%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL784-1 : 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 : 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 07:59:44 AM UTC 2026
% Result : Unsatisfiable 0.02s 0.43s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 18 unt; 0 def)
% Number of atoms : 18 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-5 aty)
% Number of variables : 12 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_conjecture_0,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_82,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_CHAINED_0_02,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('theBenchmark.p',cls_CHAINED_0_02) ).
cnf(c_83,plain,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(clausify,[status(thm)],[cls_CHAINED_0_02]) ).
fof(cls_CHAINED_0_01,axiom,
v_n____ = v_i____,
file('theBenchmark.p',cls_CHAINED_0_01) ).
cnf(c_84,plain,
v_n____ = v_i____,
inference(clausify,[status(thm)],[cls_CHAINED_0_01]) ).
cnf(c_85,plain,
v_i____ = v_n____,
inference(copy,[status(thm)],[c_84]) ).
fof(cls_CHAINED_0,axiom,
v_rs____ = c_List_Olist_ONil(tc_Lambda_OdB),
file('theBenchmark.p',cls_CHAINED_0) ).
cnf(c_86,plain,
v_rs____ = c_List_Olist_ONil(tc_Lambda_OdB),
inference(clausify,[status(thm)],[cls_CHAINED_0]) ).
fof(cls_foldl__Nil_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : c_List_Ofoldl(VAR_0,VAR_1,c_List_Olist_ONil(VAR_2),VAR_3,VAR_2) = VAR_1,
file('theBenchmark.p',cls_foldl__Nil_0) ).
cnf(c_151,plain,
c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C) = B,
inference(clausify,[status(thm)],[cls_foldl__Nil_0]) ).
fof(cls_subst__eq_0,axiom,
! [VAR_0,VAR_1] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(VAR_0)),VAR_1),VAR_0) = VAR_1,
file('theBenchmark.p',cls_subst__eq_0) ).
cnf(c_174,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A) = B,
inference(clausify,[status(thm)],[cls_subst__eq_0]) ).
cnf(c_368,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
inference(paramod,[status(thm)],[c_86,c_82]) ).
cnf(c_369,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_n____)),v_u____),v_i____))),
inference(paramod,[status(thm)],[c_151,c_368]) ).
cnf(c_370,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_n____)),v_u____),v_n____))),
inference(paramod,[status(thm)],[c_85,c_369]) ).
cnf(c_371,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
inference(paramod,[status(thm)],[c_174,c_370]) ).
cnf(c_367,plain,
$false,
inference(resolve,[status(thm)],[c_83,c_371]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL784-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n011.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 23:33:28 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.36 % Process 3187066 was started by sandbox2 on n011,
% 0.02/0.36 % Fri Sep 25 23:33:28 2026
% 0.02/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.37
% 0.02/0.37 % From the command line: assign(max_seconds, 300).
% 0.02/0.43
% 0.02/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.02/0.43
% 0.02/0.43 % Proof 1 at 0.04 (+ 0.00) seconds.
% 0.02/0.43 % Length of proof is 8.
% 0.02/0.43 % Level of proof is 2.
% 0.02/0.43 % Maximum clause weight is 16.000.
% 0.02/0.43 % Given clauses 0.
% 0.02/0.43
% 0.02/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------