%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL090-3 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 00:36:28 EDT 2022
% Result : Unsatisfiable 0.19s 0.37s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 21
% Syntax : Number of clauses : 75 ( 21 unt; 22 nHn; 74 RR)
% Number of literals : 172 ( 75 equ; 53 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 58 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(k_s,axiom,
combK != combS ).
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(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_contractE4,axiom,
( ~ ap_contractE_c1(P,Q,R)
| P = comb_app(combK,R) ) ).
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_contractE13,axiom,
( ~ ap_contractE_c4(P,Q,R)
| member(pair(Q,ap_contractE_sk3q(P,Q,R)),contract) ) ).
cnf(k_contractE,axiom,
~ member(pair(combK,R),contract) ).
cnf(s_contractE,axiom,
~ member(pair(combS,R),contract) ).
cnf(i_contract_E,negated_conjecture,
member(pair(comb_app(comb_app(combS,combK),combK),r),contract) ).
cnf(refute_0_0,plain,
( comb_app(P1,Q1) != comb_app(combS,combK)
| P1 = combS ),
inference(subst,[],[app_app1:[bind(P2,$fot(combS)),bind(Q2,$fot(combK))]]) ).
cnf(refute_0_1,plain,
( ~ ap_contractE_c1(comb_app(combS,combK),combK,r)
| comb_app(combS,combK) = comb_app(combK,r) ),
inference(subst,[],[ap_contractE4:[bind(P,$fot(comb_app(combS,combK))),bind(Q,$fot(combK)),bind(R,$fot(r))]]) ).
cnf(refute_0_2,plain,
( comb_app(P1,Q1) != comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r))
| P1 = comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)) ),
inference(subst,[],[app_app1:[bind(P2,$fot(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)))),bind(Q2,$fot(ap_contractE_sk1q(comb_app(combS,combK),combK,r)))]]) ).
cnf(refute_0_3,plain,
( ~ ap_contractE_c2(comb_app(combS,combK),combK,r)
| comb_app(combS,combK) = comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r)) ),
inference(subst,[],[ap_contractE9:[bind(P,$fot(comb_app(combS,combK))),bind(Q,$fot(combK)),bind(R,$fot(r))]]) ).
cnf(refute_0_4,plain,
( ~ ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| combS = comb_app(combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(subst,[],[ap_contractE4:[bind(P,$fot(combS)),bind(Q,$fot(combK)),bind(R,$fot(ap_contractE_sk2q(comb_app(combS,combK),combK,r)))]]) ).
cnf(refute_0_5,plain,
( ~ ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| combS = comb_app(comb_app(combS,ap_contractE_sk1p(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),ap_contractE_sk1q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))) ),
inference(subst,[],[ap_contractE9:[bind(P,$fot(combS)),bind(Q,$fot(combK)),bind(R,$fot(ap_contractE_sk2q(comb_app(combS,combK),combK,r)))]]) ).
cnf(refute_0_6,plain,
( ~ ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| member(pair(combS,ap_contractE_sk2q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract) ),
inference(subst,[],[ap_contractE10:[bind(P,$fot(combS)),bind(Q,$fot(combK)),bind(R,$fot(ap_contractE_sk2q(comb_app(combS,combK),combK,r)))]]) ).
cnf(refute_0_7,plain,
( ~ ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| member(pair(combK,ap_contractE_sk3q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract) ),
inference(subst,[],[ap_contractE13:[bind(P,$fot(combS)),bind(Q,$fot(combK)),bind(R,$fot(ap_contractE_sk2q(comb_app(combS,combK),combK,r)))]]) ).
cnf(refute_0_8,plain,
( ~ member(pair(comb_app(combS,combK),ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract)
| ap_contractE_c1(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_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(subst,[],[ap_contractE1:[bind(P,$fot(combS)),bind(Q,$fot(combK)),bind(R,$fot(ap_contractE_sk2q(comb_app(combS,combK),combK,r)))]]) ).
cnf(refute_0_9,plain,
( ~ ap_contractE_c3(comb_app(combS,combK),combK,r)
| member(pair(comb_app(combS,combK),ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract) ),
inference(subst,[],[ap_contractE10:[bind(P,$fot(comb_app(combS,combK))),bind(Q,$fot(combK)),bind(R,$fot(r))]]) ).
