%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL093-1 : TPTP v8.1.0. Released v2.7.0.
% 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 : Fri Jul 15 00:42:37 EDT 2022
% Result : Unsatisfiable 0.49s 0.67s
% Output : Refutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of clauses : 49 ( 17 unt; 7 nHn; 49 RR)
% Number of literals : 94 ( 0 equ; 46 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('COL093-1.p',unknown),
[] ).
cnf(3,axiom,
~ equal(comb_app(u,v),combS),
file('COL093-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ member(comb_app(u,v),comb)
| member(v,comb) ),
file('COL093-1.p',unknown),
[] ).
cnf(32,axiom,
( ~ member(u,comb)
| member(pair(u,u),parcontract) ),
file('COL093-1.p',unknown),
[] ).
cnf(39,axiom,
( ~ member(pair(combS,u),parcontract)
| equal(u,combS) ),
file('COL093-1.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('COL093-1.p',unknown),
[] ).
cnf(41,axiom,
( ~ ap_parcontractE_c1(u,v,w)
| member(comb_app(u,v),comb) ),
file('COL093-1.p',unknown),
[] ).
cnf(42,axiom,
( ~ ap_parcontractE_c1(u,v,w)
| equal(w,comb_app(u,v)) ),
file('COL093-1.p',unknown),
[] ).
cnf(45,axiom,
( ~ ap_parcontractE_c2(u,v,w)
| equal(u,comb_app(combK,w)) ),
file('COL093-1.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('COL093-1.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('COL093-1.p',unknown),
[] ).
cnf(51,axiom,
( ~ ap_parcontractE_c4(u,v,w)
| member(pair(u,ap_parcontractE_sk2q(u,v,w)),parcontract) ),
file('COL093-1.p',unknown),
[] ).
cnf(52,axiom,
( ~ ap_parcontractE_c4(u,v,w)
| member(pair(v,ap_parcontractE_sk2s(u,v,w)),parcontract) ),
file('COL093-1.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('COL093-1.p',unknown),
[] ).
cnf(54,axiom,
member(pair(comb_app(combS,p),r),parcontract),
file('COL093-1.p',unknown),
[] ).
cnf(55,axiom,
( ~ member(pair(p,u),parcontract)
| ~ equal(comb_app(combS,u),r) ),
file('COL093-1.p',unknown),
[] ).
cnf(60,plain,
( ~ member(p,comb)
| ~ equal(comb_app(combS,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(combS,ap_parcontractE_sk2s(u,p,v)),r) ),
inference(res,[status(thm),theory(equality)],[52,55]),
[iquote('0:Res:52.1,55.0')] ).
cnf(72,plain,
( ~ ap_parcontractE_c4(combS,u,v)
| equal(ap_parcontractE_sk2q(combS,u,v),combS) ),
inference(res,[status(thm),theory(equality)],[51,39]),
[iquote('0:Res:51.1,39.0')] ).
cnf(186,plain,
( ~ ap_parcontractE_c4(combS,u,v)
| ~ ap_parcontractE_c4(combS,u,v)
| equal(comb_app(combS,ap_parcontractE_sk2s(combS,u,v)),v) ),
inference(spr,[status(thm),theory(equality)],[72,53]),
[iquote('0:SpR:72.1,53.1')] ).
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(199,plain,
( ~ ap_parcontractE_c4(combS,u,v)
| equal(comb_app(combS,ap_parcontractE_sk2s(combS,u,v)),v) ),
inference(obv,[status(thm),theory(equality)],[186]),
[iquote('0:Obv:186.0')] ).
cnf(277,plain,
( ~ ap_parcontractE_c4(combS,p,u)
| ~ ap_parcontractE_c4(combS,p,u)
| ~ equal(u,r) ),
inference(spl,[status(thm),theory(equality)],[199,65]),
[iquote('0:SpL:199.1,65.1')] ).
cnf(281,plain,
( ~ ap_parcontractE_c4(combS,p,u)
| ~ equal(u,r) ),
inference(obv,[status(thm),theory(equality)],[277]),
[iquote('0:Obv:277.0')] ).
cnf(291,plain,
( ~ ap_parcontractE_c3(u,v,w)
| ~ equal(u,combS) ),
inference(spl,[status(thm),theory(equality)],[50,3]),
[iquote('0:SpL:50.1,3.0')] ).
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(combS,p,r)
| ap_parcontractE_c3(combS,p,r)
| ap_parcontractE_c2(combS,p,r)
| ap_parcontractE_c1(combS,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(combS,p,r)
| ap_parcontractE_c2(combS,p,r)
| ap_parcontractE_c1(combS,p,r) ),
inference(res,[status(thm),theory(equality)],[487,189]),
[iquote('0:Res:487.0,189.0')] ).
cnf(1115,plain,
( ~ equal(r,r)
| ap_parcontractE_c3(combS,p,r)
| ap_parcontractE_c2(combS,p,r)
| ap_parcontractE_c1(combS,p,r) ),
inference(res,[status(thm),theory(equality)],[487,281]),
[iquote('0:Res:487.0,281.0')] ).
cnf(1116,plain,
( ~ equal(r,combK)
| ap_parcontractE_c2(combS,p,r)
| ap_parcontractE_c1(combS,p,r) ),
inference(mrr,[status(thm)],[1112,378]),
[iquote('0:MRR:1112.1,378.0')] ).
