%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL074-3 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 06:57:37 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 19 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 2 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 12 ( 3 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(k_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(k,VAR_0),VAR_1) = VAR_0,
file('theBenchmark.p',k_definition) ).
cnf(c_1,plain,
apply(apply(k,A),B) = A,
inference(clausify,[status(thm)],[k_definition]) ).
fof(equality,axiom,
! [VAR_0] : apply(eq,pair(VAR_0,VAR_0)) = projection1,
file('theBenchmark.p',equality) ).
cnf(c_9,plain,
apply(eq,pair(A,A)) = projection1,
inference(clausify,[status(thm)],[equality]) ).
fof(extensionality1,axiom,
! [VAR_0,VAR_1] :
( apply(eq,pair(VAR_0,VAR_1)) = projection2
| VAR_0 = VAR_1 ),
file('theBenchmark.p',extensionality1) ).
cnf(c_10,plain,
( apply(eq,pair(A,B)) = projection2
| A = B ),
inference(clausify,[status(thm)],[extensionality1]) ).
fof(different_projections,axiom,
projection1 != projection2,
file('theBenchmark.p',different_projections) ).
cnf(c_13,plain,
projection1 != projection2,
inference(clausify,[status(thm)],[different_projections]) ).
fof(k_projection2,axiom,
apply(k,projection2) = k_projection2,
file('theBenchmark.p',k_projection2) ).
cnf(c_15,plain,
apply(k,projection2) = k_projection2,
inference(clausify,[status(thm)],[k_projection2]) ).
fof(self_referential,axiom,
s = apply(eq,pair(apply(k,s),apply(k,projection2))),
file('theBenchmark.p',self_referential) ).
cnf(c_16,plain,
s = apply(eq,pair(apply(k,s),apply(k,projection2))),
inference(clausify,[status(thm)],[self_referential]) ).
cnf(c_100,plain,
s = apply(eq,pair(apply(k,s),k_projection2)),
inference(paramod,[status(thm)],[c_15,c_16]) ).
cnf(c_17,plain,
apply(eq,pair(apply(k,s),k_projection2)) = s,
inference(copy,[status(thm)],[c_100]) ).
cnf(c_53,plain,
apply(k_projection2,A) = projection2,
inference(paramod,[status(thm)],[c_15,c_1]) ).
cnf(c_60,plain,
( s = projection2
| apply(k,s) = k_projection2 ),
inference(paramod,[status(thm)],[c_17,c_10]) ).
cnf(c_101,plain,
( apply(k_projection2,A) = s
| s = projection2 ),
inference(paramod,[status(thm)],[c_60,c_1]) ).
cnf(c_102,plain,
( projection2 = s
| s = projection2 ),
inference(paramod,[status(thm)],[c_53,c_101]) ).
cnf(c_103,plain,
( s = projection2
| s = projection2 ),
inference(copy,[status(thm)],[c_102]) ).
cnf(c_95,plain,
s = projection2,
inference(copy,[status(thm)],[c_103]) ).
cnf(c_104,plain,
apply(eq,pair(apply(k,projection2),k_projection2)) = s,
inference(paramod,[status(thm)],[c_95,c_17]) ).
cnf(c_105,plain,
apply(eq,pair(k_projection2,k_projection2)) = s,
inference(paramod,[status(thm)],[c_15,c_104]) ).
cnf(c_106,plain,
projection1 = s,
inference(paramod,[status(thm)],[c_9,c_105]) ).
cnf(c_107,plain,
projection1 = projection2,
inference(paramod,[status(thm)],[c_95,c_106]) ).
cnf(c_99,plain,
$false,
inference(resolve,[status(thm)],[c_13,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL074-3 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n018.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 23:13:53 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 1683182 was started by sandbox2 on n018,
% 0.10/0.36 % Sat Sep 26 23:13:53 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 11.
% 0.13/0.38 % Level of proof is 4.
% 0.13/0.38 % Maximum clause weight is 29.000.
% 0.13/0.38 % Given clauses 21.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------