cnf(refute_0_10,plain,
( ~ ap_contractE_c4(comb_app(combS,combK),combK,r)
| member(pair(combK,ap_contractE_sk3q(comb_app(combS,combK),combK,r)),contract) ),
inference(subst,[],[ap_contractE13:[bind(P,$fot(comb_app(combS,combK))),bind(Q,$fot(combK)),bind(R,$fot(r))]]) ).
cnf(refute_0_11,plain,
( ~ member(pair(comb_app(comb_app(combS,combK),combK),r),contract)
| ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c3(comb_app(combS,combK),combK,r)
| ap_contractE_c4(comb_app(combS,combK),combK,r) ),
inference(subst,[],[ap_contractE1:[bind(P,$fot(comb_app(combS,combK))),bind(Q,$fot(combK)),bind(R,$fot(r))]]) ).
cnf(refute_0_12,plain,
( ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c3(comb_app(combS,combK),combK,r)
| ap_contractE_c4(comb_app(combS,combK),combK,r) ),
inference(resolve,[$cnf( member(pair(comb_app(comb_app(combS,combK),combK),r),contract) )],[i_contract_E,refute_0_11]) ).
cnf(refute_0_13,plain,
( ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c3(comb_app(combS,combK),combK,r)
| member(pair(combK,ap_contractE_sk3q(comb_app(combS,combK),combK,r)),contract) ),
inference(resolve,[$cnf( ap_contractE_c4(comb_app(combS,combK),combK,r) )],[refute_0_12,refute_0_10]) ).
cnf(refute_0_14,plain,
~ member(pair(combK,ap_contractE_sk3q(comb_app(combS,combK),combK,r)),contract),
inference(subst,[],[k_contractE:[bind(R,$fot(ap_contractE_sk3q(comb_app(combS,combK),combK,r)))]]) ).
cnf(refute_0_15,plain,
( ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c3(comb_app(combS,combK),combK,r) ),
inference(resolve,[$cnf( member(pair(combK,ap_contractE_sk3q(comb_app(combS,combK),combK,r)),contract) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| member(pair(comb_app(combS,combK),ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract) ),
inference(resolve,[$cnf( ap_contractE_c3(comb_app(combS,combK),combK,r) )],[refute_0_15,refute_0_9]) ).
cnf(refute_0_17,plain,
( ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(resolve,[$cnf( member(pair(comb_app(combS,combK),ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract) )],[refute_0_16,refute_0_8]) ).
cnf(refute_0_18,plain,
( ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| member(pair(combK,ap_contractE_sk3q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract) ),
inference(resolve,[$cnf( ap_contractE_c4(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) )],[refute_0_17,refute_0_7]) ).
cnf(refute_0_19,plain,
~ member(pair(combK,ap_contractE_sk3q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract),
inference(subst,[],[k_contractE:[bind(R,$fot(ap_contractE_sk3q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))))]]) ).
cnf(refute_0_20,plain,
( ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) ),
inference(resolve,[$cnf( member(pair(combK,ap_contractE_sk3q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c2(comb_app(combS,combK),combK,r)
| member(pair(combS,ap_contractE_sk2q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract) ),
inference(resolve,[$cnf( ap_contractE_c3(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) )],[refute_0_20,refute_0_6]) ).
cnf(refute_0_22,plain,
~ member(pair(combS,ap_contractE_sk2q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract),
inference(subst,[],[s_contractE:[bind(R,$fot(ap_contractE_sk2q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))))]]) ).
cnf(refute_0_23,plain,
( ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c2(comb_app(combS,combK),combK,r) ),
inference(resolve,[$cnf( member(pair(combS,ap_contractE_sk2q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),contract) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( combS = comb_app(comb_app(combS,ap_contractE_sk1p(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),ap_contractE_sk1q(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))
| ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r) ),
inference(resolve,[$cnf( ap_contractE_c2(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) )],[refute_0_23,refute_0_5]) ).
cnf(refute_0_25,plain,
combS != comb_app(comb_app(combS,ap_contractE_sk1p(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),ap_contractE_sk1q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),
inference(subst,[],[s_app:[bind(P,$fot(comb_app(combS,ap_contractE_sk1p(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))))),bind(Q,$fot(ap_contractE_sk1q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))))]]) ).
cnf(refute_0_26,plain,
( ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r) ),
inference(resolve,[$cnf( $equal(combS,comb_app(comb_app(combS,ap_contractE_sk1p(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))),ap_contractE_sk1q(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( combS = comb_app(combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))
| ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r) ),
inference(resolve,[$cnf( ap_contractE_c1(combS,combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)) )],[refute_0_26,refute_0_4]) ).
