%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL092-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:57:41 AM UTC 2026
% Result : Unsatisfiable 7.63s 1.63s
% Output : CNFRefutation 7.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 14
% Syntax : Number of formulae : 103 ( 13 unt; 0 def)
% Number of atoms : 304 ( 152 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 270 ( 69 ~; 201 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 153 ( 7 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ap_parcontractE2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(comb_app(VAR_0,VAR_1),comb)
| ~ ap_parcontractE_c1(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',ap_parcontractE2) ).
cnf(c_57,plain,
( member(comb_app(A,B),comb)
| ~ ap_parcontractE_c1(A,B,C) ),
inference(clausify,[status(thm)],[ap_parcontractE2]) ).
fof(ap_parcontractE1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ap_parcontractE_c4(VAR_0,VAR_1,VAR_2)
| ap_parcontractE_c3(VAR_0,VAR_1,VAR_2)
| ap_parcontractE_c2(VAR_0,VAR_1,VAR_2)
| ap_parcontractE_c1(VAR_0,VAR_1,VAR_2)
| ~ member(pair(comb_app(VAR_0,VAR_1),VAR_2),parcontract) ),
file('theBenchmark.p',ap_parcontractE1) ).
cnf(c_58,plain,
( ap_parcontractE_c4(A,B,C)
| ap_parcontractE_c3(A,B,C)
| ap_parcontractE_c2(A,B,C)
| ap_parcontractE_c1(A,B,C)
| ~ member(pair(comb_app(A,B),C),parcontract) ),
inference(clausify,[status(thm)],[ap_parcontractE1]) ).
fof(ap_parcontractE3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = comb_app(VAR_0,VAR_1)
| ~ ap_parcontractE_c1(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',ap_parcontractE3) ).
cnf(c_59,plain,
( C = comb_app(A,B)
| ~ ap_parcontractE_c1(A,B,C) ),
inference(clausify,[status(thm)],[ap_parcontractE3]) ).
fof(ap_parcontractE6,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = comb_app(combK,VAR_2)
| ~ ap_parcontractE_c2(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',ap_parcontractE6) ).
cnf(c_60,plain,
( A = comb_app(combK,C)
| ~ ap_parcontractE_c2(A,B,C) ),
inference(clausify,[status(thm)],[ap_parcontractE6]) ).
cnf(c_61,plain,
( ap_parcontractE_c4(A,B,C)
| ap_parcontractE_c3(A,B,C)
| ap_parcontractE_c2(A,B,C)
| ~ member(pair(comb_app(A,B),C),parcontract)
| member(comb_app(A,B),comb) ),
inference(resolve,[status(thm)],[c_57,c_58]) ).
cnf(c_62,plain,
( ap_parcontractE_c4(B,C,A)
| ap_parcontractE_c3(B,C,A)
| ap_parcontractE_c2(B,C,A)
| ~ member(pair(comb_app(B,C),A),parcontract)
| A = comb_app(B,C) ),
inference(resolve,[status(thm)],[c_59,c_58]) ).
cnf(c_66,plain,
( ap_parcontractE_c4(A,C,B)
| ap_parcontractE_c3(A,C,B)
| ~ member(pair(comb_app(A,C),B),parcontract)
| member(comb_app(A,C),comb)
| A = comb_app(combK,B) ),
inference(resolve,[status(thm)],[c_60,c_61]) ).
cnf(c_67,plain,
( ap_parcontractE_c4(A,C,B)
| ap_parcontractE_c3(A,C,B)
| ~ member(pair(comb_app(A,C),B),parcontract)
| B = comb_app(A,C)
| A = comb_app(combK,B) ),
inference(resolve,[status(thm)],[c_60,c_62]) ).
fof(ap_parcontractE11,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = comb_app(comb_app(combS,ap_parcontractE_sk1p(VAR_0,VAR_1,VAR_2)),ap_parcontractE_sk1q(VAR_0,VAR_1,VAR_2))
| ~ ap_parcontractE_c3(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',ap_parcontractE11) ).
