%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN083-1 : 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 : n014.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 09:37:00 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 9 unt; 0 def)
% Number of atoms : 9 ( 8 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f_is_associative,axiom,
! [VAR_0,VAR_1,VAR_2] : f(VAR_0,f(VAR_1,VAR_2)) = f(f(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',f_is_associative) ).
cnf(c_1,plain,
f(A,f(B,C)) = f(f(A,B),C),
inference(clausify,[status(thm)],[f_is_associative]) ).
cnf(c_2,plain,
f(f(A,B),C) = f(A,f(B,C)),
inference(copy,[status(thm)],[c_1]) ).
fof(prove_this,axiom,
f(a,f(b,f(c,d))) != f(f(f(a,b),c),d),
file('theBenchmark.p',prove_this) ).
cnf(c_3,plain,
f(a,f(b,f(c,d))) != f(f(f(a,b),c),d),
inference(clausify,[status(thm)],[prove_this]) ).
cnf(c_5,plain,
f(a,f(b,f(c,d))) != f(f(a,f(b,c)),d),
inference(paramod,[status(thm)],[c_2,c_3]) ).
cnf(c_6,plain,
f(a,f(b,f(c,d))) != f(a,f(f(b,c),d)),
inference(paramod,[status(thm)],[c_2,c_5]) ).
cnf(c_7,plain,
f(a,f(b,f(c,d))) != f(a,f(b,f(c,d))),
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_4,plain,
$false,
inference(copy,[status(thm)],[c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN083-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n014.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sat Sep 26 17:10:17 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.47 % Process 3693423 was started by sandbox2 on n014,
% 0.19/0.47 % Sat Sep 26 17:10:17 2026
% 0.19/0.47 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.47
% 0.19/0.47 % From the command line: assign(max_seconds, 300).
% 0.19/0.49
% 0.19/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.49
% 0.19/0.49 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.19/0.49 % Length of proof is 4.
% 0.19/0.49 % Level of proof is 2.
% 0.19/0.49 % Maximum clause weight is 11.000.
% 0.19/0.49 % Given clauses 0.
% 0.19/0.49
% 0.19/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------