cnf(refute_0_28,plain,
combS != comb_app(combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r)),
inference(subst,[],[s_app:[bind(P,$fot(combK)),bind(Q,$fot(ap_contractE_sk2q(comb_app(combS,combK),combK,r)))]]) ).
cnf(refute_0_29,plain,
( ap_contractE_c1(comb_app(combS,combK),combK,r)
| ap_contractE_c2(comb_app(combS,combK),combK,r) ),
inference(resolve,[$cnf( $equal(combS,comb_app(combK,ap_contractE_sk2q(comb_app(combS,combK),combK,r))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( comb_app(combS,combK) = comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r))
| ap_contractE_c1(comb_app(combS,combK),combK,r) ),
inference(resolve,[$cnf( ap_contractE_c2(comb_app(combS,combK),combK,r) )],[refute_0_29,refute_0_3]) ).
cnf(refute_0_31,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_32,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_33,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( comb_app(combS,combK) != comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r))
| comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r)) = comb_app(combS,combK) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(comb_app(combS,combK))),bind(Y,$fot(comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r))))]]) ).
cnf(refute_0_35,plain,
( comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r)) = comb_app(combS,combK)
| ap_contractE_c1(comb_app(combS,combK),combK,r) ),
inference(resolve,[$cnf( $equal(comb_app(combS,combK),comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r))) )],[refute_0_30,refute_0_34]) ).
cnf(refute_0_36,plain,
( comb_app(P1,Q1) != comb_app(combS,combK)
| comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r)) != comb_app(combS,combK)
| comb_app(P1,Q1) = comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(comb_app(P1,Q1),comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r))) ),[1],$fot(comb_app(combS,combK))]]) ).
cnf(refute_0_37,plain,
( comb_app(P1,Q1) != comb_app(combS,combK)
| comb_app(P1,Q1) = comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r))
| ap_contractE_c1(comb_app(combS,combK),combK,r) ),
inference(resolve,[$cnf( $equal(comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r)),comb_app(combS,combK)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( comb_app(P1,Q1) != comb_app(combS,combK)
| P1 = comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r))
| ap_contractE_c1(comb_app(combS,combK),combK,r) ),
inference(resolve,[$cnf( $equal(comb_app(P1,Q1),comb_app(comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),ap_contractE_sk1q(comb_app(combS,combK),combK,r))) )],[refute_0_37,refute_0_2]) ).
cnf(refute_0_39,plain,
( comb_app(combS,combK) != comb_app(combS,combK)
| combS = comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r))
| ap_contractE_c1(comb_app(combS,combK),combK,r) ),
inference(subst,[],[refute_0_38:[bind(P1,$fot(combS)),bind(Q1,$fot(combK))]]) ).
cnf(refute_0_40,plain,
comb_app(combS,combK) = comb_app(combS,combK),
introduced(tautology,[refl,[$fot(comb_app(combS,combK))]]) ).
cnf(refute_0_41,plain,
( combS = comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r))
| ap_contractE_c1(comb_app(combS,combK),combK,r) ),
inference(resolve,[$cnf( $equal(comb_app(combS,combK),comb_app(combS,combK)) )],[refute_0_40,refute_0_39]) ).
cnf(refute_0_42,plain,
combS != comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r)),
inference(subst,[],[s_app:[bind(P,$fot(combS)),bind(Q,$fot(ap_contractE_sk1p(comb_app(combS,combK),combK,r)))]]) ).
cnf(refute_0_43,plain,
ap_contractE_c1(comb_app(combS,combK),combK,r),
inference(resolve,[$cnf( $equal(combS,comb_app(combS,ap_contractE_sk1p(comb_app(combS,combK),combK,r))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
comb_app(combS,combK) = comb_app(combK,r),
inference(resolve,[$cnf( ap_contractE_c1(comb_app(combS,combK),combK,r) )],[refute_0_43,refute_0_1]) ).
cnf(refute_0_45,plain,
( comb_app(P1,Q1) != comb_app(combK,r)
| comb_app(combS,combK) != comb_app(combK,r)
| comb_app(P1,Q1) = comb_app(combS,combK) ),
introduced(tautology,[equality,[$cnf( ~ $equal(comb_app(P1,Q1),comb_app(combS,combK)) ),[1],$fot(comb_app(combK,r))]]) ).
