%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL046-1 : 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 : n009.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 06:57:31 AM UTC 2026
% Result : Unsatisfiable 7.75s 1.47s
% Output : CNFRefutation 7.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 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 : 37 ( 0 sgn 8 !; 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(m_definition,axiom,
! [VAR_0] : apply(m,VAR_0) = apply(VAR_0,VAR_0),
file('theBenchmark.p',m_definition) ).
cnf(c_3,plain,
apply(m,A) = apply(A,A),
inference(clausify,[status(thm)],[m_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_6,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_18,plain,
apply(apply(apply(b,A),apply(B,C)),apply(D,C)) = apply(A,apply(apply(apply(s,B),D),C)),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_30,plain,
apply(apply(apply(b,A),m),B) = apply(A,apply(B,B)),
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_2021,plain,
apply(apply(apply(s,apply(apply(apply(b,apply(s,A)),m),B)),C),D) = apply(apply(apply(A,D),apply(apply(B,B),D)),apply(C,D)),
inference(paramod,[status(thm)],[c_30,c_6]) ).
cnf(c_3716,plain,
apply(apply(apply(b,f(apply(apply(s,A),B))),apply(A,f(apply(apply(s,A),B)))),apply(B,f(apply(apply(s,A),B)))) != apply(apply(apply(s,A),B),f(apply(apply(s,A),B))),
inference(paramod,[status(thm)],[c_18,c_5]) ).
cnf(c_3718,plain,
apply(apply(apply(A,D),apply(apply(B,B),D)),apply(C,D)) = apply(apply(apply(s,apply(apply(apply(b,apply(s,A)),m),B)),C),D),
inference(copy,[status(thm)],[c_2021]) ).
cnf(c_3717,plain,
$false,
inference(resolve,[status(thm)],[c_3716,c_3718]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL046-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n009.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 23:09:00 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 1375709 was started by sandbox on n009,
% 0.15/0.43 % Sat Sep 26 23:09:00 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 7.75/1.47
% 7.75/1.47 % SZS status Unsatisfiable for theBenchmark
% 7.75/1.47
% 7.75/1.47 % Proof 1 at 0.80 (+ 0.21) seconds.
% 7.75/1.47 % Length of proof is 11.
% 7.75/1.47 % Level of proof is 3.
% 7.75/1.47 % Maximum clause weight is 94.000.
% 7.75/1.47 % Given clauses 57.
% 7.75/1.47
% 7.75/1.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------