cnf(c_75,plain,
( A = comb_app(comb_app(combS,ap_parcontractE_sk1p(A,B,C)),ap_parcontractE_sk1q(A,B,C))
| ~ ap_parcontractE_c3(A,B,C) ),
inference(clausify,[status(thm)],[ap_parcontractE11]) ).
fof(ap_parcontractE14,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = comb_app(ap_parcontractE_sk2q(VAR_0,VAR_1,VAR_2),ap_parcontractE_sk2s(VAR_0,VAR_1,VAR_2))
| ~ ap_parcontractE_c4(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',ap_parcontractE14) ).
cnf(c_76,plain,
( C = comb_app(ap_parcontractE_sk2q(A,B,C),ap_parcontractE_sk2s(A,B,C))
| ~ ap_parcontractE_c4(A,B,C) ),
inference(clausify,[status(thm)],[ap_parcontractE14]) ).
cnf(c_97,plain,
( ap_parcontractE_c4(A,B,C)
| ~ member(pair(comb_app(A,B),C),parcontract)
| member(comb_app(A,B),comb)
| A = comb_app(combK,C)
| A = comb_app(comb_app(combS,ap_parcontractE_sk1p(A,B,C)),ap_parcontractE_sk1q(A,B,C)) ),
inference(resolve,[status(thm)],[c_75,c_66]) ).
cnf(c_98,plain,
( ap_parcontractE_c4(A,B,C)
| ~ member(pair(comb_app(A,B),C),parcontract)
| C = comb_app(A,B)
| A = comb_app(combK,C)
| A = comb_app(comb_app(combS,ap_parcontractE_sk1p(A,B,C)),ap_parcontractE_sk1q(A,B,C)) ),
inference(resolve,[status(thm)],[c_75,c_67]) ).
fof(ap_parcontractE13,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(pair(VAR_1,ap_parcontractE_sk2s(VAR_0,VAR_1,VAR_2)),parcontract)
| ~ ap_parcontractE_c4(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',ap_parcontractE13) ).
cnf(c_101,plain,
( member(pair(B,ap_parcontractE_sk2s(A,B,C)),parcontract)
| ~ ap_parcontractE_c4(A,B,C) ),
inference(clausify,[status(thm)],[ap_parcontractE13]) ).
fof(ap_parcontractE12,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(pair(VAR_0,ap_parcontractE_sk2q(VAR_0,VAR_1,VAR_2)),parcontract)
| ~ ap_parcontractE_c4(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',ap_parcontractE12) ).
cnf(c_102,plain,
( member(pair(A,ap_parcontractE_sk2q(A,B,C)),parcontract)
| ~ ap_parcontractE_c4(A,B,C) ),
inference(clausify,[status(thm)],[ap_parcontractE12]) ).
cnf(c_107,plain,
( ~ member(pair(comb_app(A,B),C),parcontract)
| C = comb_app(A,B)
| A = comb_app(combK,C)
| A = comb_app(comb_app(combS,ap_parcontractE_sk1p(A,B,C)),ap_parcontractE_sk1q(A,B,C))
| member(pair(A,ap_parcontractE_sk2q(A,B,C)),parcontract) ),
inference(resolve,[status(thm)],[c_102,c_98]) ).
cnf(c_3550,plain,
( ~ member(pair(comb_app(A,B),C),parcontract)
| C = comb_app(A,B)
| A = comb_app(combK,C)
| comb_app(comb_app(combS,ap_parcontractE_sk1p(A,B,C)),ap_parcontractE_sk1q(A,B,C)) = A
| member(pair(A,ap_parcontractE_sk2q(A,B,C)),parcontract) ),
inference(copy,[status(thm)],[c_107]) ).
cnf(c_3551,plain,
( ~ member(pair(comb_app(A,B),C),parcontract)
| C = comb_app(A,B)
| comb_app(combK,C) = A
| comb_app(comb_app(combS,ap_parcontractE_sk1p(A,B,C)),ap_parcontractE_sk1q(A,B,C)) = A
| member(pair(A,ap_parcontractE_sk2q(A,B,C)),parcontract) ),
inference(copy,[status(thm)],[c_3550]) ).
