TSTP Solution File: COL090-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL090-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 00:42:36 EDT 2022
% Result : Unsatisfiable 3.91s 4.08s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of clauses : 59 ( 22 unt; 8 nHn; 59 RR)
% Number of literals : 117 ( 0 equ; 60 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 : 16 ( 16 usr; 10 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(combS,combK),
file('COL090-1.p',unknown),
[] ).
cnf(2,axiom,
~ equal(comb_app(u,v),combK),
file('COL090-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(comb_app(u,v),combS),
file('COL090-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ equal(comb_app(u,v),comb_app(w,x))
| equal(u,w) ),
file('COL090-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ equal(comb_app(u,v),comb_app(w,x))
| equal(v,x) ),
file('COL090-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ equal(u,v)
| ~ equal(w,x)
| equal(comb_app(w,u),comb_app(x,v)) ),
file('COL090-1.p',unknown),
[] ).
cnf(15,axiom,
( ~ member(pair(comb_app(u,v),w),contract)
| ap_contractE_c4(u,v,w)
| ap_contractE_c3(u,v,w)
| ap_contractE_c2(u,v,w)
| ap_contractE_c1(u,v,w) ),
file('COL090-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ ap_contractE_c1(u,v,w)
| equal(u,comb_app(combK,w)) ),
file('COL090-1.p',unknown),
[] ).
cnf(22,axiom,
( ~ ap_contractE_c2(u,v,w)
| equal(comb_app(comb_app(ap_contractE_sk1p(u,v,w),v),comb_app(ap_contractE_sk1q(u,v,w),v)),w) ),
file('COL090-1.p',unknown),
[] ).
cnf(23,axiom,
( ~ ap_contractE_c2(u,v,w)
| equal(comb_app(comb_app(combS,ap_contractE_sk1p(u,v,w)),ap_contractE_sk1q(u,v,w)),u) ),
file('COL090-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ ap_contractE_c3(u,v,w)
| member(pair(u,ap_contractE_sk2q(u,v,w)),contract) ),
file('COL090-1.p',unknown),
[] ).
cnf(26,axiom,
( ~ ap_contractE_c3(u,v,w)
| equal(comb_app(ap_contractE_sk2q(u,v,w),v),w) ),
file('COL090-1.p',unknown),
[] ).
cnf(27,axiom,
( ~ ap_contractE_c4(u,v,w)
| member(pair(v,ap_contractE_sk3q(u,v,w)),contract) ),
file('COL090-1.p',unknown),
[] ).
cnf(30,axiom,
~ member(pair(combK,u),contract),
file('COL090-1.p',unknown),
[] ).
cnf(31,axiom,
~ member(pair(combS,u),contract),
file('COL090-1.p',unknown),
[] ).
cnf(32,axiom,
member(pair(comb_app(comb_app(combS,combK),combK),r),contract),
file('COL090-1.p',unknown),
[] ).
cnf(33,plain,
( ap_contractE_c4(comb_app(combS,combK),combK,r)
| ap_contractE_c3(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c1(comb_app(combS,combK),combK,r) ),
inference(res,[status(thm),theory(equality)],[32,15]),
[iquote('0:Res:32.0,15.0')] ).
cnf(39,plain,
~ ap_contractE_c4(u,combK,v),
inference(res,[status(thm),theory(equality)],[27,30]),
[iquote('0:Res:27.1,30.0')] ).
cnf(40,plain,
( ap_contractE_c3(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c1(comb_app(combS,combK),combK,r) ),
inference(mrr,[status(thm)],[33,39]),
[iquote('0:MRR:33.0,39.0')] ).
cnf(41,plain,
~ ap_contractE_c3(combS,u,v),
inference(res,[status(thm),theory(equality)],[24,31]),
[iquote('0:Res:24.1,31.0')] ).
cnf(49,plain,
( ~ ap_contractE_c3(u,v,w)
| ~ equal(w,comb_app(x,y))
| equal(ap_contractE_sk2q(u,v,w),x) ),
inference(spl,[status(thm),theory(equality)],[26,4]),
[iquote('0:SpL:26.1,4.0')] ).
cnf(163,plain,
( ~ ap_contractE_c2(u,v,w)
| ~ equal(u,combS) ),
inference(spl,[status(thm),theory(equality)],[23,3]),
[iquote('0:SpL:23.1,3.0')] ).
cnf(167,plain,
( ~ ap_contractE_c2(u,v,w)
| ~ equal(u,comb_app(x,y))
| equal(comb_app(combS,ap_contractE_sk1p(u,v,w)),x) ),
inference(spl,[status(thm),theory(equality)],[23,4]),
[iquote('0:SpL:23.1,4.0')] ).
cnf(195,plain,
( ~ ap_contractE_c2(u,v,w)
| ~ equal(w,comb_app(x,y))
| equal(comb_app(ap_contractE_sk1q(u,v,w),v),y) ),
inference(spl,[status(thm),theory(equality)],[22,5]),
[iquote('0:SpL:22.1,5.0')] ).
