%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL059-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 06:57:33 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 57 unt; 0 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 21 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(kestrel_exists,axiom,
! [VAR_0,VAR_1] : response(response(kestrel,VAR_0),VAR_1) = VAR_0,
file('theBenchmark.p',kestrel_exists) ).
cnf(c_1,plain,
response(response(kestrel,A),B) = A,
inference(clausify,[status(thm)],[kestrel_exists]) ).
fof(lark_exists,axiom,
! [VAR_0,VAR_1] : response(response(lark,VAR_0),VAR_1) = response(VAR_0,response(VAR_1,VAR_1)),
file('theBenchmark.p',lark_exists) ).
cnf(c_2,plain,
response(response(lark,A),B) = response(A,response(B,B)),
inference(clausify,[status(thm)],[lark_exists]) ).
fof(lark_lemma1,axiom,
! [VAR_0,VAR_1] : response(response(response(lark,lark),VAR_0),VAR_1) = response(response(VAR_0,VAR_0),response(VAR_1,VAR_1)),
file('theBenchmark.p',lark_lemma1) ).
cnf(c_3,plain,
response(response(response(lark,lark),A),B) = response(response(A,A),response(B,B)),
inference(clausify,[status(thm)],[lark_lemma1]) ).
fof(lark_lemma2,axiom,
! [VAR_0,VAR_1] : response(response(response(response(lark,lark),lark),VAR_0),VAR_1) = response(response(response(VAR_0,VAR_0),response(VAR_0,VAR_0)),response(x2,x2)),
file('theBenchmark.p',lark_lemma2) ).
cnf(c_4,plain,
response(response(response(response(lark,lark),lark),A),B) = response(response(response(A,A),response(A,A)),response(x2,x2)),
inference(clausify,[status(thm)],[lark_lemma2]) ).
cnf(c_5,plain,
response(response(response(lark,response(lark,lark)),A),B) = response(response(response(A,A),response(A,A)),response(x2,x2)),
inference(paramod,[status(thm)],[c_2,c_4]) ).
fof(lark_not_egocentric,axiom,
response(l2,l2) != l2,
file('theBenchmark.p',lark_not_egocentric) ).
cnf(c_6,plain,
response(l2,l2) != l2,
inference(clausify,[status(thm)],[lark_not_egocentric]) ).
fof(l2_definition,axiom,
response(lark,lark) = l2,
file('theBenchmark.p',l2_definition) ).
cnf(c_7,plain,
response(lark,lark) = l2,
inference(clausify,[status(thm)],[l2_definition]) ).
cnf(c_8,plain,
l2 = response(lark,lark),
inference(copy,[status(thm)],[c_7]) ).
fof(l3_definition,axiom,
response(l2,lark) = l3,
file('theBenchmark.p',l3_definition) ).
cnf(c_9,plain,
response(l2,lark) = l3,
inference(clausify,[status(thm)],[l3_definition]) ).
cnf(c_48,plain,
response(response(lark,lark),lark) = l3,
inference(paramod,[status(thm)],[c_8,c_9]) ).
cnf(c_10,plain,
response(lark,response(lark,lark)) = l3,
inference(paramod,[status(thm)],[c_2,c_48]) ).
fof(prove_l3_not_egocentric,axiom,
response(l3,l3) = l3,
file('theBenchmark.p',prove_l3_not_egocentric) ).
cnf(c_11,plain,
response(l3,l3) = l3,
inference(clausify,[status(thm)],[prove_l3_not_egocentric]) ).
cnf(c_49,plain,
response(response(lark,lark),l2) != l2,
inference(paramod,[status(thm)],[c_8,c_6]) ).
cnf(c_50,plain,
response(response(lark,lark),response(lark,lark)) != l2,
inference(paramod,[status(thm)],[c_8,c_49]) ).
cnf(c_12,plain,
response(response(lark,lark),response(lark,lark)) != response(lark,lark),
inference(paramod,[status(thm)],[c_8,c_50]) ).
cnf(c_51,plain,
response(response(l3,A),B) = response(response(response(A,A),response(A,A)),response(x2,x2)),
inference(paramod,[status(thm)],[c_10,c_5]) ).
cnf(c_13,plain,
response(response(response(A,A),response(A,A)),response(x2,x2)) = response(response(l3,A),B),
inference(copy,[status(thm)],[c_51]) ).
cnf(c_14,plain,
response(response(response(lark,kestrel),A),B) = response(A,A),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_16,plain,
response(response(lark,A),response(kestrel,B)) = response(A,B),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_52,plain,
response(l3,A) = response(response(lark,lark),response(A,A)),
inference(paramod,[status(thm)],[c_10,c_2]) ).
cnf(c_18,plain,
response(response(lark,lark),response(A,A)) = response(l3,A),
inference(copy,[status(thm)],[c_52]) ).
