%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL799-1 : 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 : 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 07:59:46 AM UTC 2026
% Result : Unsatisfiable 0.13s 10.48s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 13 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_uT_0,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('theBenchmark.p',cls_uT_0) ).
cnf(c_295,plain,
c_Type_Otyping(v_e____,v_u____,v_T____),
inference(clausify,[status(thm)],[cls_uT_0]) ).
fof(cls_argT_0,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
file('theBenchmark.p',cls_argT_0) ).
cnf(c_301,plain,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____),
inference(clausify,[status(thm)],[cls_argT_0]) ).
fof(cls_subst__lemma_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( c_Type_Otyping(VAR_0,c_Lambda_Osubst(VAR_4,VAR_1,VAR_3),VAR_5)
| ~ c_Type_Otyping(c_Type_Oshift(VAR_0,VAR_3,VAR_2,tc_Type_Otype),VAR_4,VAR_5)
| ~ c_Type_Otyping(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',cls_subst__lemma_0) ).
cnf(c_308,plain,
( c_Type_Otyping(A,c_Lambda_Osubst(E,B,D),F)
| ~ c_Type_Otyping(c_Type_Oshift(A,D,C,tc_Type_Otype),E,F)
| ~ c_Type_Otyping(A,B,C) ),
inference(clausify,[status(thm)],[cls_subst__lemma_0]) ).
fof(cls_conjecture_0,axiom,
~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_309,plain,
~ c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_582,plain,
( c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,A,v_i____),v_T_H_H____)
| ~ c_Type_Otyping(v_e____,A,v_T____) ),
inference(resolve,[status(thm)],[c_308,c_301]) ).
cnf(c_889,plain,
c_Type_Otyping(v_e____,c_Lambda_Osubst(v_a____,v_u____,v_i____),v_T_H_H____),
inference(resolve,[status(thm)],[c_582,c_295]) ).
cnf(c_888,plain,
$false,
inference(resolve,[status(thm)],[c_309,c_889]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL799-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/10.37 % Computer : n017.cluster.edu
% 0.08/10.37 % Model : x86_64 x86_64
% 0.08/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37 % Memory : 8046.5625MB
% 0.08/10.37 % OS : Linux 6.8.0-71-generic
% 0.08/10.37 % CPULimit : 300
% 0.08/10.37 % WCLimit : 300
% 0.08/10.37 % DateTime : Fri Sep 25 23:30:58 UTC 2026
% 0.08/10.37 % CPUTime :
% 0.08/10.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/10.37 % Process 3456672 was started by sandbox on n017,
% 0.08/10.37 % Fri Sep 25 23:30:58 2026
% 0.08/10.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/10.38
% 0.08/10.38 % From the command line: assign(max_seconds, 300).
% 0.13/10.48
% 0.13/10.48 % SZS status Unsatisfiable for theBenchmark
% 0.13/10.48
% 0.13/10.48 % Proof 1 at 0.08 (+ 0.02) seconds.
% 0.13/10.48 % Length of proof is 6.
% 0.13/10.48 % Level of proof is 2.
% 0.13/10.48 % Maximum clause weight is 29.000.
% 0.13/10.48 % Given clauses 253.
% 0.13/10.48
% 0.13/10.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------