%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL002-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 06:57:19 AM UTC 2026
% Result : Unsatisfiable 123.11s 17.21s
% Output : CNFRefutation 123.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 29 ( 1 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ifeq_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : ifeq(VAR_0,VAR_0,VAR_1,VAR_2) = VAR_1,
file('theBenchmark.p',ifeq_axiom) ).
cnf(c_1,plain,
ifeq(A,A,B,C) = B,
inference(clausify,[status(thm)],[ifeq_axiom]) ).
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_2,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_3,plain,
apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)),
inference(clausify,[status(thm)],[b_definition]) ).
fof(i_definition,axiom,
! [VAR_0] : apply(i,VAR_0) = VAR_0,
file('theBenchmark.p',i_definition) ).
cnf(c_5,plain,
apply(i,A) = A,
inference(clausify,[status(thm)],[i_definition]) ).
fof(weak_fixed_point,axiom,
! [VAR_0] : ifeq(VAR_0,apply(fixed_pt,VAR_0),fixed_point(VAR_0),true) = true,
file('theBenchmark.p',weak_fixed_point) ).
cnf(c_6,plain,
ifeq(A,apply(fixed_pt,A),fixed_point(A),true) = true,
inference(clausify,[status(thm)],[weak_fixed_point]) ).
fof(prove_weak_fixed_point,axiom,
! [VAR_0] : fixed_point(apply(apply(apply(s,apply(b,VAR_0)),i),apply(apply(s,apply(b,VAR_0)),i))) != true,
file('theBenchmark.p',prove_weak_fixed_point) ).
cnf(c_7,plain,
fixed_point(apply(apply(apply(s,apply(b,A)),i),apply(apply(s,apply(b,A)),i))) != true,
inference(clausify,[status(thm)],[prove_weak_fixed_point]) ).
cnf(c_57,plain,
apply(apply(apply(s,A),i),B) = apply(apply(A,B),B),
inference(paramod,[status(thm)],[c_5,c_2]) ).
cnf(c_61,plain,
ifeq(apply(A,B),apply(apply(apply(b,fixed_pt),A),B),fixed_point(apply(A,B)),true) = true,
inference(paramod,[status(thm)],[c_3,c_6]) ).
cnf(c_306,plain,
ifeq(apply(A,A),apply(apply(apply(s,apply(b,fixed_pt)),i),A),fixed_point(apply(A,A)),true) = true,
inference(paramod,[status(thm)],[c_57,c_61]) ).
cnf(c_3141,plain,
true = fixed_point(apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i))),
inference(paramod,[status(thm)],[c_306,c_1]) ).
cnf(c_3139,plain,
fixed_point(apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i))) = true,
inference(copy,[status(thm)],[c_3141]) ).
cnf(c_3140,plain,
$false,
inference(resolve,[status(thm)],[c_3139,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL002-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 23:04:09 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 4016521 was started by sandbox on n003,
% 0.09/0.36 % Sat Sep 26 23:04:09 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 123.11/17.21
% 123.11/17.21 % SZS status Unsatisfiable for theBenchmark
% 123.11/17.21
% 123.11/17.21 % Proof 1 at 0.54 (+ 0.18) seconds.
% 123.11/17.21 % Length of proof is 11.
% 123.11/17.21 % Level of proof is 4.
% 123.11/17.21 % Maximum clause weight is 78.000.
% 123.11/17.21 % Given clauses 129.
% 123.11/17.21
% 123.11/17.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------