%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL091-2 : 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 : n011.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 0.94s 0.50s
% Output : CNFRefutation 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 12 unt; 0 def)
% Number of atoms : 116 ( 51 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 108 ( 35 ~; 73 |; 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 : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 77 ( 6 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ap_contractE1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ap_contractE_c4(VAR_0,VAR_1,VAR_2)
| ap_contractE_c3(VAR_0,VAR_1,VAR_2)
| ap_contractE_c2(VAR_0,VAR_1,VAR_2)
| ap_contractE_c1(VAR_0,VAR_1,VAR_2)
| ~ member(pair(comb_app(VAR_0,VAR_1),VAR_2),contract) ),
file('theBenchmark.p',ap_contractE1) ).
cnf(c_17,plain,
( ap_contractE_c4(A,B,C)
| ap_contractE_c3(A,B,C)
| ap_contractE_c2(A,B,C)
| ap_contractE_c1(A,B,C)
| ~ member(pair(comb_app(A,B),C),contract) ),
inference(clausify,[status(thm)],[ap_contractE1]) ).
fof(ap_contractE4,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = comb_app(combK,VAR_2)
| ~ ap_contractE_c1(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',ap_contractE4) ).
cnf(c_20,plain,
( A = comb_app(combK,C)
| ~ ap_contractE_c1(A,B,C) ),
inference(clausify,[status(thm)],[ap_contractE4]) ).
cnf(c_24,plain,
( A = comb_app(combK,C)
| ap_contractE_c4(A,B,C)
| ap_contractE_c3(A,B,C)
| ap_contractE_c2(A,B,C)
| ~ member(pair(comb_app(A,B),C),contract) ),
inference(resolve,[status(thm)],[c_17,c_20]) ).
fof(ap_contractE9,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = comb_app(comb_app(combS,ap_contractE_sk1p(VAR_0,VAR_1,VAR_2)),ap_contractE_sk1q(VAR_0,VAR_1,VAR_2))
| ~ ap_contractE_c2(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',ap_contractE9) ).
cnf(c_28,plain,
( A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C))
| ~ ap_contractE_c2(A,B,C) ),
inference(clausify,[status(thm)],[ap_contractE9]) ).
cnf(c_41,plain,
( A = comb_app(combK,C)
| ap_contractE_c4(A,B,C)
| ap_contractE_c3(A,B,C)
| ~ member(pair(comb_app(A,B),C),contract)
| A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) ),
inference(resolve,[status(thm)],[c_28,c_24]) ).
fof(ap_contractE10,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(pair(VAR_0,ap_contractE_sk2q(VAR_0,VAR_1,VAR_2)),contract)
| ~ ap_contractE_c3(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',ap_contractE10) ).
cnf(c_43,plain,
( member(pair(A,ap_contractE_sk2q(A,B,C)),contract)
| ~ ap_contractE_c3(A,B,C) ),
inference(clausify,[status(thm)],[ap_contractE10]) ).
fof(ap_contractE13,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(pair(VAR_1,ap_contractE_sk3q(VAR_0,VAR_1,VAR_2)),contract)
| ~ ap_contractE_c4(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',ap_contractE13) ).
cnf(c_44,plain,
( member(pair(B,ap_contractE_sk3q(A,B,C)),contract)
| ~ ap_contractE_c4(A,B,C) ),
inference(clausify,[status(thm)],[ap_contractE13]) ).
cnf(c_70,plain,
( A = comb_app(combK,C)
| ap_contractE_c4(A,B,C)
| ~ member(pair(comb_app(A,B),C),contract)
| A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C))
| member(pair(A,ap_contractE_sk2q(A,B,C)),contract) ),
inference(resolve,[status(thm)],[c_43,c_41]) ).
fof(ap_contractE15,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = comb_app(VAR_0,ap_contractE_sk3q(VAR_0,VAR_1,VAR_2))
| ~ ap_contractE_c4(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',ap_contractE15) ).
cnf(c_72,plain,
( C = comb_app(A,ap_contractE_sk3q(A,B,C))
| ~ ap_contractE_c4(A,B,C) ),
inference(clausify,[status(thm)],[ap_contractE15]) ).
