%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET838-1 : 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 : n020.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 21.01s 3.55s
% Output : CNFRefutation 21.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 15 ~; 11 |; 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_654,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_655,plain,
( v_f(v_g(A)) != A
| A = v_x ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_656,plain,
( v_f(v_g(A)) != A
| v_x = A ),
inference(copy,[status(thm)],[c_655]) ).
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_657,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_658,plain,
( v_g(v_f(A)) != A
| v_xa(A) != A ),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_3127,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_654,c_657]) ).
cnf(c_1941,plain,
v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x)),
inference(copy,[status(thm)],[c_3127]) ).
cnf(c_3128,plain,
( v_g(v_x) != v_g(v_x)
| v_xa(v_g(v_x)) != v_g(v_x) ),
inference(paramod,[status(thm)],[c_654,c_658]) ).
cnf(c_1942,plain,
v_xa(v_g(v_x)) != v_g(v_x),
inference(copy,[status(thm)],[c_3128]) ).
cnf(c_3129,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_1941,c_656]) ).
cnf(c_3130,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_3129]) ).
cnf(c_3125,plain,
v_f(v_xa(v_g(v_x))) = v_x,
inference(copy,[status(thm)],[c_3130]) ).
cnf(c_3131,plain,
v_g(v_x) = v_xa(v_g(v_x)),
inference(paramod,[status(thm)],[c_3125,c_1941]) ).
cnf(c_3132,plain,
v_xa(v_g(v_x)) = v_g(v_x),
inference(copy,[status(thm)],[c_3131]) ).
cnf(c_3126,plain,
$false,
inference(resolve,[status(thm)],[c_1942,c_3132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET838-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n020.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 08:21:03 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 1070054 was started by sandbox2 on n020,
% 0.17/0.44 % Sat Sep 26 08:21:03 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.49
% 0.17/0.49 % From the command line: assign(max_seconds, 300).
% 21.01/3.55
% 21.01/3.55 % given #500 (I,wt=22): 933 -class_LOrder_Omeet__semilorder(A) | -c_lessequals(B,C,A) | c_in(B,c_SetInterval_OatMost(C,A),A). [resolve(88,b,78,a)].
% 21.01/3.55
% 21.01/3.55 % given #1000 (I,wt=7): 1433 class_Power_Orecpower(tc_nat) # tptp_name(clsarity_nat_45) # clausal_fof(1). [assumption].
% 21.01/3.55
% 21.01/3.55 % SZS status Unsatisfiable for theBenchmark
% 21.01/3.55
% 21.01/3.55 % Proof 1 at 2.76 (+ 0.22) seconds.
% 21.01/3.55 % Length of proof is 9.
% 21.01/3.55 % Level of proof is 3.
% 21.01/3.55 % Maximum clause weight is 34.000.
% 21.01/3.55 % Given clauses 1432.
% 21.01/3.55
% 21.01/3.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------