%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL038-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 06:57:27 AM UTC 2026
% Result : Unsatisfiable 6.63s 1.76s
% Output : CNFRefutation 6.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(b_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(b,VAR_0),VAR_1),VAR_2) = apply(VAR_0,apply(VAR_1,VAR_2)),
file('theBenchmark.p',b_definition) ).
cnf(c_1,plain,
apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
inference(clausify,[status(thm)],[b_definition]) ).
fof(m_definition,axiom,
! [VAR_0] : apply(m,VAR_0) = apply(VAR_0,VAR_0),
file('theBenchmark.p',m_definition) ).
cnf(c_2,plain,
apply(m,A) = apply(A,A),
inference(clausify,[status(thm)],[m_definition]) ).
fof(v_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(v,VAR_0),VAR_1),VAR_2) = apply(apply(VAR_2,VAR_0),VAR_1),
file('theBenchmark.p',v_definition) ).
cnf(c_3,plain,
apply(apply(apply(v,A),B),C) = apply(apply(C,A),B),
inference(clausify,[status(thm)],[v_definition]) ).
fof(prove_fixed_point,axiom,
! [VAR_0] : apply(VAR_0,f(VAR_0)) != apply(f(VAR_0),apply(VAR_0,f(VAR_0))),
file('theBenchmark.p',prove_fixed_point) ).
cnf(c_4,plain,
apply(A,f(A)) != apply(f(A),apply(A,f(A))),
inference(clausify,[status(thm)],[prove_fixed_point]) ).
cnf(c_5,plain,
apply(f(A),apply(A,f(A))) != apply(A,f(A)),
inference(copy,[status(thm)],[c_4]) ).
cnf(c_9,plain,
apply(apply(apply(b,m),A),B) = apply(apply(A,B),apply(A,B)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_16,plain,
apply(apply(apply(b,apply(apply(v,A),B)),C),D) = apply(apply(apply(C,D),A),B),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_17,plain,
apply(apply(apply(apply(v,A),B),b),C) = apply(A,apply(B,C)),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_32,plain,
apply(f(apply(apply(b,A),B)),apply(A,apply(B,f(apply(apply(b,A),B))))) != apply(apply(apply(b,A),B),f(apply(apply(b,A),B))),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_2143,plain,
apply(apply(apply(apply(b,apply(apply(v,A),b)),v),B),C) = apply(B,apply(A,C)),
inference(paramod,[status(thm)],[c_16,c_17]) ).
cnf(c_6618,plain,
apply(f(apply(apply(b,m),A)),apply(m,apply(A,f(apply(apply(b,m),A))))) != apply(apply(A,f(apply(apply(b,m),A))),apply(A,f(apply(apply(b,m),A)))),
inference(paramod,[status(thm)],[c_9,c_32]) ).
cnf(c_6616,plain,
apply(apply(A,f(apply(apply(b,m),A))),apply(A,f(apply(apply(b,m),A)))) != apply(f(apply(apply(b,m),A)),apply(m,apply(A,f(apply(apply(b,m),A))))),
inference(copy,[status(thm)],[c_6618]) ).
cnf(c_6617,plain,
$false,
inference(resolve,[status(thm)],[c_6616,c_2143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL038-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n005.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % 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 23:07:03 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 3322902 was started by sandbox on n005,
% 0.08/0.35 % Sat Sep 26 23:07:03 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 6.63/1.76
% 6.63/1.76 % SZS status Unsatisfiable for theBenchmark
% 6.63/1.76
% 6.63/1.76 % Proof 1 at 0.74 (+ 0.13) seconds.
% 6.63/1.76 % Length of proof is 12.
% 6.63/1.76 % Level of proof is 4.
% 6.63/1.76 % Maximum clause weight is 86.000.
% 6.63/1.76 % Given clauses 97.
% 6.63/1.76
% 6.63/1.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------