cnf(c_73,plain,
( B = comb_app(combK,A)
| ~ member(pair(comb_app(B,C),A),contract)
| B = comb_app(comb_app(combS,ap_contractE_sk1p(B,C,A)),ap_contractE_sk1q(B,C,A))
| member(pair(B,ap_contractE_sk2q(B,C,A)),contract)
| A = comb_app(B,ap_contractE_sk3q(B,C,A)) ),
inference(resolve,[status(thm)],[c_72,c_70]) ).
cnf(c_1097,plain,
( B = comb_app(combK,A)
| ~ member(pair(comb_app(B,C),A),contract)
| B = comb_app(comb_app(combS,ap_contractE_sk1p(B,C,A)),ap_contractE_sk1q(B,C,A))
| member(pair(B,ap_contractE_sk2q(B,C,A)),contract)
| comb_app(B,ap_contractE_sk3q(B,C,A)) = A ),
inference(copy,[status(thm)],[c_73]) ).
cnf(c_1098,plain,
( B = comb_app(combK,A)
| ~ member(pair(comb_app(B,C),A),contract)
| comb_app(comb_app(combS,ap_contractE_sk1p(B,C,A)),ap_contractE_sk1q(B,C,A)) = B
| member(pair(B,ap_contractE_sk2q(B,C,A)),contract)
| comb_app(B,ap_contractE_sk3q(B,C,A)) = A ),
inference(copy,[status(thm)],[c_1097]) ).
cnf(c_74,plain,
( comb_app(combK,C) = A
| ~ member(pair(comb_app(A,B),C),contract)
| comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) = A
| member(pair(A,ap_contractE_sk2q(A,B,C)),contract)
| comb_app(A,ap_contractE_sk3q(A,B,C)) = C ),
inference(copy,[status(thm)],[c_1098]) ).
cnf(c_155,plain,
( B = comb_app(combK,C)
| ~ member(pair(comb_app(B,A),C),contract)
| B = comb_app(comb_app(combS,ap_contractE_sk1p(B,A,C)),ap_contractE_sk1q(B,A,C))
| member(pair(B,ap_contractE_sk2q(B,A,C)),contract)
| member(pair(A,ap_contractE_sk3q(B,A,C)),contract) ),
inference(resolve,[status(thm)],[c_44,c_70]) ).
cnf(c_1099,plain,
( B = comb_app(combK,C)
| ~ member(pair(comb_app(B,A),C),contract)
| comb_app(comb_app(combS,ap_contractE_sk1p(B,A,C)),ap_contractE_sk1q(B,A,C)) = B
| member(pair(B,ap_contractE_sk2q(B,A,C)),contract)
| member(pair(A,ap_contractE_sk3q(B,A,C)),contract) ),
inference(copy,[status(thm)],[c_155]) ).
cnf(c_156,plain,
( comb_app(combK,C) = B
| ~ member(pair(comb_app(B,A),C),contract)
| comb_app(comb_app(combS,ap_contractE_sk1p(B,A,C)),ap_contractE_sk1q(B,A,C)) = B
| member(pair(B,ap_contractE_sk2q(B,A,C)),contract)
| member(pair(A,ap_contractE_sk3q(B,A,C)),contract) ),
inference(copy,[status(thm)],[c_1099]) ).
fof(k1_contractD_c1,axiom,
! [VAR_0] :
( ~ member(pair(p,VAR_0),contract)
| r != comb_app(combK,VAR_0) ),
file('theBenchmark.p',k1_contractD_c1) ).
cnf(c_194,plain,
( ~ member(pair(p,A),contract)
| r != comb_app(combK,A) ),
inference(clausify,[status(thm)],[k1_contractD_c1]) ).
cnf(c_195,plain,
( ~ member(pair(p,A),contract)
| comb_app(combK,A) != r ),
inference(copy,[status(thm)],[c_194]) ).
fof(k1_contractD_h1,axiom,
member(pair(comb_app(combK,p),r),contract),
file('theBenchmark.p',k1_contractD_h1) ).
cnf(c_196,plain,
member(pair(comb_app(combK,p),r),contract),
inference(clausify,[status(thm)],[k1_contractD_h1]) ).
