%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL006-1 : 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 : n011.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 06:57:22 AM UTC 2026
% Result : Unsatisfiable 18.27s 2.79s
% Output : CNFRefutation 18.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 2 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 : 57 ( 9 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(s,VAR_0),VAR_1),VAR_2) = apply(apply(VAR_0,VAR_2),apply(VAR_1,VAR_2)),
file('theBenchmark.p',s_definition) ).
cnf(c_1,plain,
apply(apply(apply(s,A),B),C) = apply(apply(A,C),apply(B,C)),
inference(clausify,[status(thm)],[s_definition]) ).
fof(k_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(k,VAR_0),VAR_1) = VAR_0,
file('theBenchmark.p',k_definition) ).
cnf(c_2,plain,
apply(apply(k,A),B) = A,
inference(clausify,[status(thm)],[k_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_5,plain,
apply(apply(apply(s,apply(apply(s,A),B)),C),D) = apply(apply(apply(A,D),apply(B,D)),apply(C,D)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_11,plain,
apply(apply(apply(s,apply(k,A)),B),C) = apply(A,apply(B,C)),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_12,plain,
apply(apply(apply(s,A),apply(k,B)),C) = apply(apply(A,C),B),
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_13,plain,
apply(apply(apply(s,k),A),B) = B,
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_35,plain,
apply(apply(apply(s,apply(apply(s,k),A)),B),C) = apply(C,apply(B,C)),
inference(paramod,[status(thm)],[c_2,c_5]) ).
cnf(c_49,plain,
apply(apply(apply(s,A),apply(apply(s,k),B)),C) = apply(apply(A,C),C),
inference(paramod,[status(thm)],[c_13,c_1]) ).
cnf(c_70,plain,
apply(apply(apply(apply(s,s),k),A),B) = apply(apply(A,B),A),
inference(paramod,[status(thm)],[c_1,c_12]) ).
cnf(c_245,plain,
apply(apply(apply(s,apply(s,A)),apply(apply(s,k),B)),C) = apply(apply(A,C),apply(C,C)),
inference(paramod,[status(thm)],[c_49,c_1]) ).
cnf(c_248,plain,
apply(apply(apply(apply(s,s),apply(s,k)),A),B) = apply(apply(A,B),B),
inference(paramod,[status(thm)],[c_1,c_49]) ).
cnf(c_281,plain,
apply(apply(apply(s,apply(A,B)),apply(apply(s,k),C)),A) = apply(apply(apply(apply(apply(s,s),k),A),B),A),
inference(paramod,[status(thm)],[c_70,c_49]) ).
cnf(c_411,plain,
apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,A))),B) = apply(A,apply(B,B)),
inference(paramod,[status(thm)],[c_248,c_11]) ).
cnf(c_980,plain,
apply(apply(apply(s,apply(apply(s,k),A)),B),f(B)) != apply(B,f(B)),
inference(paramod,[status(thm)],[c_35,c_4]) ).
cnf(c_1188,plain,
apply(apply(apply(s,apply(apply(apply(s,s),A),k)),B),f(B)) != apply(B,f(B)),
inference(paramod,[status(thm)],[c_1,c_980]) ).
cnf(c_3545,plain,
apply(apply(apply(s,apply(apply(apply(apply(s,apply(s,s)),apply(apply(s,k),A)),s),k)),B),f(B)) != apply(B,f(B)),
inference(paramod,[status(thm)],[c_245,c_1188]) ).
cnf(c_3273,plain,
apply(apply(apply(s,apply(apply(apply(apply(apply(apply(s,s),k),s),s),s),k)),A),f(A)) != apply(A,f(A)),
inference(paramod,[status(thm)],[c_281,c_3545]) ).
cnf(c_3546,plain,
apply(apply(apply(s,apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,A)))),apply(k,B)),C) = apply(apply(A,apply(C,C)),B),
inference(paramod,[status(thm)],[c_411,c_12]) ).
cnf(c_3543,plain,
apply(apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,A))),B),C) = apply(apply(A,apply(B,B)),C),
inference(paramod,[status(thm)],[c_12,c_3546]) ).
cnf(c_3547,plain,
apply(A,f(A)) != apply(apply(apply(s,apply(apply(apply(apply(apply(apply(s,s),k),s),s),s),k)),A),f(A)),
inference(copy,[status(thm)],[c_3273]) ).
cnf(c_3544,plain,
$false,
inference(resolve,[status(thm)],[c_3543,c_3547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 23:04:44 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 1773849 was started by sandbox2 on n011,
% 0.10/0.36 % Sat Sep 26 23:04:44 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 18.27/2.79
% 18.27/2.79 % Assigning unary symbol f kb_weight 0 and highest precedence (5).
% 18.27/2.79
% 18.27/2.79 % SZS status Unsatisfiable for theBenchmark
% 18.27/2.79
% 18.27/2.79 % Proof 1 at 1.91 (+ 0.34) seconds.
% 18.27/2.79 % Length of proof is 20.
% 18.27/2.79 % Level of proof is 6.
% 18.27/2.79 % Maximum clause weight is 91.000.
% 18.27/2.79 % Given clauses 113.
% 18.27/2.79
% 18.27/2.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------