%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN083+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 11 unt; 0 def)
% Number of atoms : 11 ( 10 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 18 ( 0 sgn 11 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p61_1,axiom,
! [X,Y,Z] : f(X,f(Y,Z)) = f(f(X,Y),Z),
file('theBenchmark.p',p61_1) ).
fof(pel61,conjecture,
! [X,Y,Z,W] : f(X,f(Y,f(Z,W))) = f(f(f(X,Y),Z),W),
file('theBenchmark.p',pel61) ).
fof(pel61_neg,negated_conjecture,
~ ! [X,Y,Z,W] : f(X,f(Y,f(Z,W))) = f(f(f(X,Y),Z),W),
inference(assume_negation,[status(cth)],[pel61]) ).
cnf(c_3,plain,
f(f(A,B),C) = f(A,f(B,C)),
inference(clausify,[status(thm)],[p61_1]) ).
fof(nnf_2,plain,
? [X,Y,Z,W] : f(f(f(X,Y),Z),W) != f(X,f(Y,f(Z,W))),
inference(fof_nnf,[status(thm)],[pel61_neg]) ).
fof(sk_pel61_neg,plain,
f(f(f(sK0,sK1),sK2),sK3) != f(sK0,f(sK1,f(sK2,sK3))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X,sK0),skolemize(Y,sK1),skolemize(Z,sK2),skolemize(W,sK3)],[nnf_2]) ).
cnf(c_4,negated_conjecture,
f(f(f(sK0,sK1),sK2),sK3) != f(sK0,f(sK1,f(sK2,sK3))),
inference(split_conjunct,[status(thm)],[sk_pel61_neg]) ).
cnf(c_6,negated_conjecture,
f(f(sK0,f(sK1,sK2)),sK3) != f(sK0,f(sK1,f(sK2,sK3))),
inference(paramod,[status(thm)],[c_3,c_4]) ).
cnf(c_7,negated_conjecture,
f(sK0,f(f(sK1,sK2),sK3)) != f(sK0,f(sK1,f(sK2,sK3))),
inference(paramod,[status(thm)],[c_3,c_6]) ).
cnf(c_8,negated_conjecture,
f(sK0,f(sK1,f(sK2,sK3))) != f(sK0,f(sK1,f(sK2,sK3))),
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_5,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN083+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % 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 17:10:30 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 1121723 was started by sandbox2 on n011,
% 0.09/0.36 % Sat Sep 26 17:10:30 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 5.
% 0.13/0.38 % Level of proof is 2.
% 0.13/0.38 % Maximum clause weight is 11.000.
% 0.13/0.38 % Given clauses 0.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------