%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET838-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 08:37:05 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 11 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 16 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 7 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
v_f(v_g(v_x)) = v_x,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_1,plain,
v_f(v_g(v_x)) = v_x,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] :
( v_f(v_g(VAR_0)) != VAR_0
| VAR_0 = v_x ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2,plain,
( v_f(v_g(A)) != A
| A = v_x ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_3,plain,
( v_f(v_g(A)) != A
| v_x = A ),
inference(copy,[status(thm)],[c_2]) ).
fof(cls_conjecture_2,axiom,
! [VAR_0] :
( v_g(v_f(VAR_0)) != VAR_0
| v_g(v_f(v_xa(VAR_0))) = v_xa(VAR_0) ),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_4,plain,
( v_g(v_f(A)) != A
| v_g(v_f(v_xa(A))) = v_xa(A) ),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
! [VAR_0] :
( v_g(v_f(VAR_0)) != VAR_0
| v_xa(VAR_0) != VAR_0 ),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_5,plain,
( v_g(v_f(A)) != A
| v_xa(A) != A ),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_12,plain,
( v_g(v_x) != v_g(v_x)
| v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x)) ),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_6,plain,
v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x)),
inference(copy,[status(thm)],[c_12]) ).
cnf(c_8,plain,
v_xa(v_xa(v_g(v_x))) != v_xa(v_g(v_x)),
inference(resolve,[status(thm)],[c_5,c_6]) ).
cnf(c_13,plain,
( v_f(v_xa(v_g(v_x))) != v_f(v_xa(v_g(v_x)))
| v_x = v_f(v_xa(v_g(v_x))) ),
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_14,plain,
( v_f(v_xa(v_g(v_x))) != v_f(v_xa(v_g(v_x)))
| v_f(v_xa(v_g(v_x))) = v_x ),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_9,plain,
v_f(v_xa(v_g(v_x))) = v_x,
inference(copy,[status(thm)],[c_14]) ).
cnf(c_15,plain,
v_g(v_x) = v_xa(v_g(v_x)),
inference(paramod,[status(thm)],[c_9,c_6]) ).
cnf(c_10,plain,
v_xa(v_g(v_x)) = v_g(v_x),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_16,plain,
v_xa(v_g(v_x)) != v_xa(v_g(v_x)),
inference(paramod,[status(thm)],[c_10,c_8]) ).
cnf(c_17,plain,
v_g(v_x) != v_xa(v_g(v_x)),
inference(paramod,[status(thm)],[c_10,c_16]) ).
cnf(c_18,plain,
v_g(v_x) != v_g(v_x),
inference(paramod,[status(thm)],[c_10,c_17]) ).
cnf(c_11,plain,
$false,
inference(copy,[status(thm)],[c_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET838-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 08:21:53 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 2426594 was started by sandbox2 on n003,
% 0.09/0.36 % Sat Sep 26 08:21:53 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 10.
% 0.09/0.38 % Level of proof is 4.
% 0.09/0.38 % Maximum clause weight is 12.000.
% 0.09/0.38 % Given clauses 5.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------