%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL034-1 : 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 06:57:27 AM UTC 2026
% Result : Unsatisfiable 1.84s 1.18s
% Output : CNFRefutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% 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 : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 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 : 32 ( 0 sgn 7 !; 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(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_11,plain,
apply(apply(apply(t,A),apply(b,B)),C) = apply(B,apply(A,C)),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_1308,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_20,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_1308]) ).
cnf(c_642,plain,
apply(m,apply(apply(t,A),apply(b,B))) = apply(B,apply(A,apply(apply(t,A),apply(b,B)))),
inference(paramod,[status(thm)],[c_11,c_2]) ).
cnf(c_1309,plain,
apply(f(apply(apply(b,A),apply(apply(b,B),C))),apply(A,apply(B,apply(C,f(apply(apply(b,A),apply(apply(b,B),C))))))) != apply(A,apply(apply(apply(b,B),C),f(apply(apply(b,A),apply(apply(b,B),C))))),
inference(paramod,[status(thm)],[c_1,c_20]) ).
cnf(c_1306,plain,
apply(f(apply(apply(b,A),apply(apply(b,B),C))),apply(A,apply(B,apply(C,f(apply(apply(b,A),apply(apply(b,B),C))))))) != apply(A,apply(B,apply(C,f(apply(apply(b,A),apply(apply(b,B),C)))))),
inference(paramod,[status(thm)],[c_1,c_1309]) ).
cnf(c_1310,plain,
apply(B,apply(A,apply(apply(t,A),apply(b,B)))) = apply(m,apply(apply(t,A),apply(b,B))),
inference(copy,[status(thm)],[c_642]) ).
cnf(c_1307,plain,
$false,
inference(resolve,[status(thm)],[c_1306,c_1310]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL034-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.76 % Computer : n016.cluster.edu
% 0.12/0.76 % Model : x86_64 x86_64
% 0.12/0.76 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.76 % Memory : 8046.5625MB
% 0.12/0.76 % OS : Linux 6.8.0-71-generic
% 0.12/0.76 % CPULimit : 300
% 0.12/0.76 % WCLimit : 300
% 0.12/0.76 % DateTime : Sat Sep 26 23:11:47 UTC 2026
% 0.12/0.76 % CPUTime :
% 0.12/0.76 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.76 % Process 1966495 was started by sandbox on n016,
% 0.12/0.76 % Sat Sep 26 23:11:47 2026
% 0.12/0.76 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.77
% 0.12/0.77 % From the command line: assign(max_seconds, 300).
% 1.84/1.18
% 1.84/1.18 % SZS status Unsatisfiable for theBenchmark
% 1.84/1.18
% 1.84/1.18 % Proof 1 at 0.20 (+ 0.04) seconds.
% 1.84/1.18 % Length of proof is 10.
% 1.84/1.18 % Level of proof is 4.
% 1.84/1.18 % Maximum clause weight is 44.000.
% 1.84/1.18 % Given clauses 68.
% 1.84/1.18
% 1.84/1.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------