cnf(449,plain,
( ~ ap_contractE_c3(u,v,comb_app(w,x))
| equal(ap_contractE_sk2q(u,v,comb_app(w,x)),w) ),
inference(eqr,[status(thm),theory(equality)],[49]),
[iquote('0:EqR:49.1')] ).
cnf(458,plain,
( ~ ap_contractE_c3(u,v,comb_app(w,x))
| ~ ap_contractE_c3(u,v,comb_app(w,x))
| member(pair(u,w),contract) ),
inference(spr,[status(thm),theory(equality)],[449,24]),
[iquote('0:SpR:449.1,24.1')] ).
cnf(471,plain,
( ~ ap_contractE_c3(u,v,comb_app(w,x))
| member(pair(u,w),contract) ),
inference(obv,[status(thm),theory(equality)],[458]),
[iquote('0:Obv:458.0')] ).
cnf(481,plain,
( ~ ap_contractE_c3(u,v,w)
| ~ ap_contractE_c3(x,y,w)
| member(pair(x,ap_contractE_sk2q(u,v,w)),contract) ),
inference(spl,[status(thm),theory(equality)],[26,471]),
[iquote('0:SpL:26.1,471.0')] ).
cnf(630,plain,
( ~ ap_contractE_c2(comb_app(u,v),w,x)
| equal(comb_app(combS,ap_contractE_sk1p(comb_app(u,v),w,x)),u) ),
inference(eqr,[status(thm),theory(equality)],[167]),
[iquote('0:EqR:167.1')] ).
cnf(819,plain,
( ~ ap_contractE_c2(u,v,comb_app(w,x))
| equal(comb_app(ap_contractE_sk1q(u,v,comb_app(w,x)),v),x) ),
inference(eqr,[status(thm),theory(equality)],[195]),
[iquote('0:EqR:195.1')] ).
cnf(1010,plain,
( ~ ap_contractE_c2(comb_app(u,v),w,x)
| ~ equal(u,combS) ),
inference(spl,[status(thm),theory(equality)],[630,3]),
[iquote('0:SpL:630.1,3.0')] ).
cnf(1091,plain,
( ~ equal(u,v)
| ~ equal(w,x)
| ~ ap_contractE_c2(comb_app(w,u),y,z)
| ~ equal(x,combS) ),
inference(spl,[status(thm),theory(equality)],[6,1010]),
[iquote('0:SpL:6.2,1010.0')] ).
cnf(1098,plain,
( ~ equal(u,v)
| ~ ap_contractE_c2(comb_app(u,w),x,y)
| ~ equal(v,combS) ),
inference(aed,[status(thm),theory(equality)],[1,1091]),
[iquote('0:AED:1.0,1091.0')] ).
cnf(2365,plain,
( ~ ap_contractE_c2(u,v,comb_app(w,x))
| ~ equal(x,combK) ),
inference(spl,[status(thm),theory(equality)],[819,2]),
[iquote('0:SpL:819.1,2.0')] ).
cnf(2509,plain,
( ~ ap_contractE_c3(u,v,w)
| ~ ap_contractE_c2(x,y,w)
| ~ equal(v,combK) ),
inference(spl,[status(thm),theory(equality)],[26,2365]),
[iquote('0:SpL:26.1,2365.0')] ).
cnf(2597,plain,
( ~ ap_contractE_c2(u,v,r)
| ~ equal(combK,combK)
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c1(comb_app(combS,combK),combK,r) ),
inference(res,[status(thm),theory(equality)],[40,2509]),
[iquote('0:Res:40.0,2509.0')] ).
cnf(2598,plain,
( ~ ap_contractE_c2(u,v,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c1(comb_app(combS,combK),combK,r) ),
inference(obv,[status(thm),theory(equality)],[2597]),
[iquote('0:Obv:2597.1')] ).
cnf(2979,plain,
ap_contractE_c1(comb_app(combS,combK),combK,r),
inference(spt,[spt(split,[position(s1)])],[2598]),
[iquote('1:Spt:2598.2')] ).
cnf(2982,plain,
equal(comb_app(combS,combK),comb_app(combK,r)),
inference(res,[status(thm),theory(equality)],[2979,18]),
[iquote('1:Res:2979.0,18.0')] ).
cnf(3045,plain,
( ~ equal(comb_app(combK,r),comb_app(u,v))
| equal(combS,u) ),
inference(spl,[status(thm),theory(equality)],[2982,4]),
[iquote('1:SpL:2982.0,4.0')] ).
cnf(3270,plain,
equal(combS,combK),
inference(eqr,[status(thm),theory(equality)],[3045]),
[iquote('1:EqR:3045.0')] ).
cnf(3286,plain,
$false,
inference(mrr,[status(thm)],[3270,1]),
[iquote('1:MRR:3270.0,1.0')] ).