cnf(c_108,plain,
( ~ member(pair(comb_app(A,B),C),parcontract)
| comb_app(A,B) = C
| comb_app(combK,C) = A
| comb_app(comb_app(combS,ap_parcontractE_sk1p(A,B,C)),ap_parcontractE_sk1q(A,B,C)) = A
| member(pair(A,ap_parcontractE_sk2q(A,B,C)),parcontract) ),
inference(copy,[status(thm)],[c_3551]) ).
cnf(c_109,plain,
( ~ member(pair(comb_app(A,B),C),parcontract)
| member(comb_app(A,B),comb)
| A = comb_app(combK,C)
| A = comb_app(comb_app(combS,ap_parcontractE_sk1p(A,B,C)),ap_parcontractE_sk1q(A,B,C))
| member(pair(A,ap_parcontractE_sk2q(A,B,C)),parcontract) ),
inference(resolve,[status(thm)],[c_102,c_97]) ).
cnf(c_3552,plain,
( ~ member(pair(comb_app(A,B),C),parcontract)
| member(comb_app(A,B),comb)
| A = comb_app(combK,C)
| comb_app(comb_app(combS,ap_parcontractE_sk1p(A,B,C)),ap_parcontractE_sk1q(A,B,C)) = A
| member(pair(A,ap_parcontractE_sk2q(A,B,C)),parcontract) ),
inference(copy,[status(thm)],[c_109]) ).
cnf(c_110,plain,
( ~ member(pair(comb_app(A,B),C),parcontract)
| member(comb_app(A,B),comb)
| comb_app(combK,C) = A
| comb_app(comb_app(combS,ap_parcontractE_sk1p(A,B,C)),ap_parcontractE_sk1q(A,B,C)) = A
| member(pair(A,ap_parcontractE_sk2q(A,B,C)),parcontract) ),
inference(copy,[status(thm)],[c_3552]) ).
cnf(c_145,plain,
( ~ member(pair(comb_app(B,A),C),parcontract)
| C = comb_app(B,A)
| B = comb_app(combK,C)
| B = comb_app(comb_app(combS,ap_parcontractE_sk1p(B,A,C)),ap_parcontractE_sk1q(B,A,C))
| member(pair(A,ap_parcontractE_sk2s(B,A,C)),parcontract) ),
inference(resolve,[status(thm)],[c_101,c_98]) ).
cnf(c_3553,plain,
( ~ member(pair(comb_app(B,A),C),parcontract)
| C = comb_app(B,A)
| B = comb_app(combK,C)
| comb_app(comb_app(combS,ap_parcontractE_sk1p(B,A,C)),ap_parcontractE_sk1q(B,A,C)) = B
| member(pair(A,ap_parcontractE_sk2s(B,A,C)),parcontract) ),
inference(copy,[status(thm)],[c_145]) ).
cnf(c_3554,plain,
( ~ member(pair(comb_app(B,A),C),parcontract)
| C = comb_app(B,A)
| comb_app(combK,C) = B
| comb_app(comb_app(combS,ap_parcontractE_sk1p(B,A,C)),ap_parcontractE_sk1q(B,A,C)) = B
| member(pair(A,ap_parcontractE_sk2s(B,A,C)),parcontract) ),
inference(copy,[status(thm)],[c_3553]) ).
cnf(c_146,plain,
( ~ member(pair(comb_app(B,A),C),parcontract)
| comb_app(B,A) = C
| comb_app(combK,C) = B
| comb_app(comb_app(combS,ap_parcontractE_sk1p(B,A,C)),ap_parcontractE_sk1q(B,A,C)) = B
| member(pair(A,ap_parcontractE_sk2s(B,A,C)),parcontract) ),
inference(copy,[status(thm)],[c_3554]) ).
cnf(c_147,plain,
( ~ member(pair(comb_app(B,A),C),parcontract)
| member(comb_app(B,A),comb)
| B = comb_app(combK,C)
| B = comb_app(comb_app(combS,ap_parcontractE_sk1p(B,A,C)),ap_parcontractE_sk1q(B,A,C))
| member(pair(A,ap_parcontractE_sk2s(B,A,C)),parcontract) ),
inference(resolve,[status(thm)],[c_101,c_97]) ).
