TSTP Solution File: COL095-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COL095-1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n014.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 : 300s
% DateTime : Wed Aug 30 18:22:36 EDT 2023
% Result : Unsatisfiable 1.58s 1.71s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 58
% Syntax : Number of formulae : 111 ( 19 unt; 35 typ; 0 def)
% Number of atoms : 150 ( 30 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 150 ( 76 ~; 74 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 67 ( 26 >; 41 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 9 con; 0-3 aty)
% Number of variables : 138 ( 30 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
combK: $i ).
tff(decl_23,type,
combS: $i ).
tff(decl_24,type,
comb_app: ( $i * $i ) > $i ).
tff(decl_25,type,
comb: $i ).
tff(decl_26,type,
member: ( $i * $i ) > $o ).
tff(decl_27,type,
pair: ( $i * $i ) > $i ).
tff(decl_28,type,
contract: $i ).
tff(decl_29,type,
rtrancl: $i > $i ).
tff(decl_30,type,
ap_contractE_c1: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
ap_contractE_c2: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
ap_contractE_c3: ( $i * $i * $i ) > $o ).
tff(decl_33,type,
ap_contractE_c4: ( $i * $i * $i ) > $o ).
tff(decl_34,type,
ap_contractE_sk1p: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
ap_contractE_sk1q: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
ap_contractE_sk2q: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
ap_contractE_sk3q: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
parcontract: $i ).
tff(decl_39,type,
ap_parcontractE_c1: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
ap_parcontractE_c2: ( $i * $i * $i ) > $o ).
tff(decl_41,type,
ap_parcontractE_c3: ( $i * $i * $i ) > $o ).
tff(decl_42,type,
ap_parcontractE_c4: ( $i * $i * $i ) > $o ).
tff(decl_43,type,
ap_parcontractE_sk1p: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
ap_parcontractE_sk1q: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
ap_parcontractE_sk2q: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
ap_parcontractE_sk2s: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
k1_parcontractD_sk1: ( $i * $i ) > $i ).
tff(decl_48,type,
s1_parcontractD_sk1: ( $i * $i ) > $i ).
tff(decl_49,type,
s2_parcontractD_sk1p: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
s2_parcontractD_sk1q: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
eptset: $i ).
tff(decl_52,type,
inl: $i > $i ).
tff(decl_53,type,
inr: $i > $i ).
tff(decl_54,type,
p: $i ).
tff(decl_55,type,
q: $i ).
tff(decl_56,type,
yp: $i ).
cnf(ap_E2,axiom,
( member(X2,comb)
| ~ member(comb_app(X1,X2),comb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_E2) ).
cnf(k1_parcontractD_1,axiom,
( X2 = comb_app(combK,k1_parcontractD_sk1(X1,X2))
| ~ member(pair(comb_app(combK,X1),X2),parcontract) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k1_parcontractD_1) ).
cnf(parcontract_combD2,axiom,
( member(X2,comb)
| ~ member(pair(X1,X2),parcontract) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',parcontract_combD2) ).
cnf(app_app1,axiom,
( X1 = X3
| comb_app(X1,X2) != comb_app(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app1) ).
cnf(ap_parcontractE11,axiom,
( X1 = comb_app(comb_app(combS,ap_parcontractE_sk1p(X1,X2,X3)),ap_parcontractE_sk1q(X1,X2,X3))
| ~ ap_parcontractE_c3(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE11) ).
cnf(parcontract_intros2,axiom,
( member(pair(comb_app(comb_app(combK,X1),X2),X1),parcontract)
| ~ member(X1,comb)
| ~ member(X2,comb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',parcontract_intros2) ).
cnf(ap_parcontractE13,axiom,
( member(pair(X2,ap_parcontractE_sk2s(X1,X2,X3)),parcontract)
| ~ ap_parcontractE_c4(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE13) ).
cnf(k_app,axiom,
combK != comb_app(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_app) ).
cnf(diamond_parcontract_2c2,negated_conjecture,
( ~ member(pair(p,X1),parcontract)
| ~ member(pair(yp,X1),parcontract) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_parcontract_2c2) ).
cnf(k1_parcontractD_2,axiom,
( member(pair(X1,k1_parcontractD_sk1(X1,X2)),parcontract)
| ~ member(pair(comb_app(combK,X1),X2),parcontract) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k1_parcontractD_2) ).
