%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : COL091-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n022.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 0.18s 0.46s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 23 ( 7 unt; 5 nHn; 23 RR)
% Number of literals : 47 ( 0 equ; 22 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ equal(comb_app(u,v),combK),
file('COL091-1.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('COL091-1.p',unknown),
[] ).
cnf(18,axiom,
( ~ ap_contractE_c1(u,v,w)
| equal(u,comb_app(combK,w)) ),
file('COL091-1.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('COL091-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ ap_contractE_c3(u,v,w)
| member(pair(u,ap_contractE_sk2q(u,v,w)),contract) ),
file('COL091-1.p',unknown),
[] ).
cnf(27,axiom,
( ~ ap_contractE_c4(u,v,w)
| member(pair(v,ap_contractE_sk3q(u,v,w)),contract) ),
file('COL091-1.p',unknown),
[] ).
cnf(29,axiom,
( ~ ap_contractE_c4(u,v,w)
| equal(comb_app(u,ap_contractE_sk3q(u,v,w)),w) ),
file('COL091-1.p',unknown),
[] ).
cnf(30,axiom,
~ member(pair(combK,u),contract),
file('COL091-1.p',unknown),
[] ).
cnf(32,axiom,
member(pair(comb_app(combK,p),r),contract),
file('COL091-1.p',unknown),
[] ).
cnf(33,axiom,
( ~ member(pair(p,u),contract)
| ~ equal(comb_app(combK,u),r) ),
file('COL091-1.p',unknown),
[] ).
cnf(40,plain,
( ~ ap_contractE_c4(u,p,v)
| ~ equal(comb_app(combK,ap_contractE_sk3q(u,p,v)),r) ),
inference(res,[status(thm),theory(equality)],[27,33]),
[iquote('0:Res:27.1,33.0')] ).
cnf(42,plain,
~ ap_contractE_c3(combK,u,v),
inference(res,[status(thm),theory(equality)],[24,30]),
[iquote('0:Res:24.1,30.0')] ).
cnf(156,plain,
( ~ ap_contractE_c2(u,v,w)
| ~ equal(u,combK) ),
inference(spl,[status(thm),theory(equality)],[23,2]),
[iquote('0:SpL:23.1,2.0')] ).
cnf(168,plain,
( ~ ap_contractE_c4(combK,p,u)
| ~ ap_contractE_c4(combK,p,u)
| ~ equal(u,r) ),
inference(spl,[status(thm),theory(equality)],[29,40]),
[iquote('0:SpL:29.1,40.1')] ).
cnf(169,plain,
( ~ ap_contractE_c4(combK,p,u)
| ~ equal(u,r) ),
inference(obv,[status(thm),theory(equality)],[168]),
[iquote('0:Obv:168.0')] ).
cnf(205,plain,
( ap_contractE_c4(combK,p,r)
| ap_contractE_c3(combK,p,r)
| ap_contractE_c2(combK,p,r)
| ap_contractE_c1(combK,p,r) ),
inference(res,[status(thm),theory(equality)],[32,15]),
[iquote('0:Res:32.0,15.0')] ).
cnf(209,plain,
( ap_contractE_c4(combK,p,r)
| ap_contractE_c2(combK,p,r)
| ap_contractE_c1(combK,p,r) ),
inference(mrr,[status(thm)],[205,42]),
[iquote('0:MRR:205.1,42.0')] ).
cnf(221,plain,
( ~ equal(r,r)
| ap_contractE_c2(combK,p,r)
| ap_contractE_c1(combK,p,r) ),
inference(res,[status(thm),theory(equality)],[209,169]),
[iquote('0:Res:209.0,169.0')] ).
cnf(224,plain,
( ap_contractE_c2(combK,p,r)
| ap_contractE_c1(combK,p,r) ),
inference(obv,[status(thm),theory(equality)],[221]),
[iquote('0:Obv:221.0')] ).
cnf(270,plain,
( ~ equal(combK,combK)
| ap_contractE_c1(combK,p,r) ),
inference(res,[status(thm),theory(equality)],[224,156]),
[iquote('0:Res:224.0,156.0')] ).
cnf(274,plain,
ap_contractE_c1(combK,p,r),
inference(obv,[status(thm),theory(equality)],[270]),
[iquote('0:Obv:270.0')] ).
cnf(283,plain,
equal(comb_app(combK,r),combK),
inference(res,[status(thm),theory(equality)],[274,18]),
[iquote('0:Res:274.0,18.0')] ).
cnf(286,plain,
$false,
inference(mrr,[status(thm)],[283,2]),
[iquote('0:MRR:283.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COL091-1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n022.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 : Tue May 31 06:39:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.46
% 0.18/0.46 SPASS V 3.9
% 0.18/0.46 SPASS beiseite: Proof found.
% 0.18/0.46 % SZS status Theorem
% 0.18/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 SPASS derived 205 clauses, backtracked 0 clauses, performed 0 splits and kept 159 clauses.
% 0.18/0.46 SPASS allocated 63537 KBytes.
% 0.18/0.46 SPASS spent 0:00:00.11 on the problem.
% 0.18/0.46 0:00:00.04 for the input.
% 0.18/0.46 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.46 0:00:00.01 for inferences.
% 0.18/0.46 0:00:00.00 for the backtracking.
% 0.18/0.46 0:00:00.04 for the reduction.
% 0.18/0.46
% 0.18/0.46
% 0.18/0.46 Here is a proof with depth 5, length 23 :
% 0.18/0.46 % SZS output start Refutation
% See solution above
% 0.18/0.46 Formulae used in the proof : k_app ap_contractE1 ap_contractE4 ap_contractE9 ap_contractE10 ap_contractE13 ap_contractE15 k_contractE k1_contractD_h1 k1_contractD_c1
% 0.18/0.46
%------------------------------------------------------------------------------