cnf(c_3555,plain,
( ~ member(pair(comb_app(B,A),C),parcontract)
| member(comb_app(B,A),comb)
| B = comb_app(combK,C)
| comb_app(comb_app(combS,ap_parcontractE_sk1p(B,A,C)),ap_parcontractE_sk1q(B,A,C)) = B
| member(pair(A,ap_parcontractE_sk2s(B,A,C)),parcontract) ),
inference(copy,[status(thm)],[c_147]) ).
cnf(c_148,plain,
( ~ member(pair(comb_app(B,A),C),parcontract)
| member(comb_app(B,A),comb)
| comb_app(combK,C) = B
| comb_app(comb_app(combS,ap_parcontractE_sk1p(B,A,C)),ap_parcontractE_sk1q(B,A,C)) = B
| member(pair(A,ap_parcontractE_sk2s(B,A,C)),parcontract) ),
inference(copy,[status(thm)],[c_3555]) ).
cnf(c_183,plain,
( ~ member(pair(comb_app(B,C),A),parcontract)
| A = comb_app(B,C)
| B = comb_app(combK,A)
| B = comb_app(comb_app(combS,ap_parcontractE_sk1p(B,C,A)),ap_parcontractE_sk1q(B,C,A))
| A = comb_app(ap_parcontractE_sk2q(B,C,A),ap_parcontractE_sk2s(B,C,A)) ),
inference(resolve,[status(thm)],[c_76,c_98]) ).
cnf(c_3556,plain,
( ~ member(pair(comb_app(B,C),A),parcontract)
| A = comb_app(B,C)
| B = comb_app(combK,A)
| B = comb_app(comb_app(combS,ap_parcontractE_sk1p(B,C,A)),ap_parcontractE_sk1q(B,C,A))
| comb_app(ap_parcontractE_sk2q(B,C,A),ap_parcontractE_sk2s(B,C,A)) = A ),
inference(copy,[status(thm)],[c_183]) ).
cnf(c_3557,plain,
( ~ member(pair(comb_app(B,C),A),parcontract)
| A = comb_app(B,C)
| B = comb_app(combK,A)
| comb_app(comb_app(combS,ap_parcontractE_sk1p(B,C,A)),ap_parcontractE_sk1q(B,C,A)) = B
| comb_app(ap_parcontractE_sk2q(B,C,A),ap_parcontractE_sk2s(B,C,A)) = A ),
inference(copy,[status(thm)],[c_3556]) ).
cnf(c_3558,plain,
( ~ member(pair(comb_app(B,C),A),parcontract)
| A = comb_app(B,C)
| comb_app(combK,A) = B
| comb_app(comb_app(combS,ap_parcontractE_sk1p(B,C,A)),ap_parcontractE_sk1q(B,C,A)) = B
| comb_app(ap_parcontractE_sk2q(B,C,A),ap_parcontractE_sk2s(B,C,A)) = A ),
inference(copy,[status(thm)],[c_3557]) ).
cnf(c_184,plain,
( ~ member(pair(comb_app(A,B),C),parcontract)
| comb_app(A,B) = C
| comb_app(combK,C) = A
| comb_app(comb_app(combS,ap_parcontractE_sk1p(A,B,C)),ap_parcontractE_sk1q(A,B,C)) = A
| comb_app(ap_parcontractE_sk2q(A,B,C),ap_parcontractE_sk2s(A,B,C)) = C ),
inference(copy,[status(thm)],[c_3558]) ).
cnf(c_185,plain,
( ~ member(pair(comb_app(B,C),A),parcontract)
| member(comb_app(B,C),comb)
| B = comb_app(combK,A)
| B = comb_app(comb_app(combS,ap_parcontractE_sk1p(B,C,A)),ap_parcontractE_sk1q(B,C,A))
| A = comb_app(ap_parcontractE_sk2q(B,C,A),ap_parcontractE_sk2s(B,C,A)) ),
inference(resolve,[status(thm)],[c_76,c_97]) ).