cnf(refute_0_46,plain,
( comb_app(P1,Q1) != comb_app(combK,r)
| comb_app(P1,Q1) = comb_app(combS,combK) ),
inference(resolve,[$cnf( $equal(comb_app(combS,combK),comb_app(combK,r)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( comb_app(P1,Q1) != comb_app(combK,r)
| P1 = combS ),
inference(resolve,[$cnf( $equal(comb_app(P1,Q1),comb_app(combS,combK)) )],[refute_0_46,refute_0_0]) ).
cnf(refute_0_48,plain,
( comb_app(P1,Q1) != comb_app(combS,combK)
| Q1 = combK ),
inference(subst,[],[app_app2:[bind(P2,$fot(combS)),bind(Q2,$fot(combK))]]) ).
cnf(refute_0_49,plain,
( comb_app(P1,Q1) != comb_app(combK,r)
| Q1 = combK ),
inference(resolve,[$cnf( $equal(comb_app(P1,Q1),comb_app(combS,combK)) )],[refute_0_46,refute_0_48]) ).
cnf(refute_0_50,plain,
( comb_app(combK,r) != comb_app(combK,r)
| r = combK ),
inference(subst,[],[refute_0_49:[bind(P1,$fot(combK)),bind(Q1,$fot(r))]]) ).
cnf(refute_0_51,plain,
comb_app(combK,r) = comb_app(combK,r),
introduced(tautology,[refl,[$fot(comb_app(combK,r))]]) ).
cnf(refute_0_52,plain,
r = combK,
inference(resolve,[$cnf( $equal(comb_app(combK,r),comb_app(combK,r)) )],[refute_0_51,refute_0_50]) ).
cnf(refute_0_53,plain,
( comb_app(combK,r) != comb_app(combK,r)
| r != combK
| comb_app(combK,r) = comb_app(combK,combK) ),
introduced(tautology,[equality,[$cnf( $equal(comb_app(combK,r),comb_app(combK,r)) ),[1,1],$fot(combK)]]) ).
cnf(refute_0_54,plain,
( r != combK
| comb_app(combK,r) = comb_app(combK,combK) ),
inference(resolve,[$cnf( $equal(comb_app(combK,r),comb_app(combK,r)) )],[refute_0_51,refute_0_53]) ).
cnf(refute_0_55,plain,
comb_app(combK,r) = comb_app(combK,combK),
inference(resolve,[$cnf( $equal(r,combK) )],[refute_0_52,refute_0_54]) ).
cnf(refute_0_56,plain,
( comb_app(P1,Q1) != comb_app(combK,combK)
| comb_app(combK,r) != comb_app(combK,combK)
| comb_app(P1,Q1) = comb_app(combK,r) ),
introduced(tautology,[equality,[$cnf( ~ $equal(comb_app(P1,Q1),comb_app(combK,r)) ),[1],$fot(comb_app(combK,combK))]]) ).
cnf(refute_0_57,plain,
( comb_app(P1,Q1) != comb_app(combK,combK)
| comb_app(P1,Q1) = comb_app(combK,r) ),
inference(resolve,[$cnf( $equal(comb_app(combK,r),comb_app(combK,combK)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( comb_app(P1,Q1) != comb_app(combK,combK)
| P1 = combS ),
inference(resolve,[$cnf( $equal(comb_app(P1,Q1),comb_app(combK,r)) )],[refute_0_57,refute_0_47]) ).
cnf(refute_0_59,plain,
( comb_app(combK,combK) != comb_app(combK,combK)
| combK = combS ),
inference(subst,[],[refute_0_58:[bind(P1,$fot(combK)),bind(Q1,$fot(combK))]]) ).
cnf(refute_0_60,plain,
comb_app(combK,combK) = comb_app(combK,combK),
introduced(tautology,[refl,[$fot(comb_app(combK,combK))]]) ).
cnf(refute_0_61,plain,
combK = combS,
inference(resolve,[$cnf( $equal(comb_app(combK,combK),comb_app(combK,combK)) )],[refute_0_60,refute_0_59]) ).
cnf(refute_0_62,plain,
$false,
inference(resolve,[$cnf( $equal(combK,combS) )],[refute_0_61,k_s]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL090-3 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue May 31 07:01:50 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.37
% 0.19/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.38
%------------------------------------------------------------------------------