cnf(3290,plain,
~ ap_contractE_c1(comb_app(combS,combK),combK,r),
inference(spt,[spt(split,[position(sa)])],[3286,2979]),
[iquote('1:Spt:3286.0,2598.2,2979.0')] ).
cnf(3291,plain,
( ~ ap_contractE_c2(u,v,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r) ),
inference(spt,[spt(split,[position(s2)])],[2598]),
[iquote('1:Spt:3286.0,2598.0,2598.1')] ).
cnf(3292,plain,
( ap_contractE_c3(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r) ),
inference(mrr,[status(thm)],[40,3290]),
[iquote('1:MRR:40.2,3290.0')] ).
cnf(3310,plain,
ap_contractE_c2(comb_app(combS,combK),combK,r),
inference(spt,[spt(split,[position(s2s1)])],[3292]),
[iquote('2:Spt:3292.1')] ).
cnf(3342,plain,
( ~ equal(combS,u)
| ~ equal(u,combS) ),
inference(res,[status(thm),theory(equality)],[3310,1098]),
[iquote('2:Res:3310.0,1098.1')] ).
cnf(3346,plain,
~ equal(u,combS),
inference(obv,[status(thm),theory(equality)],[3342]),
[iquote('2:Obv:3342.0')] ).
cnf(3347,plain,
$false,
inference(aed,[status(thm),theory(equality)],[1,3346]),
[iquote('2:AED:1.0,3346.0')] ).
cnf(3350,plain,
~ ap_contractE_c2(comb_app(combS,combK),combK,r),
inference(spt,[spt(split,[position(s2sa)])],[3347,3310]),
[iquote('2:Spt:3347.0,3292.1,3310.0')] ).
cnf(3351,plain,
ap_contractE_c3(comb_app(combS,combK),combK,r),
inference(spt,[spt(split,[position(s2s2)])],[3292]),
[iquote('2:Spt:3347.0,3292.0')] ).
cnf(5078,plain,
( ~ ap_contractE_c3(u,v,r)
| member(pair(u,ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract) ),
inference(res,[status(thm),theory(equality)],[3351,481]),
[iquote('2:Res:3351.0,481.0')] ).
cnf(5080,plain,
member(pair(comb_app(combS,combK),ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract),
inference(res,[status(thm),theory(equality)],[3351,5078]),
[iquote('2:Res:3351.0,5078.0')] ).
cnf(5086,plain,
( ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(res,[status(thm),theory(equality)],[5080,15]),
[iquote('2:Res:5080.0,15.0')] ).
cnf(5088,plain,
( ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(mrr,[status(thm)],[5086,39,41]),
[iquote('2:MRR:5086.0,5086.1,39.0,41.0')] ).
cnf(5178,plain,
( ~ equal(combS,combS)
| ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(res,[status(thm),theory(equality)],[5088,163]),
[iquote('2:Res:5088.0,163.0')] ).
cnf(5180,plain,
ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)),
inference(obv,[status(thm),theory(equality)],[5178]),
[iquote('2:Obv:5178.0')] ).
cnf(5183,plain,
equal(comb_app(combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)),combS),
inference(res,[status(thm),theory(equality)],[5180,18]),
[iquote('2:Res:5180.0,18.0')] ).
cnf(5186,plain,
$false,
inference(mrr,[status(thm)],[5183,3]),
[iquote('2:MRR:5183.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : COL090-1 : TPTP v8.1.0. Released v2.7.0.
% 0.13/0.14 % Command : run_spass %d %s
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue May 31 08:49:21 EDT 2022
% 0.14/0.36 % CPUTime :
% 3.91/4.08
% 3.91/4.08 SPASS V 3.9
% 3.91/4.08 SPASS beiseite: Proof found.
% 3.91/4.08 % SZS status Theorem
% 3.91/4.08 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.91/4.08 SPASS derived 3681 clauses, backtracked 50 clauses, performed 2 splits and kept 2060 clauses.
% 3.91/4.08 SPASS allocated 71178 KBytes.
% 3.91/4.08 SPASS spent 0:00:03.64 on the problem.
% 3.91/4.08 0:00:00.04 for the input.
% 3.91/4.08 0:00:00.00 for the FLOTTER CNF translation.
% 3.91/4.08 0:00:00.10 for inferences.
% 3.91/4.08 0:00:00.01 for the backtracking.
% 3.91/4.08 0:00:03.46 for the reduction.
% 3.91/4.08
% 3.91/4.08
% 3.91/4.08 Here is a proof with depth 9, length 59 :
% 3.91/4.08 % SZS output start Refutation
% See solution above
% 3.91/4.08 Formulae used in the proof : k_s k_app s_app app_app1 app_app2 app_app3 ap_contractE1 ap_contractE4 ap_contractE8 ap_contractE9 ap_contractE10 ap_contractE12 ap_contractE13 k_contractE s_contractE i_contract_E
% 3.91/4.08
%------------------------------------------------------------------------------