cnf(c_3559,plain,
( ~ member(pair(comb_app(B,C),A),parcontract)
| member(comb_app(B,C),comb)
| B = comb_app(combK,A)
| B = comb_app(comb_app(combS,ap_parcontractE_sk1p(B,C,A)),ap_parcontractE_sk1q(B,C,A))
| comb_app(ap_parcontractE_sk2q(B,C,A),ap_parcontractE_sk2s(B,C,A)) = A ),
inference(copy,[status(thm)],[c_185]) ).
cnf(c_3560,plain,
( ~ member(pair(comb_app(B,C),A),parcontract)
| member(comb_app(B,C),comb)
| B = comb_app(combK,A)
| comb_app(comb_app(combS,ap_parcontractE_sk1p(B,C,A)),ap_parcontractE_sk1q(B,C,A)) = B
| comb_app(ap_parcontractE_sk2q(B,C,A),ap_parcontractE_sk2s(B,C,A)) = A ),
inference(copy,[status(thm)],[c_3559]) ).
cnf(c_186,plain,
( ~ member(pair(comb_app(A,B),C),parcontract)
| member(comb_app(A,B),comb)
| comb_app(combK,C) = A
| comb_app(comb_app(combS,ap_parcontractE_sk1p(A,B,C)),ap_parcontractE_sk1q(A,B,C)) = A
| comb_app(ap_parcontractE_sk2q(A,B,C),ap_parcontractE_sk2s(A,B,C)) = C ),
inference(copy,[status(thm)],[c_3560]) ).
fof(k_app,axiom,
! [VAR_0,VAR_1] : combK != comb_app(VAR_0,VAR_1),
file('theBenchmark.p',k_app) ).
cnf(c_346,plain,
combK != comb_app(A,B),
inference(clausify,[status(thm)],[k_app]) ).
cnf(c_347,plain,
comb_app(A,B) != combK,
inference(copy,[status(thm)],[c_346]) ).
fof(ap_E2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_1,comb)
| ~ member(comb_app(VAR_0,VAR_1),comb) ),
file('theBenchmark.p',ap_E2) ).
cnf(c_354,plain,
( member(B,comb)
| ~ member(comb_app(A,B),comb) ),
inference(clausify,[status(thm)],[ap_E2]) ).
fof(parcontract_intros1,axiom,
! [VAR_0] :
( member(pair(VAR_0,VAR_0),parcontract)
| ~ member(VAR_0,comb) ),
file('theBenchmark.p',parcontract_intros1) ).
cnf(c_363,plain,
( member(pair(A,A),parcontract)
| ~ member(A,comb) ),
inference(clausify,[status(thm)],[parcontract_intros1]) ).
fof(k_parcontractE2,axiom,
! [VAR_0] :
( VAR_0 = combK
| ~ member(pair(combK,VAR_0),parcontract) ),
file('theBenchmark.p',k_parcontractE2) ).
cnf(c_367,plain,
( A = combK
| ~ member(pair(combK,A),parcontract) ),
inference(clausify,[status(thm)],[k_parcontractE2]) ).
cnf(c_368,plain,
( combK = A
| ~ member(pair(combK,A),parcontract) ),
inference(copy,[status(thm)],[c_367]) ).
fof(k1_parcontractD_h1,axiom,
member(pair(comb_app(combK,p),r),parcontract),
file('theBenchmark.p',k1_parcontractD_h1) ).
cnf(c_371,plain,
member(pair(comb_app(combK,p),r),parcontract),
inference(clausify,[status(thm)],[k1_parcontractD_h1]) ).
fof(k1_parcontractD_c1,axiom,
! [VAR_0] :
( ~ member(pair(p,VAR_0),parcontract)
| r != comb_app(combK,VAR_0) ),
file('theBenchmark.p',k1_parcontractD_c1) ).
