%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV925-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 09:09:21 AM UTC 2026
% Result : Unsatisfiable 0.25s 0.53s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 14 ( 4 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_nat_Osimps_I2_J_0,axiom,
! [VAR_0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(VAR_0),
file('theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
cnf(c_78,plain,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(A),
inference(clausify,[status(thm)],[cls_nat_Osimps_I2_J_0]) ).
cnf(c_79,plain,
c_Suc(A) != c_HOL_Ozero__class_Ozero(tc_nat),
inference(copy,[status(thm)],[c_78]) ).
fof(cls_Suc__length__conv_2,axiom,
! [VAR_0,VAR_1,VAR_2] : c_Suc(c_Nat_Osize__class_Osize(VAR_0,tc_List_Olist(VAR_1))) = c_Nat_Osize__class_Osize(c_List_Olist_OCons(VAR_2,VAR_0,VAR_1),tc_List_Olist(VAR_1)),
file('theBenchmark.p',cls_Suc__length__conv_2) ).
cnf(c_594,plain,
c_Suc(c_Nat_Osize__class_Osize(A,tc_List_Olist(B))) = c_Nat_Osize__class_Osize(c_List_Olist_OCons(C,A,B),tc_List_Olist(B)),
inference(clausify,[status(thm)],[cls_Suc__length__conv_2]) ).
cnf(c_595,plain,
c_Nat_Osize__class_Osize(c_List_Olist_OCons(A,B,C),tc_List_Olist(C)) = c_Suc(c_Nat_Osize__class_Osize(B,tc_List_Olist(C))),
inference(copy,[status(thm)],[c_594]) ).
fof(cls_length__0__conv_1,axiom,
! [VAR_0] : c_Nat_Osize__class_Osize(c_List_Olist_ONil(VAR_0),tc_List_Olist(VAR_0)) = c_HOL_Ozero__class_Ozero(tc_nat),
file('theBenchmark.p',cls_length__0__conv_1) ).
cnf(c_603,plain,
c_Nat_Osize__class_Osize(c_List_Olist_ONil(A),tc_List_Olist(A)) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(clausify,[status(thm)],[cls_length__0__conv_1]) ).
fof(cls_conjecture_1,axiom,
c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_623,plain,
c_Nat_Osize__class_Osize(c_List_Olist_OCons(v_aj,v_ak,tc_Value_Oval),tc_List_Olist(tc_Value_Oval)) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
cnf(c_625,plain,
c_Suc(c_Nat_Osize__class_Osize(v_ak,tc_List_Olist(tc_Value_Oval))) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(tc_Type_Oty),tc_List_Olist(tc_Type_Oty)),
inference(paramod,[status(thm)],[c_595,c_623]) ).
cnf(c_626,plain,
c_Suc(c_Nat_Osize__class_Osize(v_ak,tc_List_Olist(tc_Value_Oval))) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(paramod,[status(thm)],[c_603,c_625]) ).
cnf(c_624,plain,
$false,
inference(resolve,[status(thm)],[c_79,c_626]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV925-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n017.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 15:05:48 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 1023383 was started by sandbox2 on n017,
% 0.17/0.43 % Sat Sep 26 15:05:48 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.47
% 0.17/0.47 % From the command line: assign(max_seconds, 300).
% 0.25/0.53
% 0.25/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.25/0.53
% 0.25/0.53 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.25/0.53 % Length of proof is 7.
% 0.25/0.53 % Level of proof is 2.
% 0.25/0.53 % Maximum clause weight is 33.000.
% 0.25/0.53 % Given clauses 0.
% 0.25/0.53
% 0.25/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------