cnf(ap_parcontractE14,axiom,
( X3 = comb_app(ap_parcontractE_sk2q(X1,X2,X3),ap_parcontractE_sk2s(X1,X2,X3))
| ~ ap_parcontractE_c4(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE14) ).
cnf(app_app2,axiom,
( X2 = X4
| comb_app(X1,X2) != comb_app(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app_app2) ).
cnf(ap_parcontractE1,axiom,
( ap_parcontractE_c1(X1,X2,X3)
| ap_parcontractE_c2(X1,X2,X3)
| ap_parcontractE_c3(X1,X2,X3)
| ap_parcontractE_c4(X1,X2,X3)
| ~ member(pair(comb_app(X1,X2),X3),parcontract) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE1) ).
cnf(diamond_parcontract_2c1,negated_conjecture,
member(pair(comb_app(comb_app(combK,p),q),yp),parcontract),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_parcontract_2c1) ).
cnf(k_parcontractE2,axiom,
( X1 = combK
| ~ member(pair(combK,X1),parcontract) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_parcontractE2) ).
cnf(ap_parcontractE3,axiom,
( X3 = comb_app(X1,X2)
| ~ ap_parcontractE_c1(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE3) ).
cnf(ap_parcontractE12,axiom,
( member(pair(X1,ap_parcontractE_sk2q(X1,X2,X3)),parcontract)
| ~ ap_parcontractE_c4(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE12) ).
cnf(parcontract_intros4,axiom,
( member(pair(comb_app(X1,X3),comb_app(X2,X4)),parcontract)
| ~ member(pair(X1,X2),parcontract)
| ~ member(pair(X3,X4),parcontract) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',parcontract_intros4) ).
cnf(ap_parcontractE6,axiom,
( X1 = comb_app(combK,X3)
| ~ ap_parcontractE_c2(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_parcontractE6) ).
cnf(parcontract_intros1,axiom,
( member(pair(X1,X1),parcontract)
| ~ member(X1,comb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',parcontract_intros1) ).
cnf(diamond_parcontract_2h1,hypothesis,
member(p,comb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_parcontract_2h1) ).
cnf(comb_intros1,axiom,
member(combK,comb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',comb_intros1) ).
cnf(diamond_parcontract_2h2,hypothesis,
member(q,comb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_parcontract_2h2) ).
cnf(c_0_23,axiom,
( member(X2,comb)
| ~ member(comb_app(X1,X2),comb) ),
ap_E2 ).
cnf(c_0_24,axiom,
( X2 = comb_app(combK,k1_parcontractD_sk1(X1,X2))
| ~ member(pair(comb_app(combK,X1),X2),parcontract) ),
k1_parcontractD_1 ).
cnf(c_0_25,axiom,
( member(X2,comb)
| ~ member(pair(X1,X2),parcontract) ),
parcontract_combD2 ).
cnf(c_0_26,axiom,
( X1 = X3
| comb_app(X1,X2) != comb_app(X3,X4) ),
app_app1 ).
cnf(c_0_27,axiom,
( X1 = comb_app(comb_app(combS,ap_parcontractE_sk1p(X1,X2,X3)),ap_parcontractE_sk1q(X1,X2,X3))
| ~ ap_parcontractE_c3(X1,X2,X3) ),
ap_parcontractE11 ).
cnf(c_0_28,axiom,
( member(pair(comb_app(comb_app(combK,X1),X2),X1),parcontract)
| ~ member(X1,comb)
| ~ member(X2,comb) ),
parcontract_intros2 ).
cnf(c_0_29,plain,
( member(k1_parcontractD_sk1(X1,X2),comb)
| ~ member(pair(comb_app(combK,X1),X2),parcontract) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_30,axiom,
( member(pair(X2,ap_parcontractE_sk2s(X1,X2,X3)),parcontract)
| ~ ap_parcontractE_c4(X1,X2,X3) ),
ap_parcontractE13 ).
cnf(c_0_31,axiom,
combK != comb_app(X1,X2),
k_app ).
cnf(c_0_32,plain,
( comb_app(combS,ap_parcontractE_sk1p(comb_app(X1,X2),X3,X4)) = X1
| ~ ap_parcontractE_c3(comb_app(X1,X2),X3,X4) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27])]) ).
cnf(c_0_33,negated_conjecture,
( ~ member(pair(p,X1),parcontract)
| ~ member(pair(yp,X1),parcontract) ),
diamond_parcontract_2c2 ).
