TPTP Problem File: COL089-1.p
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%--------------------------------------------------------------------------
% File : COL089-1 : TPTP v8.2.0. Released v2.7.0.
% Domain : Combinatory Logic
% Problem : ap_reduce2_2c1
% Version : Reduced > Especial.
% English :
% Refs : [Men03] Meng (2003), Email to G. Sutcliffe
% Source : [Men03]
% Names :
% Status : Unsatisfiable
% Rating : 0.25 v8.2.0, 0.29 v8.1.0, 0.21 v7.5.0, 0.26 v7.4.0, 0.24 v7.3.0, 0.17 v7.1.0, 0.08 v7.0.0, 0.27 v6.3.0, 0.18 v6.2.0, 0.20 v6.1.0, 0.21 v6.0.0, 0.30 v5.5.0, 0.55 v5.3.0, 0.61 v5.2.0, 0.50 v5.1.0, 0.59 v5.0.0, 0.50 v4.1.0, 0.62 v4.0.1, 0.55 v4.0.0, 0.45 v3.7.0, 0.20 v3.5.0, 0.27 v3.4.0, 0.42 v3.3.0, 0.50 v3.2.0, 0.54 v3.1.0, 0.36 v2.7.0
% Syntax : Number of clauses : 44 ( 14 unt; 1 nHn; 43 RR)
% Number of literals : 93 ( 15 equ; 52 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 0 prp; 1-3 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-3 aty)
% Number of variables : 97 ( 25 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments : Problem coming out of an Isabelle proof.
%--------------------------------------------------------------------------
%----axioms from CombZF.thy.
%----free algebra for K, S, comb_app(P,Q).
cnf(k_s,axiom,
combK != combS ).
cnf(k_app,axiom,
combK != comb_app(P,Q) ).
cnf(s_app,axiom,
combS != comb_app(P,Q) ).
cnf(app_app1,axiom,
( comb_app(P1,Q1) != comb_app(P2,Q2)
| P1 = P2 ) ).
cnf(app_app2,axiom,
( comb_app(P1,Q1) != comb_app(P2,Q2)
| Q1 = Q2 ) ).
cnf(app_app3,axiom,
( P1 != P2
| Q1 != Q2
| comb_app(P1,Q1) = comb_app(P2,Q2) ) ).
%----add in Ap_E.
cnf(ap_E1,axiom,
( ~ member(comb_app(P,Q),comb)
| member(P,comb) ) ).
cnf(ap_E2,axiom,
( ~ member(comb_app(P,Q),comb)
| member(Q,comb) ) ).
%----add in comb.intros(three of them).
cnf(comb_intros1,axiom,
member(combK,comb) ).
cnf(comb_intros2,axiom,
member(combS,comb) ).
cnf(comb_intros3,axiom,
( ~ member(P,comb)
| ~ member(Q,comb)
| member(comb_app(P,Q),comb) ) ).
%----add in reduction_refl [intro!]:
cnf(reduction_refl,axiom,
( ~ member(A,comb)
| member(pair(A,A),rtrancl(contract)) ) ).
%----add in contract.K
cnf(contract_K,axiom,
( ~ member(P,comb)
| ~ member(Q,comb)
| member(pair(comb_app(comb_app(combK,P),Q),P),contract) ) ).
%----add in contract.S
cnf(contract_S,axiom,
( ~ member(P,comb)
| ~ member(Q,comb)
| ~ member(R,comb)
| member(pair(comb_app(comb_app(comb_app(combS,P),Q),R),comb_app(comb_app(P,R),comb_app(Q,R))),contract) ) ).
%----this manually rename the formula Ap_contractE
cnf(ap_contractE1,axiom,
( ~ member(pair(comb_app(P,Q),R),contract)
| ap_contractE_c1(P,Q,R)
| ap_contractE_c2(P,Q,R)
| ap_contractE_c3(P,Q,R)
| ap_contractE_c4(P,Q,R) ) ).
cnf(ap_contractE2,axiom,
( ~ ap_contractE_c1(P,Q,R)
| member(R,comb) ) ).
cnf(ap_contractE3,axiom,
( ~ ap_contractE_c1(P,Q,R)
| member(Q,comb) ) ).
cnf(ap_contractE4,axiom,
( ~ ap_contractE_c1(P,Q,R)
| P = comb_app(combK,R) ) ).
cnf(ap_contractE5,axiom,
( ~ ap_contractE_c2(P,Q,R)
| member(ap_contractE_sk1p(P,Q,R),comb) ) ).
cnf(ap_contractE6,axiom,
( ~ ap_contractE_c2(P,Q,R)
| member(ap_contractE_sk1q(P,Q,R),comb) ) ).
