%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : COM009-1 : 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 : n013.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 06:59:37 AM UTC 2026
% Result : Unsatisfiable 22.67s 3.43s
% Output : CNFRefutation 22.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 6 unt; 0 def)
% Number of atoms : 20 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 7 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 1 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_UNITY_Oall__total__imp__totalize_0,axiom,
! [VAR_0,VAR_1] :
( c_UNITY_Ototalize(VAR_0,VAR_1) = VAR_0
| ~ c_UNITY_Oall__total(VAR_0,VAR_1) ),
file('theBenchmark.p',cls_UNITY_Oall__total__imp__totalize_0) ).
cnf(c_2461,plain,
( c_UNITY_Ototalize(A,B) = A
| ~ c_UNITY_Oall__total(A,B) ),
inference(clausify,[status(thm)],[cls_UNITY_Oall__total__imp__totalize_0]) ).
fof(cls_UNITY_Oall__total__totalize_0,axiom,
! [VAR_0,VAR_1] : c_UNITY_Oall__total(c_UNITY_Ototalize(VAR_0,VAR_1),VAR_1),
file('theBenchmark.p',cls_UNITY_Oall__total__totalize_0) ).
cnf(c_2462,plain,
c_UNITY_Oall__total(c_UNITY_Ototalize(A,B),B),
inference(clausify,[status(thm)],[cls_UNITY_Oall__total__totalize_0]) ).
fof(cls_conjecture_0,axiom,
( ~ c_UNITY_Oall__total(v_F,t_a)
| c_UNITY_Ototalize(v_F,t_a) != v_F ),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_2472,plain,
( ~ c_UNITY_Oall__total(v_F,t_a)
| c_UNITY_Ototalize(v_F,t_a) != v_F ),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
( c_UNITY_Ototalize(v_F,t_a) = v_F
| c_UNITY_Oall__total(v_F,t_a) ),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_2473,plain,
( c_UNITY_Ototalize(v_F,t_a) = v_F
| c_UNITY_Oall__total(v_F,t_a) ),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_3834,plain,
( c_UNITY_Ototalize(v_F,t_a) = v_F
| c_UNITY_Ototalize(v_F,t_a) = v_F ),
inference(resolve,[status(thm)],[c_2473,c_2461]) ).
cnf(c_3513,plain,
c_UNITY_Ototalize(v_F,t_a) = v_F,
inference(copy,[status(thm)],[c_3834]) ).
cnf(c_3514,plain,
~ c_UNITY_Oall__total(v_F,t_a),
inference(resolve,[status(thm)],[c_3513,c_2472]) ).
cnf(c_3835,plain,
c_UNITY_Oall__total(v_F,t_a),
inference(paramod,[status(thm)],[c_3513,c_2462]) ).
cnf(c_3833,plain,
$false,
inference(resolve,[status(thm)],[c_3514,c_3835]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM009-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 23:19:36 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 3808217 was started by sandbox2 on n013,
% 0.08/0.35 % Sat Sep 26 23:19:36 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.39
% 0.13/0.39 % From the command line: assign(max_seconds, 300).
% 22.67/3.43
% 22.67/3.43 % given #500 (I,wt=27): 2292 c_lessequals(c_Nat_Osize(c_List_Oremdups(A,B),tc_List_Olist(B)),c_Nat_Osize(A,tc_List_Olist(B)),tc_nat) # tptp_name(cls_List_Olength__remdups__leq_0) # clausal_fof(1). [assumption].
% 22.67/3.43
% 22.67/3.43 % SZS status Unsatisfiable for theBenchmark
% 22.67/3.43
% 22.67/3.43 % Proof 1 at 2.97 (+ 0.04) seconds.
% 22.67/3.43 % Length of proof is 7.
% 22.67/3.43 % Level of proof is 3.
% 22.67/3.43 % Maximum clause weight is 18.000.
% 22.67/3.43 % Given clauses 716.
% 22.67/3.43
% 22.67/3.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------