%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : LCL826-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n015.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 01:08:32 PM UTC 2026
% Result : Unsatisfiable 0.46s 0.75s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 9 RR)
% Number of literals : 15 ( 0 equ; 10 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 16 ( 16 usr; 14 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(355,axiom,
( ~ hBOOL(hAPP(c_InductTermi_OIT,u))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v),u),v_T____))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v),w),v_T____)),v_a____),x))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),u),w))) ),
file('LCL826-1.p',unknown),
[] ).
cnf(410,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_a____),v_xa)),
file('LCL826-1.p',unknown),
[] ).
cnf(411,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
file('LCL826-1.p',unknown),
[] ).
cnf(412,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
file('LCL826-1.p',unknown),
[] ).
cnf(413,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_xb),v_xc))),
file('LCL826-1.p',unknown),
[] ).
cnf(479,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,u),v_xb),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),u),v_xc),v_T____)),v_a____),v)) ),
inference(res,[status(thm),theory(equality)],[355,413]),
[iquote('0:Res:355.3,413.0')] ).
cnf(497,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,u),v_xb),v_T____))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),u),v_xc),v_T____)),v_a____),v)) ),
inference(mrr,[status(thm)],[479,411]),
[iquote('0:MRR:479.1,411.0')] ).
cnf(528,plain,
~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
inference(res,[status(thm),theory(equality)],[410,497]),
[iquote('0:Res:410.0,497.1')] ).
cnf(539,plain,
$false,
inference(mrr,[status(thm)],[528,412]),
[iquote('0:MRR:528.0,412.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL826-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_spass %d %s
% 0.12/0.37 % Computer : n015.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 5 09:28:57 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.46/0.75
% 0.46/0.75 SPASS V 3.9
% 0.46/0.75 SPASS beiseite: Proof found.
% 0.46/0.75 % SZS status Theorem
% 0.46/0.75 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.75 SPASS derived 67 clauses, backtracked 0 clauses, performed 0 splits and kept 378 clauses.
% 0.46/0.75 SPASS allocated 77455 KBytes.
% 0.46/0.75 SPASS spent 0:00:00.34 on the problem.
% 0.46/0.75 0:00:00.07 for the input.
% 0.46/0.75 0:00:00.00 for the FLOTTER CNF translation.
% 0.46/0.75 0:00:00.00 for inferences.
% 0.46/0.75 0:00:00.00 for the backtracking.
% 0.46/0.75 0:00:00.15 for the reduction.
% 0.46/0.75
% 0.46/0.75
% 0.46/0.75 Here is a proof with depth 2, length 9 :
% 0.46/0.75 % SZS output start Refutation
% See solution above
% 0.46/0.75 Formulae used in the proof : cls_Cons_I1_J_0 cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3
% 0.46/0.75
%------------------------------------------------------------------------------