cnf(c_0_34,axiom,
( member(pair(X1,k1_parcontractD_sk1(X1,X2)),parcontract)
| ~ member(pair(comb_app(combK,X1),X2),parcontract) ),
k1_parcontractD_2 ).
cnf(c_0_35,plain,
( member(pair(comb_app(X1,X2),k1_parcontractD_sk1(X3,X1)),parcontract)
| ~ member(pair(comb_app(combK,X3),X1),parcontract)
| ~ member(X2,comb) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_24]),c_0_29]) ).
cnf(c_0_36,axiom,
( X3 = comb_app(ap_parcontractE_sk2q(X1,X2,X3),ap_parcontractE_sk2s(X1,X2,X3))
| ~ ap_parcontractE_c4(X1,X2,X3) ),
ap_parcontractE14 ).
cnf(c_0_37,plain,
( member(ap_parcontractE_sk2s(X1,X2,X3),comb)
| ~ ap_parcontractE_c4(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_30]) ).
cnf(c_0_38,axiom,
( X2 = X4
| comb_app(X1,X2) != comb_app(X3,X4) ),
app_app2 ).
cnf(c_0_39,axiom,
( ap_parcontractE_c1(X1,X2,X3)
| ap_parcontractE_c2(X1,X2,X3)
| ap_parcontractE_c3(X1,X2,X3)
| ap_parcontractE_c4(X1,X2,X3)
| ~ member(pair(comb_app(X1,X2),X3),parcontract) ),
ap_parcontractE1 ).
cnf(c_0_40,negated_conjecture,
member(pair(comb_app(comb_app(combK,p),q),yp),parcontract),
diamond_parcontract_2c1 ).
cnf(c_0_41,plain,
~ ap_parcontractE_c3(comb_app(combK,X1),X2,X3),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32])]) ).
cnf(c_0_42,negated_conjecture,
( ~ member(pair(yp,k1_parcontractD_sk1(p,X1)),parcontract)
| ~ member(pair(comb_app(combK,p),X1),parcontract) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_43,plain,
( member(pair(X1,k1_parcontractD_sk1(X2,ap_parcontractE_sk2q(X3,X4,X1))),parcontract)
| ~ ap_parcontractE_c4(X3,X4,X1)
| ~ member(pair(comb_app(combK,X2),ap_parcontractE_sk2q(X3,X4,X1)),parcontract) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_44,axiom,
( X1 = combK
| ~ member(pair(combK,X1),parcontract) ),
k_parcontractE2 ).
cnf(c_0_45,plain,
( k1_parcontractD_sk1(X1,comb_app(X2,X3)) = X3
| ~ member(pair(comb_app(combK,X1),comb_app(X2,X3)),parcontract) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_24])]) ).
cnf(c_0_46,axiom,
( X3 = comb_app(X1,X2)
| ~ ap_parcontractE_c1(X1,X2,X3) ),
ap_parcontractE3 ).
cnf(c_0_47,negated_conjecture,
( ap_parcontractE_c4(comb_app(combK,p),q,yp)
| ap_parcontractE_c2(comb_app(combK,p),q,yp)
| ap_parcontractE_c1(comb_app(combK,p),q,yp) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_48,negated_conjecture,
( ~ ap_parcontractE_c4(X1,X2,yp)
| ~ member(pair(comb_app(combK,p),ap_parcontractE_sk2q(X1,X2,yp)),parcontract) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,axiom,
( member(pair(X1,ap_parcontractE_sk2q(X1,X2,X3)),parcontract)
| ~ ap_parcontractE_c4(X1,X2,X3) ),
ap_parcontractE12 ).
cnf(c_0_50,plain,
( k1_parcontractD_sk1(combK,X1) = combK
| ~ member(pair(comb_app(combK,combK),X1),parcontract) ),
inference(spm,[status(thm)],[c_0_44,c_0_34]) ).
cnf(c_0_51,negated_conjecture,
( ~ member(pair(comb_app(combK,p),comb_app(X1,X2)),parcontract)
| ~ member(pair(yp,X2),parcontract) ),
inference(spm,[status(thm)],[c_0_42,c_0_45]) ).
