%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL090-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 06:57:40 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 42 ( 17 unt; 0 def)
% Number of atoms : 99 ( 41 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 91 ( 34 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 77 ( 16 sgn 23 !; 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_2,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_4,plain,
( A = comb_app(combK,C)
| ~ ap_contractE_c1(A,B,C) ),
inference(clausify,[status(thm)],[ap_contractE4]) ).
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_5,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_8,plain,
( ap_contractE_c4(A,C,B)
| ap_contractE_c3(A,C,B)
| ap_contractE_c2(A,C,B)
| ~ member(pair(comb_app(A,C),B),contract)
| A = comb_app(combK,B) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
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_13,plain,
( member(pair(A,ap_contractE_sk2q(A,B,C)),contract)
| ~ ap_contractE_c3(A,B,C) ),
inference(clausify,[status(thm)],[ap_contractE10]) ).
cnf(c_16,plain,
( ap_contractE_c4(A,B,C)
| ap_contractE_c3(A,B,C)
| ~ member(pair(comb_app(A,B),C),contract)
| A = comb_app(combK,C)
| A = comb_app(comb_app(combS,ap_contractE_sk1p(A,B,C)),ap_contractE_sk1q(A,B,C)) ),
inference(resolve,[status(thm)],[c_5,c_8]) ).
cnf(c_31,plain,
( ap_contractE_c4(A,B,C)
| ~ member(pair(comb_app(A,B),C),contract)
| A = comb_app(combK,C)
| 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_13,c_16]) ).
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_56,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_92,plain,
( ~ member(pair(comb_app(B,A),C),contract)
| B = comb_app(combK,C)
| 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_56,c_31]) ).
cnf(c_260,plain,
( ~ member(pair(comb_app(B,A),C),contract)
| B = comb_app(combK,C)
| 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_92]) ).
cnf(c_93,plain,
( ~ member(pair(comb_app(B,A),C),contract)
| comb_app(combK,C) = B
| 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_260]) ).
fof(k_s,axiom,
combK != combS,
file('theBenchmark.p',k_s) ).
cnf(c_180,plain,
combK != combS,
inference(clausify,[status(thm)],[k_s]) ).
cnf(c_181,plain,
combS != combK,
inference(copy,[status(thm)],[c_180]) ).
fof(s_app,axiom,
! [VAR_0,VAR_1] : combS != comb_app(VAR_0,VAR_1),
file('theBenchmark.p',s_app) ).
cnf(c_184,plain,
combS != comb_app(A,B),
inference(clausify,[status(thm)],[s_app]) ).
cnf(c_185,plain,
comb_app(A,B) != combS,
inference(copy,[status(thm)],[c_184]) ).
fof(app_app1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_0 = VAR_2
| comb_app(VAR_0,VAR_1) != comb_app(VAR_2,VAR_3) ),
file('theBenchmark.p',app_app1) ).
cnf(c_186,plain,
( A = C
| comb_app(A,B) != comb_app(C,D) ),
inference(clausify,[status(thm)],[app_app1]) ).
fof(k_contractE,axiom,
! [VAR_0] : ~ member(pair(combK,VAR_0),contract),
file('theBenchmark.p',k_contractE) ).
cnf(c_197,plain,
~ member(pair(combK,A),contract),
inference(clausify,[status(thm)],[k_contractE]) ).
fof(s_contractE,axiom,
! [VAR_0] : ~ member(pair(combS,VAR_0),contract),
file('theBenchmark.p',s_contractE) ).
cnf(c_198,plain,
~ member(pair(combS,A),contract),
inference(clausify,[status(thm)],[s_contractE]) ).
fof(i_contract_E,axiom,
member(pair(comb_app(comb_app(combS,combK),combK),r),contract),
file('theBenchmark.p',i_contract_E) ).
cnf(c_199,plain,
member(pair(comb_app(comb_app(combS,combK),combK),r),contract),
inference(clausify,[status(thm)],[i_contract_E]) ).
cnf(c_220,plain,
comb_app(comb_app(A,B),C) != comb_app(combS,D),
inference(resolve,[status(thm)],[c_186,c_185]) ).
cnf(c_222,plain,
comb_app(combS,A) != comb_app(combK,B),
inference(resolve,[status(thm)],[c_186,c_181]) ).
cnf(c_261,plain,
( ~ member(pair(comb_app(A,combK),B),contract)
| comb_app(combK,B) = A
| comb_app(comb_app(combS,ap_contractE_sk1p(A,combK,B)),ap_contractE_sk1q(A,combK,B)) = A
| member(pair(A,ap_contractE_sk2q(A,combK,B)),contract) ),
inference(resolve,[status(thm)],[c_93,c_197]) ).
cnf(c_262,plain,
( ~ member(pair(comb_app(combS,combK),A),contract)
| comb_app(combK,A) = combS
| comb_app(comb_app(combS,ap_contractE_sk1p(combS,combK,A)),ap_contractE_sk1q(combS,combK,A)) = combS ),
inference(resolve,[status(thm)],[c_261,c_198]) ).
cnf(c_263,plain,
( ~ member(pair(comb_app(combS,combK),A),contract)
| comb_app(combK,A) = combS ),
inference(resolve,[status(thm)],[c_262,c_185]) ).
cnf(c_252,plain,
~ member(pair(comb_app(combS,combK),A),contract),
inference(resolve,[status(thm)],[c_263,c_185]) ).
cnf(c_264,plain,
( comb_app(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)) = comb_app(combS,combK)
| member(pair(comb_app(combS,combK),ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract)
| member(pair(combK,ap_contractE_sk3q(comb_app(combS,combK),combK,r)),contract) ),
inference(resolve,[status(thm)],[c_199,c_93]) ).
cnf(c_265,plain,
( comb_app(combS,combK) = comb_app(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)
| member(pair(comb_app(combS,combK),ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract)
| member(pair(combK,ap_contractE_sk3q(comb_app(combS,combK),combK,r)),contract) ),
inference(copy,[status(thm)],[c_264]) ).
cnf(c_266,plain,
( comb_app(combS,combK) = comb_app(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)
| member(pair(comb_app(combS,combK),ap_contractE_sk2q(comb_app(combS,combK),combK,r)),contract) ),
inference(resolve,[status(thm)],[c_197,c_265]) ).
cnf(c_267,plain,
( comb_app(combS,combK) = comb_app(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(resolve,[status(thm)],[c_252,c_266]) ).
cnf(c_268,plain,
comb_app(combS,combK) = comb_app(combK,r),
inference(resolve,[status(thm)],[c_220,c_267]) ).
cnf(c_259,plain,
$false,
inference(resolve,[status(thm)],[c_222,c_268]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL090-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 23:13:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3791895 was started by sandbox on n013,
% 0.09/0.36 % Sat Sep 26 23:13:06 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.40
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.40
% 0.13/0.40 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.13/0.40 % Length of proof is 22.
% 0.13/0.40 % Level of proof is 7.
% 0.13/0.40 % Maximum clause weight is 41.000.
% 0.13/0.40 % Given clauses 68.
% 0.13/0.40
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------