cnf(1118,plain,
( ap_parcontractE_c3(combS,p,r)
| ap_parcontractE_c2(combS,p,r)
| ap_parcontractE_c1(combS,p,r) ),
inference(obv,[status(thm),theory(equality)],[1115]),
[iquote('0:Obv:1115.0')] ).
cnf(1119,plain,
ap_parcontractE_c2(combS,p,r),
inference(spt,[spt(split,[position(s1)])],[1116]),
[iquote('1:Spt:1116.1')] ).
cnf(1120,plain,
equal(comb_app(combK,r),combS),
inference(res,[status(thm),theory(equality)],[1119,45]),
[iquote('1:Res:1119.0,45.0')] ).
cnf(1125,plain,
$false,
inference(mrr,[status(thm)],[1120,3]),
[iquote('1:MRR:1120.0,3.0')] ).
cnf(1126,plain,
~ ap_parcontractE_c2(combS,p,r),
inference(spt,[spt(split,[position(sa)])],[1125,1119]),
[iquote('1:Spt:1125.0,1116.1,1119.0')] ).
cnf(1127,plain,
( ~ equal(r,combK)
| ap_parcontractE_c1(combS,p,r) ),
inference(spt,[spt(split,[position(s2)])],[1116]),
[iquote('1:Spt:1125.0,1116.0,1116.2')] ).
cnf(1129,plain,
( ap_parcontractE_c3(combS,p,r)
| ap_parcontractE_c1(combS,p,r) ),
inference(mrr,[status(thm)],[1118,1126]),
[iquote('1:MRR:1118.1,1126.0')] ).
cnf(1136,plain,
ap_parcontractE_c1(combS,p,r),
inference(spt,[spt(split,[position(s2s1)])],[1129]),
[iquote('2:Spt:1129.1')] ).
cnf(1137,plain,
equal(comb_app(combS,p),r),
inference(res,[status(thm),theory(equality)],[1136,42]),
[iquote('2:Res:1136.0,42.0')] ).
cnf(1138,plain,
member(comb_app(combS,p),comb),
inference(res,[status(thm),theory(equality)],[1136,41]),
[iquote('2:Res:1136.0,41.0')] ).
cnf(1140,plain,
( ~ member(p,comb)
| ~ equal(r,r) ),
inference(rew,[status(thm),theory(equality)],[1137,60]),
[iquote('2:Rew:1137.0,60.1')] ).
cnf(1141,plain,
member(r,comb),
inference(rew,[status(thm),theory(equality)],[1137,1138]),
[iquote('2:Rew:1137.0,1138.0')] ).
cnf(1142,plain,
~ member(p,comb),
inference(obv,[status(thm),theory(equality)],[1140]),
[iquote('2:Obv:1140.1')] ).
cnf(1173,plain,
( ~ member(r,comb)
| member(p,comb) ),
inference(spl,[status(thm),theory(equality)],[1137,8]),
[iquote('2:SpL:1137.0,8.0')] ).
cnf(1204,plain,
$false,
inference(mrr,[status(thm)],[1173,1141,1142]),
[iquote('2:MRR:1173.0,1173.1,1141.0,1142.0')] ).
cnf(1216,plain,
~ ap_parcontractE_c1(combS,p,r),
inference(spt,[spt(split,[position(s2sa)])],[1204,1136]),
[iquote('2:Spt:1204.0,1129.1,1136.0')] ).
cnf(1217,plain,
ap_parcontractE_c3(combS,p,r),
inference(spt,[spt(split,[position(s2s2)])],[1129]),
[iquote('2:Spt:1204.0,1129.0')] ).
cnf(1235,plain,
~ equal(combS,combS),
inference(res,[status(thm),theory(equality)],[1217,291]),
[iquote('2:Res:1217.0,291.0')] ).
cnf(1239,plain,
$false,
inference(obv,[status(thm),theory(equality)],[1235]),
[iquote('2:Obv:1235.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL093-1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue May 31 15:57:30 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.49/0.67
% 0.49/0.67 SPASS V 3.9
% 0.49/0.67 SPASS beiseite: Proof found.
% 0.49/0.67 % SZS status Theorem
% 0.49/0.67 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.49/0.67 SPASS derived 935 clauses, backtracked 18 clauses, performed 2 splits and kept 666 clauses.
% 0.49/0.67 SPASS allocated 64568 KBytes.
% 0.49/0.67 SPASS spent 0:00:00.31 on the problem.
% 0.49/0.67 0:00:00.03 for the input.
% 0.49/0.67 0:00:00.00 for the FLOTTER CNF translation.
% 0.49/0.67 0:00:00.02 for inferences.
% 0.49/0.67 0:00:00.00 for the backtracking.
% 0.49/0.67 0:00:00.22 for the reduction.
% 0.49/0.67
% 0.49/0.67
% 0.49/0.67 Here is a proof with depth 7, length 49 :
% 0.49/0.67 % SZS output start Refutation
% See solution above
% 0.49/0.67 Formulae used in the proof : k_app s_app ap_E2 parcontract_intros1 s_parcontractE2 ap_parcontractE1 ap_parcontractE2 ap_parcontractE3 ap_parcontractE6 ap_parcontractE10 ap_parcontractE11 ap_parcontractE12 ap_parcontractE13 ap_parcontractE14 s1_parcontractD_h1 s1_parcontractD_c1
% 0.49/0.67
%------------------------------------------------------------------------------