cnf(c_19,plain,
response(l3,lark) != response(lark,lark),
inference(paramod,[status(thm)],[c_18,c_12]) ).
cnf(c_53,plain,
response(response(l3,response(l3,l3)),response(x2,x2)) = response(response(l3,l3),A),
inference(paramod,[status(thm)],[c_11,c_13]) ).
cnf(c_54,plain,
response(response(l3,l3),response(x2,x2)) = response(response(l3,l3),A),
inference(paramod,[status(thm)],[c_11,c_53]) ).
cnf(c_55,plain,
response(l3,response(x2,x2)) = response(response(l3,l3),A),
inference(paramod,[status(thm)],[c_11,c_54]) ).
cnf(c_24,plain,
response(l3,response(x2,x2)) = response(l3,A),
inference(paramod,[status(thm)],[c_11,c_55]) ).
cnf(c_31,plain,
response(l3,response(x2,x2)) = l3,
inference(paramod,[status(thm)],[c_24,c_11]) ).
cnf(c_56,plain,
response(response(response(l3,response(x2,x2)),response(l3,l3)),response(x2,x2)) = response(response(l3,l3),A),
inference(paramod,[status(thm)],[c_24,c_13]) ).
cnf(c_57,plain,
response(response(l3,response(l3,l3)),response(x2,x2)) = response(response(l3,l3),A),
inference(paramod,[status(thm)],[c_31,c_56]) ).
cnf(c_58,plain,
response(response(l3,l3),response(x2,x2)) = response(response(l3,l3),A),
inference(paramod,[status(thm)],[c_11,c_57]) ).
cnf(c_59,plain,
response(l3,response(x2,x2)) = response(response(l3,l3),A),
inference(paramod,[status(thm)],[c_11,c_58]) ).
cnf(c_60,plain,
l3 = response(response(l3,l3),A),
inference(paramod,[status(thm)],[c_31,c_59]) ).
cnf(c_61,plain,
l3 = response(l3,A),
inference(paramod,[status(thm)],[c_11,c_60]) ).
cnf(c_32,plain,
response(l3,A) = l3,
inference(copy,[status(thm)],[c_61]) ).
cnf(c_62,plain,
response(l3,response(x2,x2)) != response(lark,lark),
inference(paramod,[status(thm)],[c_24,c_19]) ).
cnf(c_63,plain,
l3 != response(lark,lark),
inference(paramod,[status(thm)],[c_32,c_62]) ).
cnf(c_34,plain,
response(lark,lark) != l3,
inference(copy,[status(thm)],[c_63]) ).
cnf(c_64,plain,
response(response(response(lark,lark),lark),kestrel) = response(lark,kestrel),
inference(paramod,[status(thm)],[c_16,c_3]) ).
cnf(c_65,plain,
response(response(lark,response(lark,lark)),kestrel) = response(lark,kestrel),
inference(paramod,[status(thm)],[c_2,c_64]) ).
cnf(c_66,plain,
response(l3,kestrel) = response(lark,kestrel),
inference(paramod,[status(thm)],[c_10,c_65]) ).
cnf(c_67,plain,
l3 = response(lark,kestrel),
inference(paramod,[status(thm)],[c_32,c_66]) ).
cnf(c_44,plain,
response(lark,kestrel) = l3,
inference(copy,[status(thm)],[c_67]) ).
cnf(c_68,plain,
response(response(lark,response(response(lark,kestrel),A)),response(kestrel,B)) = response(A,A),
inference(paramod,[status(thm)],[c_14,c_16]) ).
cnf(c_69,plain,
response(response(lark,response(l3,A)),response(kestrel,B)) = response(A,A),
inference(paramod,[status(thm)],[c_44,c_68]) ).
cnf(c_70,plain,
response(response(lark,l3),response(kestrel,B)) = response(A,A),
inference(paramod,[status(thm)],[c_32,c_69]) ).
cnf(c_71,plain,
response(l3,B) = response(A,A),
inference(paramod,[status(thm)],[c_16,c_70]) ).
cnf(c_72,plain,
l3 = response(A,A),
inference(paramod,[status(thm)],[c_32,c_71]) ).
cnf(c_46,plain,
response(A,A) = l3,
inference(copy,[status(thm)],[c_72]) ).
cnf(c_47,plain,
$false,
inference(resolve,[status(thm)],[c_46,c_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL059-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n010.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 23:09:46 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 272785 was started by sandbox2 on n010,
% 0.07/0.35 % Sat Sep 26 23:09:46 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.37
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.37
% 0.12/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.37 % Length of proof is 24.
% 0.12/0.37 % Level of proof is 9.
% 0.12/0.37 % Maximum clause weight is 45.000.
% 0.12/0.37 % Given clauses 16.
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------