%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL036-1 : 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 : n004.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 0.17s 5.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 20 unt; 0 def)
% Number of atoms : 20 ( 19 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 : 45 ( 0 sgn 9 !; 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(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_2,plain,
apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
inference(clausify,[status(thm)],[b_definition]) ).
fof(t_definition,axiom,
! [VAR_0,VAR_1] : apply(apply(t,VAR_0),VAR_1) = apply(VAR_1,VAR_0),
file('theBenchmark.p',t_definition) ).
cnf(c_3,plain,
apply(apply(t,A),B) = apply(B,A),
inference(clausify,[status(thm)],[t_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_164,plain,
apply(apply(apply(b,apply(apply(s,A),B)),C),D) = apply(apply(A,apply(C,D)),apply(B,apply(C,D))),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_165,plain,
apply(apply(apply(s,A),B),apply(C,D)) = apply(apply(A,apply(C,D)),apply(B,apply(C,D))),
inference(paramod,[status(thm)],[c_2,c_164]) ).
cnf(c_16,plain,
apply(apply(A,apply(B,C)),apply(D,apply(B,C))) = apply(apply(apply(s,A),D),apply(B,C)),
inference(copy,[status(thm)],[c_165]) ).
cnf(c_20,plain,
apply(apply(apply(s,t),A),B) = apply(apply(A,B),B),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_166,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_2,c_5]) ).
cnf(c_21,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_2,c_166]) ).
cnf(c_40,plain,
apply(apply(apply(s,t),apply(b,A)),B) = apply(A,apply(B,B)),
inference(paramod,[status(thm)],[c_20,c_2]) ).
cnf(c_167,plain,
apply(apply(apply(s,apply(s,t)),A),apply(b,B)) = apply(B,apply(apply(A,apply(b,B)),apply(A,apply(b,B)))),
inference(paramod,[status(thm)],[c_40,c_1]) ).
cnf(c_162,plain,
apply(apply(apply(s,apply(s,t)),A),apply(b,B)) = apply(B,apply(apply(apply(s,A),A),apply(b,B))),
inference(paramod,[status(thm)],[c_16,c_167]) ).
cnf(c_168,plain,
apply(A,apply(B,f(apply(apply(b,A),B)))) != apply(f(apply(apply(b,A),B)),apply(A,apply(B,f(apply(apply(b,A),B))))),
inference(copy,[status(thm)],[c_21]) ).
cnf(c_163,plain,
$false,
inference(resolve,[status(thm)],[c_162,c_168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL036-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.44 % Computer : n004.cluster.edu
% 0.17/5.44 % Model : x86_64 x86_64
% 0.17/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.44 % Memory : 8046.5625MB
% 0.17/5.44 % OS : Linux 6.8.0-71-generic
% 0.17/5.44 % CPULimit : 300
% 0.17/5.44 % WCLimit : 300
% 0.17/5.44 % DateTime : Sat Sep 26 23:06:42 UTC 2026
% 0.17/5.44 % CPUTime :
% 0.17/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/5.44 % Process 2853553 was started by sandbox2 on n004,
% 0.17/5.44 % Sat Sep 26 23:06:42 2026
% 0.17/5.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/5.45
% 0.17/5.45 % From the command line: assign(max_seconds, 300).
% 0.17/5.49
% 0.17/5.49 % Assigning unary symbol f kb_weight 0 and highest precedence (6).
% 0.17/5.49
% 0.17/5.49 % SZS status Unsatisfiable for theBenchmark
% 0.17/5.49
% 0.17/5.49 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.17/5.49 % Length of proof is 11.
% 0.17/5.49 % Level of proof is 4.
% 0.17/5.49 % Maximum clause weight is 93.000.
% 0.17/5.49 % Given clauses 21.
% 0.17/5.49
% 0.17/5.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------