cnf(ap_contractE7,axiom,
( ~ ap_contractE_c2(P,Q,R)
| member(Q,comb) ) ).
cnf(ap_contractE8,axiom,
( ~ ap_contractE_c2(P,Q,R)
| R = comb_app(comb_app(ap_contractE_sk1p(P,Q,R),Q),comb_app(ap_contractE_sk1q(P,Q,R),Q)) ) ).
cnf(ap_contractE9,axiom,
( ~ ap_contractE_c2(P,Q,R)
| P = comb_app(comb_app(combS,ap_contractE_sk1p(P,Q,R)),ap_contractE_sk1q(P,Q,R)) ) ).
cnf(ap_contractE10,axiom,
( ~ ap_contractE_c3(P,Q,R)
| member(pair(P,ap_contractE_sk2q(P,Q,R)),contract) ) ).
cnf(ap_contractE11,axiom,
( ~ ap_contractE_c3(P,Q,R)
| member(Q,comb) ) ).
cnf(ap_contractE12,axiom,
( ~ ap_contractE_c3(P,Q,R)
| R = comb_app(ap_contractE_sk2q(P,Q,R),Q) ) ).
cnf(ap_contractE13,axiom,
( ~ ap_contractE_c4(P,Q,R)
| member(pair(Q,ap_contractE_sk3q(P,Q,R)),contract) ) ).
cnf(ap_contractE14,axiom,
( ~ ap_contractE_c4(P,Q,R)
| member(P,comb) ) ).
cnf(ap_contractE15,axiom,
( ~ ap_contractE_c4(P,Q,R)
| R = comb_app(P,ap_contractE_sk3q(P,Q,R)) ) ).
%----add in K_contractE[elim!]:
cnf(k_contractE,axiom,
~ member(pair(combK,R),contract) ).
%----add in S_contractE [elim!]:
%----converted by tptp2X(Ap_contractE+cls_otter.tptp)
cnf(s_contractE,axiom,
~ member(pair(combS,R),contract) ).
%----local axioms
%----axiom reduction_rls
cnf(reduction_rls_1,axiom,
( ~ member(B,comb)
| ~ member(Q3,comb)
| ~ member(pair(B,C),rtrancl(contract))
| member(pair(comb_app(comb_app(combK,B),Q3),C),rtrancl(contract)) ) ).
cnf(reduction_rls_2,axiom,
( ~ member(P3,comb)
| ~ member(Q3,comb)
| ~ member(R3,comb)
| ~ member(pair(comb_app(comb_app(P3,R3),comb_app(Q3,R3)),C),rtrancl(contract))
| member(pair(comb_app(comb_app(comb_app(combS,P3),Q3),R3),C),rtrancl(contract)) ) ).
cnf(reduction_rls_3,axiom,
( ~ member(pair(P3,Q3),contract)
| ~ member(R3,comb)
| ~ member(pair(comb_app(Q3,R3),C),rtrancl(contract))
| member(pair(comb_app(P3,R3),C),rtrancl(contract)) ) ).
cnf(reduction_rls_4,axiom,
( ~ member(pair(P3,Q3),contract)
| ~ member(R3,comb)
| ~ member(pair(comb_app(R3,Q3),C),rtrancl(contract))
| member(pair(comb_app(R3,P3),C),rtrancl(contract)) ) ).
%----local axioms.
%----axoim reduction_rls(same as above)
%----axiom trans_rtrancl
cnf(trans_rtrancl,axiom,
trans(rtrancl(R)) ).
%----axiom transD
cnf(transD,axiom,
( ~ trans(R)
| ~ member(pair(A,B),R)
| ~ member(pair(B,C),R)
| member(pair(A,C),R) ) ).
%----axiom contract_combD2
cnf(contract_combD2,axiom,
( ~ member(pair(A,B),contract)
| member(B,comb) ) ).
cnf(ap_reduce2_2h1,hypothesis,
member(r,comb) ).
cnf(ap_reduce2_2h2,hypothesis,
member(p,comb) ).
cnf(ap_reduce2_2h3,hypothesis,
member(pair(p,y),rtrancl(contract)) ).
cnf(ap_reduce2_2h4,hypothesis,
member(pair(y,z),contract) ).
cnf(ap_reduce2_2h5,hypothesis,
member(pair(comb_app(r,p),comb_app(r,y)),rtrancl(contract)) ).
cnf(ap_reduce2_2c1,negated_conjecture,
~ member(pair(comb_app(r,p),comb_app(r,z)),rtrancl(contract)) ).
%--------------------------------------------------------------------------