cnf(c_372,plain,
( ~ member(pair(p,A),parcontract)
| r != comb_app(combK,A) ),
inference(clausify,[status(thm)],[k1_parcontractD_c1]) ).
cnf(c_373,plain,
( ~ member(pair(p,A),parcontract)
| comb_app(combK,A) != r ),
inference(copy,[status(thm)],[c_372]) ).
cnf(c_3561,plain,
( member(comb_app(combK,p),comb)
| comb_app(combK,r) = combK
| comb_app(comb_app(combS,ap_parcontractE_sk1p(combK,p,r)),ap_parcontractE_sk1q(combK,p,r)) = combK
| comb_app(ap_parcontractE_sk2q(combK,p,r),ap_parcontractE_sk2s(combK,p,r)) = r ),
inference(resolve,[status(thm)],[c_371,c_186]) ).
cnf(c_3562,plain,
( member(comb_app(combK,p),comb)
| comb_app(combK,r) = combK
| comb_app(ap_parcontractE_sk2q(combK,p,r),ap_parcontractE_sk2s(combK,p,r)) = r ),
inference(resolve,[status(thm)],[c_347,c_3561]) ).
cnf(c_437,plain,
( member(comb_app(combK,p),comb)
| comb_app(ap_parcontractE_sk2q(combK,p,r),ap_parcontractE_sk2s(combK,p,r)) = r ),
inference(resolve,[status(thm)],[c_347,c_3562]) ).
cnf(c_3563,plain,
( comb_app(combK,p) = r
| comb_app(combK,r) = combK
| comb_app(comb_app(combS,ap_parcontractE_sk1p(combK,p,r)),ap_parcontractE_sk1q(combK,p,r)) = combK
| comb_app(ap_parcontractE_sk2q(combK,p,r),ap_parcontractE_sk2s(combK,p,r)) = r ),
inference(resolve,[status(thm)],[c_371,c_184]) ).
cnf(c_3564,plain,
( comb_app(combK,p) = r
| comb_app(combK,r) = combK
| comb_app(ap_parcontractE_sk2q(combK,p,r),ap_parcontractE_sk2s(combK,p,r)) = r ),
inference(resolve,[status(thm)],[c_347,c_3563]) ).
cnf(c_438,plain,
( comb_app(combK,p) = r
| comb_app(ap_parcontractE_sk2q(combK,p,r),ap_parcontractE_sk2s(combK,p,r)) = r ),
inference(resolve,[status(thm)],[c_347,c_3564]) ).
cnf(c_3565,plain,
( member(comb_app(combK,p),comb)
| comb_app(combK,r) = combK
| comb_app(comb_app(combS,ap_parcontractE_sk1p(combK,p,r)),ap_parcontractE_sk1q(combK,p,r)) = combK
| member(pair(p,ap_parcontractE_sk2s(combK,p,r)),parcontract) ),
inference(resolve,[status(thm)],[c_371,c_148]) ).
cnf(c_3566,plain,
( member(comb_app(combK,p),comb)
| comb_app(combK,r) = combK
| member(pair(p,ap_parcontractE_sk2s(combK,p,r)),parcontract) ),
inference(resolve,[status(thm)],[c_347,c_3565]) ).
cnf(c_445,plain,
( member(comb_app(combK,p),comb)
| member(pair(p,ap_parcontractE_sk2s(combK,p,r)),parcontract) ),
inference(resolve,[status(thm)],[c_347,c_3566]) ).
cnf(c_3567,plain,
( comb_app(combK,p) = r
| comb_app(combK,r) = combK
| comb_app(comb_app(combS,ap_parcontractE_sk1p(combK,p,r)),ap_parcontractE_sk1q(combK,p,r)) = combK
| member(pair(p,ap_parcontractE_sk2s(combK,p,r)),parcontract) ),
inference(resolve,[status(thm)],[c_371,c_146]) ).
cnf(c_3568,plain,
( comb_app(combK,p) = r
| comb_app(combK,r) = combK
| member(pair(p,ap_parcontractE_sk2s(combK,p,r)),parcontract) ),
inference(resolve,[status(thm)],[c_347,c_3567]) ).
