%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COL057-1 : 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 : n007.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 06:57:32 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 11 !; 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(c_definition,axiom,
! [VAR_0,VAR_1,VAR_2] : apply(apply(apply(c,VAR_0),VAR_1),VAR_2) = apply(apply(VAR_0,VAR_2),VAR_1),
file('theBenchmark.p',c_definition) ).
cnf(c_3,plain,
apply(apply(apply(c,A),B),C) = apply(apply(A,C),B),
inference(clausify,[status(thm)],[c_definition]) ).
fof(i_definition,axiom,
! [VAR_0] : apply(i,VAR_0) = VAR_0,
file('theBenchmark.p',i_definition) ).
cnf(c_4,plain,
apply(i,A) = A,
inference(clausify,[status(thm)],[i_definition]) ).
fof(prove_strong_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_strong_fixed_point) ).
cnf(c_5,plain,
apply(A,f(A)) != apply(f(A),apply(A,f(A))),
inference(clausify,[status(thm)],[prove_strong_fixed_point]) ).
cnf(c_6,plain,
apply(f(A),apply(A,f(A))) != apply(A,f(A)),
inference(copy,[status(thm)],[c_5]) ).
cnf(c_24,plain,
apply(apply(apply(s,i),A),B) = apply(B,apply(A,B)),
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_239,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_6]) ).
cnf(c_26,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_239]) ).
cnf(c_240,plain,
apply(f(apply(apply(b,A),i)),apply(A,f(apply(apply(b,A),i)))) != apply(A,apply(i,f(apply(apply(b,A),i)))),
inference(paramod,[status(thm)],[c_4,c_26]) ).
cnf(c_35,plain,
apply(f(apply(apply(b,A),i)),apply(A,f(apply(apply(b,A),i)))) != apply(A,f(apply(apply(b,A),i))),
inference(paramod,[status(thm)],[c_4,c_240]) ).
cnf(c_57,plain,
apply(apply(apply(s,i),i),A) = apply(A,A),
inference(paramod,[status(thm)],[c_4,c_24]) ).
cnf(c_61,plain,
apply(apply(apply(s,i),A),f(apply(apply(b,A),i))) != apply(A,f(apply(apply(b,A),i))),
inference(paramod,[status(thm)],[c_24,c_35]) ).
cnf(c_241,plain,
apply(apply(apply(c,apply(apply(s,i),i)),A),B) = apply(apply(B,B),A),
inference(paramod,[status(thm)],[c_57,c_3]) ).
cnf(c_80,plain,
apply(apply(apply(apply(s,i),i),A),B) = apply(apply(A,A),B),
inference(paramod,[status(thm)],[c_3,c_241]) ).
cnf(c_237,plain,
apply(apply(apply(apply(s,i),i),apply(apply(b,A),B)),C) = apply(apply(A,apply(B,apply(apply(b,A),B))),C),
inference(paramod,[status(thm)],[c_2,c_80]) ).
cnf(c_242,plain,
apply(A,f(apply(apply(b,A),i))) != apply(apply(apply(s,i),A),f(apply(apply(b,A),i))),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_238,plain,
$false,
inference(resolve,[status(thm)],[c_237,c_242]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL057-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.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 23:07:39 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 725434 was started by sandbox on n007,
% 0.09/0.36 % Sat Sep 26 23:07:39 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).
% 0.14/0.44
% 0.14/0.44 % Assigning unary symbol f kb_weight 0 and highest precedence (7).
% 0.14/0.44
% 0.14/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.44
% 0.14/0.44 % Proof 1 at 0.05 (+ 0.01) seconds.
% 0.14/0.44 % Length of proof is 14.
% 0.14/0.44 % Level of proof is 5.
% 0.14/0.44 % Maximum clause weight is 100.000.
% 0.14/0.44 % Given clauses 25.
% 0.14/0.44
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------