,[status(thm),theory(equality)],[487,189]),
[iquote('0:Res:487.0,189.0')] ).
cnf(1117,plain,
( ~ equal(r,r)
| ap_parcontractE_c3(combK,p,r)
| ap_parcontractE_c2(combK,p,r)
| ap_parcontractE_c1(combK,p,r) ),
inference(res,[status(thm),theory(equality)],[487,319]),
[iquote('0:Res:487.0,319.0')] ).
cnf(1118,plain,
( ~ equal(r,combK)
| ap_parcontractE_c2(combK,p,r)
| ap_parcontractE_c1(combK,p,r) ),
inference(mrr,[status(thm)],[1112,378]),
[iquote('0:MRR:1112.1,378.0')] ).
cnf(1120,plain,
( ap_parcontractE_c3(combK,p,r)
| ap_parcontractE_c2(combK,p,r)
| ap_parcontractE_c1(combK,p,r) ),
inference(obv,[status(thm),theory(equality)],[1117]),
[iquote('0:Obv:1117.0')] ).
cnf(1121,plain,
ap_parcontractE_c2(combK,p,r),
inference(spt,[spt(split,[position(s1)])],[1118]),
[iquote('1:Spt:1118.1')] ).
cnf(1122,plain,
equal(comb_app(combK,r),combK),
inference(res,[status(thm),theory(equality)],[1121,45]),
[iquote('1:Res:1121.0,45.0')] ).
cnf(1127,plain,
$false,
inference(mrr,[status(thm)],[1122,2]),
[iquote('1:MRR:1122.0,2.0')] ).
cnf(1128,plain,
~ ap_parcontractE_c2(combK,p,r),
inference(spt,[spt(split,[position(sa)])],[1127,1121]),
[iquote('1:Spt:1127.0,1118.1,1121.0')] ).
cnf(1129,plain,
( ~ equal(r,combK)
| ap_parcontractE_c1(combK,p,r) ),
inference(spt,[spt(split,[position(s2)])],[1118]),
[iquote('1:Spt:1127.0,1118.0,1118.2')] ).
cnf(1131,plain,
( ap_parcontractE_c3(combK,p,r)
| ap_parcontractE_c1(combK,p,r) ),
inference(mrr,[status(thm)],[1120,1128]),
[iquote('1:MRR:1120.1,1128.0')] ).
cnf(1138,plain,
ap_parcontractE_c1(combK,p,r),
inference(spt,[spt(split,[position(s2s1)])],[1131]),
[iquote('2:Spt:1131.1')] ).
cnf(1139,plain,
equal(comb_app(combK,p),r),
inference(res,[status(thm),theory(equality)],[1138,42]),
[iquote('2:Res:1138.0,42.0')] ).
cnf(1140,plain,
member(comb_app(combK,p),comb),
inference(res,[status(thm),theory(equality)],[1138,41]),
[iquote('2:Res:1138.0,41.0')] ).
cnf(1142,plain,
( ~ member(p,comb)
| ~ equal(r,r) ),
inference(rew,[status(thm),theory(equality)],[1139,60]),
[iquote('2:Rew:1139.0,60.1')] ).
cnf(1143,plain,
member(r,comb),
inference(rew,[status(thm),theory(equality)],[1139,1140]),
[iquote('2:Rew:1139.0,1140.0')] ).
cnf(1144,plain,
~ member(p,comb),
inference(obv,[status(thm),theory(equality)],[1142]),
[iquote('2:Obv:1142.1')] ).
cnf(1175,plain,
( ~ member(r,comb)
| member(p,comb) ),
inference(spl,[status(thm),theory(equality)],[1139,8]),
[iquote('2:SpL:1139.0,8.0')] ).
cnf(1206,plain,
$false,
inference(mrr,[status(thm)],[1175,1143,1144]),
[iquote('2:MRR:1175.0,1175.1,1143.0,1144.0')] ).
cnf(1218,plain,
~ ap_parcontractE_c1(combK,p,r),
inference(spt,[spt(split,[position(s2sa)])],[1206,1138]),
[iquote('2:Spt:1206.0,1131.1,1138.0')] ).
cnf(1219,plain,
ap_parcontractE_c3(combK,p,r),
inference(spt,[spt(split,[position(s2s2)])],[1131]),
[iquote('2:Spt:1206.0,1131.0')] ).
cnf(1236,plain,
~ equal(combK,combK),
inference(res,[status(thm),theory(equality)],[1219,290]),
[iquote('2:Res:1219.0,290.0')] ).
cnf(1241,plain,
$false,
inference(obv,[status(thm),theory(equality)],[1236]),
[iquote('2:Obv:1236.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COL092-1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue May 31 16:08:13 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.55/0.75
% 0.55/0.75 SPASS V 3.9
% 0.55/0.75 SPASS beiseite: Proof found.
% 0.55/0.75 % SZS status Theorem
% 0.55/0.75 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.55/0.75 SPASS derived 937 clauses, backtracked 18 clauses, performed 2 splits and kept 666 clauses.
% 0.55/0.75 SPASS allocated 64567 KBytes.
% 0.55/0.75 SPASS spent 0:00:00.38 on the problem.
% 0.55/0.75 0:00:00.04 for the input.
% 0.55/0.75 0:00:00.00 for the FLOTTER CNF translation.
% 0.55/0.75 0:00:00.03 for inferences.
% 0.55/0.75 0:00:00.00 for the backtracking.
% 0.55/0.75 0:00:00.28 for the reduction.
% 0.55/0.75
% 0.55/0.75
% 0.55/0.75 Here is a proof with depth 7, length 48 :
% 0.55/0.75 % SZS output start Refutation
% See solution above
% 0.55/0.75 Formulae used in the proof : k_app ap_E2 parcontract_intros1 k_parcontractE2 ap_parcontractE1 ap_parcontractE2 ap_parcontractE3 ap_parcontractE6 ap_parcontractE10 ap_parcontractE11 ap_parcontractE12 ap_parcontractE13 ap_parcontractE14 k1_parcontractD_h1 k1_parcontractD_c1
% 0.55/0.75
%------------------------------------------------------------------------------