cnf(c_446,plain,
( comb_app(combK,p) = r
| member(pair(p,ap_parcontractE_sk2s(combK,p,r)),parcontract) ),
inference(resolve,[status(thm)],[c_347,c_3568]) ).
cnf(c_3569,plain,
( member(comb_app(combK,p),comb)
| comb_app(combK,r) = combK
| comb_app(comb_app(combS,ap_parcontractE_sk1p(combK,p,r)),ap_parcontractE_sk1q(combK,p,r)) = combK
| member(pair(combK,ap_parcontractE_sk2q(combK,p,r)),parcontract) ),
inference(resolve,[status(thm)],[c_371,c_110]) ).
cnf(c_3570,plain,
( member(comb_app(combK,p),comb)
| comb_app(combK,r) = combK
| member(pair(combK,ap_parcontractE_sk2q(combK,p,r)),parcontract) ),
inference(resolve,[status(thm)],[c_347,c_3569]) ).
cnf(c_453,plain,
( member(comb_app(combK,p),comb)
| member(pair(combK,ap_parcontractE_sk2q(combK,p,r)),parcontract) ),
inference(resolve,[status(thm)],[c_347,c_3570]) ).
cnf(c_3571,plain,
( comb_app(combK,p) = r
| comb_app(combK,r) = combK
| comb_app(comb_app(combS,ap_parcontractE_sk1p(combK,p,r)),ap_parcontractE_sk1q(combK,p,r)) = combK
| member(pair(combK,ap_parcontractE_sk2q(combK,p,r)),parcontract) ),
inference(resolve,[status(thm)],[c_371,c_108]) ).
cnf(c_3572,plain,
( comb_app(combK,p) = r
| comb_app(combK,r) = combK
| member(pair(combK,ap_parcontractE_sk2q(combK,p,r)),parcontract) ),
inference(resolve,[status(thm)],[c_347,c_3571]) ).
cnf(c_454,plain,
( comb_app(combK,p) = r
| member(pair(combK,ap_parcontractE_sk2q(combK,p,r)),parcontract) ),
inference(resolve,[status(thm)],[c_347,c_3572]) ).
cnf(c_815,plain,
( member(p,comb)
| comb_app(ap_parcontractE_sk2q(combK,p,r),ap_parcontractE_sk2s(combK,p,r)) = r ),
inference(resolve,[status(thm)],[c_437,c_354]) ).
cnf(c_827,plain,
( ~ member(pair(p,p),parcontract)
| comb_app(ap_parcontractE_sk2q(combK,p,r),ap_parcontractE_sk2s(combK,p,r)) = r ),
inference(resolve,[status(thm)],[c_438,c_373]) ).
cnf(c_880,plain,
( member(p,comb)
| member(pair(p,ap_parcontractE_sk2s(combK,p,r)),parcontract) ),
inference(resolve,[status(thm)],[c_445,c_354]) ).
cnf(c_884,plain,
( comb_app(combK,ap_parcontractE_sk2s(combK,p,r)) != r
| comb_app(combK,p) = r ),
inference(resolve,[status(thm)],[c_446,c_373]) ).
cnf(c_906,plain,
( comb_app(combK,ap_parcontractE_sk2s(combK,p,r)) != r
| member(p,comb) ),
inference(resolve,[status(thm)],[c_880,c_373]) ).
cnf(c_3573,plain,
( combK = ap_parcontractE_sk2q(combK,p,r)
| member(comb_app(combK,p),comb) ),
inference(resolve,[status(thm)],[c_453,c_368]) ).
cnf(c_966,plain,
( ap_parcontractE_sk2q(combK,p,r) = combK
| member(comb_app(combK,p),comb) ),
inference(copy,[status(thm)],[c_3573]) ).
cnf(c_3574,plain,
( combK = ap_parcontractE_sk2q(combK,p,r)
| comb_app(combK,p) = r ),
inference(resolve,[status(thm)],[c_454,c_368]) ).
cnf(c_984,plain,
( ap_parcontractE_sk2q(combK,p,r) = combK
| comb_app(combK,p) = r ),
inference(copy,[status(thm)],[c_3574]) ).
