%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL748-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 07:59:38 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.80s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 10 unt; 0 def)
% Number of atoms : 14 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 12 ( 3 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_lift_Osimps_I3_J_0,axiom,
! [VAR_0,VAR_1] : c_Lambda_Olift(c_Lambda_OdB_OAbs(VAR_0),VAR_1) = c_Lambda_OdB_OAbs(c_Lambda_Olift(VAR_0,c_HOL_Oplus__class_Oplus(VAR_1,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
file('theBenchmark.p',cls_lift_Osimps_I3_J_0) ).
cnf(c_296,plain,
c_Lambda_Olift(c_Lambda_OdB_OAbs(A),B) = c_Lambda_OdB_OAbs(c_Lambda_Olift(A,c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(tc_nat),tc_nat))),
inference(clausify,[status(thm)],[cls_lift_Osimps_I3_J_0]) ).
cnf(c_297,plain,
c_Lambda_OdB_OAbs(c_Lambda_Olift(A,c_HOL_Oplus__class_Oplus(B,c_HOL_Oone__class_Oone(tc_nat),tc_nat))) = c_Lambda_Olift(c_Lambda_OdB_OAbs(A),B),
inference(copy,[status(thm)],[c_296]) ).
fof(cls_Lambda_0,axiom,
! [VAR_0] :
( ~ c_InductTermi_OIT(VAR_0)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(VAR_0)) ),
file('theBenchmark.p',cls_Lambda_0) ).
cnf(c_305,plain,
( ~ c_InductTermi_OIT(A)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(A)) ),
inference(clausify,[status(thm)],[cls_Lambda_0]) ).
fof(cls_conjecture_1,axiom,
! [VAR_0] : c_InductTermi_OIT(c_Lambda_Olift(v_r,VAR_0)),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_310,plain,
c_InductTermi_OIT(c_Lambda_Olift(v_r,A)),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia)),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_311,plain,
~ c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),v_ia)),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
cnf(c_1656,plain,
c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Olift(v_r,A))),
inference(resolve,[status(thm)],[c_310,c_305]) ).
cnf(c_2784,plain,
c_InductTermi_OIT(c_Lambda_Olift(c_Lambda_OdB_OAbs(v_r),A)),
inference(paramod,[status(thm)],[c_297,c_1656]) ).
cnf(c_2785,plain,
$false,
inference(resolve,[status(thm)],[c_2784,c_311]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL748-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.55 % Computer : n026.cluster.edu
% 0.11/0.55 % Model : x86_64 x86_64
% 0.11/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.55 % Memory : 8046.5625MB
% 0.11/0.55 % OS : Linux 6.8.0-71-generic
% 0.11/0.55 % CPULimit : 300
% 0.11/0.55 % WCLimit : 300
% 0.11/0.55 % DateTime : Fri Sep 25 23:31:40 UTC 2026
% 0.11/0.55 % CPUTime :
% 0.11/0.55 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.55 % Process 3726872 was started by sandbox on n026,
% 0.11/0.55 % Fri Sep 25 23:31:40 2026
% 0.11/0.55 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.57
% 0.14/0.57 % From the command line: assign(max_seconds, 300).
% 0.14/0.80
% 0.14/0.80 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.80
% 0.14/0.80 % Proof 1 at 0.18 (+ 0.04) seconds.
% 0.14/0.80 % Length of proof is 8.
% 0.14/0.80 % Level of proof is 3.
% 0.14/0.80 % Maximum clause weight is 38.000.
% 0.14/0.80 % Given clauses 203.
% 0.14/0.80
% 0.14/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------