fof(k_contractE,axiom,
! [VAR_0] : ~ member(pair(combK,VAR_0),contract),
file('theBenchmark.p',k_contractE) ).
cnf(c_198,plain,
~ member(pair(combK,A),contract),
inference(clausify,[status(thm)],[k_contractE]) ).
fof(k_app,axiom,
! [VAR_0,VAR_1] : combK != comb_app(VAR_0,VAR_1),
file('theBenchmark.p',k_app) ).
cnf(c_212,plain,
combK != comb_app(A,B),
inference(clausify,[status(thm)],[k_app]) ).
cnf(c_213,plain,
comb_app(A,B) != combK,
inference(copy,[status(thm)],[c_212]) ).
cnf(c_1100,plain,
( comb_app(combK,r) = combK
| comb_app(comb_app(combS,ap_contractE_sk1p(combK,p,r)),ap_contractE_sk1q(combK,p,r)) = combK
| member(pair(combK,ap_contractE_sk2q(combK,p,r)),contract)
| member(pair(p,ap_contractE_sk3q(combK,p,r)),contract) ),
inference(resolve,[status(thm)],[c_196,c_156]) ).
cnf(c_1101,plain,
( comb_app(combK,r) = combK
| comb_app(comb_app(combS,ap_contractE_sk1p(combK,p,r)),ap_contractE_sk1q(combK,p,r)) = combK
| member(pair(p,ap_contractE_sk3q(combK,p,r)),contract) ),
inference(resolve,[status(thm)],[c_198,c_1100]) ).
cnf(c_1102,plain,
( comb_app(combK,r) = combK
| member(pair(p,ap_contractE_sk3q(combK,p,r)),contract) ),
inference(resolve,[status(thm)],[c_213,c_1101]) ).
cnf(c_411,plain,
member(pair(p,ap_contractE_sk3q(combK,p,r)),contract),
inference(resolve,[status(thm)],[c_213,c_1102]) ).
cnf(c_1103,plain,
( comb_app(combK,r) = combK
| comb_app(comb_app(combS,ap_contractE_sk1p(combK,p,r)),ap_contractE_sk1q(combK,p,r)) = combK
| member(pair(combK,ap_contractE_sk2q(combK,p,r)),contract)
| comb_app(combK,ap_contractE_sk3q(combK,p,r)) = r ),
inference(resolve,[status(thm)],[c_196,c_74]) ).
cnf(c_1104,plain,
( comb_app(combK,r) = combK
| comb_app(comb_app(combS,ap_contractE_sk1p(combK,p,r)),ap_contractE_sk1q(combK,p,r)) = combK
| comb_app(combK,ap_contractE_sk3q(combK,p,r)) = r ),
inference(resolve,[status(thm)],[c_198,c_1103]) ).
cnf(c_1105,plain,
( comb_app(combK,r) = combK
| comb_app(combK,ap_contractE_sk3q(combK,p,r)) = r ),
inference(resolve,[status(thm)],[c_213,c_1104]) ).
cnf(c_422,plain,
comb_app(combK,ap_contractE_sk3q(combK,p,r)) = r,
inference(resolve,[status(thm)],[c_213,c_1105]) ).
cnf(c_1106,plain,
comb_app(combK,ap_contractE_sk3q(combK,p,r)) != r,
inference(resolve,[status(thm)],[c_411,c_195]) ).
cnf(c_1107,plain,
r != r,
inference(paramod,[status(thm)],[c_422,c_1106]) ).
cnf(c_1096,plain,
$false,
inference(copy,[status(thm)],[c_1107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL091-2 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 23:13:14 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 1799049 was started by sandbox2 on n011,
% 0.08/0.35 % Sat Sep 26 23:13:14 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.94/0.50
% 0.94/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.94/0.50
% 0.94/0.50 % Proof 1 at 0.10 (+ 0.03) seconds.
% 0.94/0.50 % Length of proof is 22.
% 0.94/0.50 % Level of proof is 7.
% 0.94/0.50 % Maximum clause weight is 51.000.
% 0.94/0.50 % Given clauses 227.
% 0.94/0.50
% 0.94/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------