%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL042-1 : 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 : n016.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 06:57:28 AM UTC 2026
% Result : Unsatisfiable 92.27s 13.12s
% Output : CNFRefutation 92.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 6 !; 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(w1_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(w1,VAR_0),VAR_1) = apply(apply(VAR_1,VAR_0),VAR_0),
file('theBenchmark.p',w1_definition) ).
cnf(c_2,plain,
apply(apply(w1,A),B) = apply(apply(B,A),A),
inference(clausify,[status(thm)],[w1_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_3,plain,
apply(A,f(A)) != apply(f(A),apply(A,f(A))),
inference(clausify,[status(thm)],[prove_fixed_point]) ).
cnf(c_4,plain,
apply(f(A),apply(A,f(A))) != apply(A,f(A)),
inference(copy,[status(thm)],[c_3]) ).
cnf(c_6,plain,
apply(apply(w1,A),apply(b,B)) = apply(B,apply(A,A)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_7,plain,
apply(apply(w1,A),apply(apply(b,B),C)) = apply(apply(B,apply(C,A)),A),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_10263,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_4]) ).
cnf(c_11,plain,
apply(f(apply(apply(b,A),B)),apply(A,apply(B,f(apply(apply(b,A),B))))) != apply(A,apply(B,f(apply(apply(b,A),B)))),
inference(paramod,[status(thm)],[c_1,c_10263]) ).
cnf(c_10264,plain,
apply(f(apply(apply(b,apply(apply(b,A),B)),C)),apply(A,apply(B,apply(C,f(apply(apply(b,apply(apply(b,A),B)),C)))))) != apply(apply(apply(b,A),B),apply(C,f(apply(apply(b,apply(apply(b,A),B)),C)))),
inference(paramod,[status(thm)],[c_1,c_11]) ).
cnf(c_31,plain,
apply(f(apply(apply(b,apply(apply(b,A),B)),C)),apply(A,apply(B,apply(C,f(apply(apply(b,apply(apply(b,A),B)),C)))))) != apply(A,apply(B,apply(C,f(apply(apply(b,apply(apply(b,A),B)),C))))),
inference(paramod,[status(thm)],[c_1,c_10264]) ).
cnf(c_137,plain,
apply(apply(apply(apply(w1,A),apply(b,b)),B),C) = apply(apply(A,A),apply(B,C)),
inference(paramod,[status(thm)],[c_6,c_1]) ).
cnf(c_310,plain,
apply(apply(w1,A),apply(apply(b,apply(b,B)),C)) = apply(B,apply(apply(C,A),A)),
inference(paramod,[status(thm)],[c_7,c_1]) ).
cnf(c_313,plain,
apply(apply(w1,A),apply(apply(b,w1),B)) = apply(apply(A,apply(B,A)),apply(B,A)),
inference(paramod,[status(thm)],[c_7,c_2]) ).
cnf(c_10265,plain,
apply(f(apply(apply(b,apply(apply(b,apply(apply(apply(w1,A),apply(b,b)),B)),C)),D)),apply(apply(A,A),apply(B,apply(C,apply(D,f(apply(apply(b,apply(apply(b,apply(apply(apply(w1,A),apply(b,b)),B)),C)),D))))))) != apply(apply(apply(apply(w1,A),apply(b,b)),B),apply(C,apply(D,f(apply(apply(b,apply(apply(b,apply(apply(apply(w1,A),apply(b,b)),B)),C)),D))))),
inference(paramod,[status(thm)],[c_137,c_31]) ).
cnf(c_3828,plain,
apply(f(apply(apply(b,apply(apply(b,apply(apply(apply(w1,A),apply(b,b)),B)),C)),D)),apply(apply(A,A),apply(B,apply(C,apply(D,f(apply(apply(b,apply(apply(b,apply(apply(apply(w1,A),apply(b,b)),B)),C)),D))))))) != apply(apply(A,A),apply(B,apply(C,apply(D,f(apply(apply(b,apply(apply(b,apply(apply(apply(w1,A),apply(b,b)),B)),C)),D)))))),
inference(paramod,[status(thm)],[c_137,c_10265]) ).
cnf(c_9984,plain,
apply(apply(w1,apply(A,B)),B) = apply(apply(w1,B),apply(apply(b,w1),A)),
inference(paramod,[status(thm)],[c_313,c_2]) ).
cnf(c_10266,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,A)))) = apply(A,apply(apply(w1,apply(apply(b,apply(b,A)),w1)),apply(apply(b,apply(b,A)),w1))),
inference(paramod,[status(thm)],[c_313,c_310]) ).
cnf(c_10267,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,A)))) = apply(A,apply(apply(w1,apply(apply(b,apply(b,A)),w1)),w1)),
inference(paramod,[status(thm)],[c_2,c_10266]) ).
cnf(c_10268,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,A)))) = apply(A,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,A))))),
inference(paramod,[status(thm)],[c_9984,c_10267]) ).
cnf(c_10261,plain,
apply(A,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,A))))) = apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,A)))),
inference(copy,[status(thm)],[c_10268]) ).
cnf(c_10262,plain,
$false,
inference(resolve,[status(thm)],[c_10261,c_3828]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL042-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n016.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 23:12:16 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 1968209 was started by sandbox on n016,
% 0.16/0.43 % Sat Sep 26 23:12:16 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 92.27/13.12
% 92.27/13.12 % SZS status Unsatisfiable for theBenchmark
% 92.27/13.12
% 92.27/13.12 % Proof 1 at 11.78 (+ 0.84) seconds.
% 92.27/13.12 % Length of proof is 15.
% 92.27/13.12 % Level of proof is 5.
% 92.27/13.12 % Maximum clause weight is 76.000.
% 92.27/13.12 % Given clauses 109.
% 92.27/13.12
% 92.27/13.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------