cnf(c_1018,plain,
( member(p,comb)
| ap_parcontractE_sk2q(combK,p,r) = combK ),
inference(resolve,[status(thm)],[c_966,c_354]) ).
cnf(c_1052,plain,
( member(pair(p,p),parcontract)
| ap_parcontractE_sk2q(combK,p,r) = combK ),
inference(resolve,[status(thm)],[c_1018,c_363]) ).
cnf(c_1062,plain,
( ~ member(pair(p,p),parcontract)
| ap_parcontractE_sk2q(combK,p,r) = combK ),
inference(resolve,[status(thm)],[c_984,c_373]) ).
cnf(c_3575,plain,
( ap_parcontractE_sk2q(combK,p,r) = combK
| ap_parcontractE_sk2q(combK,p,r) = combK ),
inference(resolve,[status(thm)],[c_1062,c_1052]) ).
cnf(c_1216,plain,
ap_parcontractE_sk2q(combK,p,r) = combK,
inference(copy,[status(thm)],[c_3575]) ).
cnf(c_1245,plain,
( ~ member(pair(p,p),parcontract)
| comb_app(combK,ap_parcontractE_sk2s(combK,p,r)) = r ),
inference(paramod,[status(thm)],[c_1216,c_827]) ).
cnf(c_1251,plain,
( member(p,comb)
| comb_app(combK,ap_parcontractE_sk2s(combK,p,r)) = r ),
inference(paramod,[status(thm)],[c_1216,c_815]) ).
cnf(c_3576,plain,
( member(p,comb)
| member(p,comb) ),
inference(resolve,[status(thm)],[c_1251,c_906]) ).
cnf(c_3254,plain,
member(p,comb),
inference(copy,[status(thm)],[c_3576]) ).
cnf(c_3330,plain,
member(pair(p,p),parcontract),
inference(resolve,[status(thm)],[c_3254,c_363]) ).
cnf(c_3336,plain,
comb_app(combK,ap_parcontractE_sk2s(combK,p,r)) = r,
inference(resolve,[status(thm)],[c_3330,c_1245]) ).
cnf(c_3577,plain,
( r != r
| comb_app(combK,p) = r ),
inference(paramod,[status(thm)],[c_3336,c_884]) ).
cnf(c_3346,plain,
comb_app(combK,p) = r,
inference(copy,[status(thm)],[c_3577]) ).
cnf(c_3578,plain,
comb_app(combK,p) != r,
inference(resolve,[status(thm)],[c_3330,c_373]) ).
cnf(c_3579,plain,
r != r,
inference(paramod,[status(thm)],[c_3346,c_3578]) ).
cnf(c_3549,plain,
$false,
inference(copy,[status(thm)],[c_3579]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL092-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.63 % Computer : n008.cluster.edu
% 0.16/0.63 % Model : x86_64 x86_64
% 0.16/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.63 % Memory : 8046.5625MB
% 0.16/0.63 % OS : Linux 6.8.0-71-generic
% 0.16/0.63 % CPULimit : 300
% 0.16/0.63 % WCLimit : 300
% 0.16/0.63 % DateTime : Sat Sep 26 23:14:26 UTC 2026
% 0.16/0.64 % CPUTime :
% 0.16/0.64 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.64 % Process 602445 was started by sandbox2 on n008,
% 0.16/0.64 % Sat Sep 26 23:14:26 2026
% 0.16/0.64 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.65
% 0.16/0.65 % From the command line: assign(max_seconds, 300).
% 7.63/1.63
% 7.63/1.63 % SZS status Unsatisfiable for theBenchmark
% 7.63/1.63
% 7.63/1.63 % Proof 1 at 0.66 (+ 0.27) seconds.
% 7.63/1.63 % Length of proof is 59.
% 7.63/1.63 % Level of proof is 16.
% 7.63/1.63 % Maximum clause weight is 51.000.
% 7.63/1.63 % Given clauses 381.
% 7.63/1.63
% 7.63/1.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------