%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL839-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% 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 : Mon Sep 7 01:08:34 PM UTC 2026
% Result : Unsatisfiable 0.31s 0.60s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 7 RR)
% Number of literals : 9 ( 0 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 12 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(136,axiom,
( ~ c_Type_Otyping(u,hAPP(hAPP(c_Lambda_OdB_OApp,v),w),x)
| c_Type_Otyping(u,w,c_Type_Osko__Type__Xtyping__elims__2__1(x,u,v,w)) ),
file('LCL839-1.p',unknown),
[] ).
cnf(364,axiom,
c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_r____)),v_a____),v_Ua____),
file('LCL839-1.p',unknown),
[] ).
cnf(388,axiom,
~ v_thesis____,
file('LCL839-1.p',unknown),
[] ).
cnf(389,axiom,
( ~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,u)
| v_thesis____ ),
file('LCL839-1.p',unknown),
[] ).
cnf(390,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,u),
inference(mrr,[status(thm)],[389,388]),
[iquote('0:MRR:389.1,388.0')] ).
cnf(428,plain,
~ c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,u),v_a____),v),
inference(res,[status(thm),theory(equality)],[136,390]),
[iquote('0:Res:136.1,390.0')] ).
cnf(433,plain,
$false,
inference(unc,[status(thm)],[428,364]),
[iquote('0:UnC:428.0,364.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL839-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 4 20:52:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.31/0.60
% 0.31/0.60 SPASS V 3.9
% 0.31/0.60 SPASS beiseite: Proof found.
% 0.31/0.60 % SZS status Theorem
% 0.31/0.60 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.31/0.60 SPASS derived 8 clauses, backtracked 0 clauses, performed 0 splits and kept 319 clauses.
% 0.31/0.60 SPASS allocated 76295 KBytes.
% 0.31/0.60 SPASS spent 0:00:00.20 on the problem.
% 0.31/0.60 0:00:00.07 for the input.
% 0.31/0.60 0:00:00.00 for the FLOTTER CNF translation.
% 0.31/0.60 0:00:00.00 for inferences.
% 0.31/0.60 0:00:00.00 for the backtracking.
% 0.31/0.60 0:00:00.07 for the reduction.
% 0.31/0.60
% 0.31/0.60
% 0.31/0.60 Here is a proof with depth 1, length 7 :
% 0.31/0.60 % SZS output start Refutation
% See solution above
% 0.31/0.60 Formulae used in the proof : cls_typing__elims_I2_J_1 cls_CHAINED_0 cls_conjecture_0 cls_conjecture_1
% 0.31/0.60
%------------------------------------------------------------------------------