cnf(c_0_52,negated_conjecture,
( comb_app(comb_app(combK,p),q) = yp
| ap_parcontractE_c4(comb_app(combK,p),q,yp)
| ap_parcontractE_c2(comb_app(combK,p),q,yp) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_53,negated_conjecture,
~ ap_parcontractE_c4(comb_app(combK,p),X1,yp),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,plain,
( member(pair(combK,combK),parcontract)
| ~ member(pair(comb_app(combK,combK),X1),parcontract) ),
inference(spm,[status(thm)],[c_0_34,c_0_50]) ).
cnf(c_0_55,axiom,
( member(pair(comb_app(X1,X3),comb_app(X2,X4)),parcontract)
| ~ member(pair(X1,X2),parcontract)
| ~ member(pair(X3,X4),parcontract) ),
parcontract_intros4 ).
cnf(c_0_56,negated_conjecture,
( ~ member(pair(comb_app(combK,p),X1),parcontract)
| ~ member(pair(yp,k1_parcontractD_sk1(X2,X1)),parcontract)
| ~ member(pair(comb_app(combK,X2),X1),parcontract) ),
inference(spm,[status(thm)],[c_0_51,c_0_24]) ).
cnf(c_0_57,axiom,
( X1 = comb_app(combK,X3)
| ~ ap_parcontractE_c2(X1,X2,X3) ),
ap_parcontractE6 ).
cnf(c_0_58,negated_conjecture,
( comb_app(comb_app(combK,p),q) = yp
| ap_parcontractE_c2(comb_app(combK,p),q,yp) ),
inference(sr,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,axiom,
( member(pair(X1,X1),parcontract)
| ~ member(X1,comb) ),
parcontract_intros1 ).
cnf(c_0_60,hypothesis,
member(p,comb),
diamond_parcontract_2h1 ).
cnf(c_0_61,plain,
( member(pair(combK,combK),parcontract)
| ~ member(pair(combK,X1),parcontract)
| ~ member(pair(combK,X2),parcontract) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,axiom,
member(combK,comb),
comb_intros1 ).
cnf(c_0_63,negated_conjecture,
( ~ member(pair(comb_app(combK,p),X1),parcontract)
| ~ member(pair(comb_app(combK,yp),X1),parcontract) ),
inference(spm,[status(thm)],[c_0_56,c_0_34]) ).
cnf(c_0_64,negated_conjecture,
( comb_app(comb_app(combK,p),q) = yp
| comb_app(combK,p) = comb_app(combK,yp) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_65,hypothesis,
member(q,comb),
diamond_parcontract_2h2 ).
cnf(c_0_66,negated_conjecture,
~ member(pair(yp,p),parcontract),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_59]),c_0_60])]) ).
cnf(c_0_67,plain,
( member(comb_app(X1,X2),comb)
| ~ member(pair(X3,X2),parcontract)
| ~ member(pair(X4,X1),parcontract) ),
inference(spm,[status(thm)],[c_0_25,c_0_55]) ).
cnf(c_0_68,plain,
( member(pair(combK,combK),parcontract)
| ~ member(pair(combK,X1),parcontract) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_59]),c_0_62])]) ).
cnf(c_0_69,negated_conjecture,
~ member(pair(comb_app(combK,yp),comb_app(combK,p)),parcontract),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_59]),c_0_25]) ).
cnf(c_0_70,negated_conjecture,
comb_app(combK,p) = comb_app(combK,yp),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_64]),c_0_65]),c_0_60])]),c_0_66]) ).
cnf(c_0_71,negated_conjecture,
( member(comb_app(X1,yp),comb)
| ~ member(pair(X2,X1),parcontract) ),
inference(spm,[status(thm)],[c_0_67,c_0_40]) ).
cnf(c_0_72,plain,
member(pair(combK,combK),parcontract),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_59]),c_0_62])]) ).
cnf(c_0_73,negated_conjecture,
~ member(pair(comb_app(combK,yp),comb_app(combK,yp)),parcontract),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,negated_conjecture,
member(comb_app(combK,yp),comb),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_75,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_59]),c_0_74])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL095-1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.35 % Computer : n014.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Sun Aug 27 03:51:47 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 1.58/1.71 % Version : CSE_E---1.5
% 1.58/1.71 % Problem : theBenchmark.p
% 1.58/1.71 % Proof found
% 1.58/1.71 % SZS status Theorem for theBenchmark.p
% 1.58/1.71 % SZS output start Proof
% See solution above
% 1.58/1.71 % Total time : 1.131000 s
% 1.58/1.71 % SZS output end Proof
% 1.58/1.71 % Total time : 1.135000 s
%------------------------------------------------------------------------------