%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : LCL844-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n014.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 12:07:12 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.45s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL844-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 08:36:57 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.45 GeoParameters:
% 0.13/0.45
% 0.13/0.45 tptp_input = 1
% 0.13/0.45 tptp_output = 0
% 0.13/0.45 nonempty = 1
% 0.13/0.45 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.45 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 0.13/0.45
% 0.13/0.45
% 0.13/0.45 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.45 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.45
% 0.13/0.45 RuleSystem INPUT:
% 0.13/0.45
% 0.13/0.45 Initial Rules:
% 0.13/0.45 #0: input, references = 3, size of lhs = 4:
% 0.13/0.45 P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), class_Ring__and__Field_Oordered__semidom-{F}(V0), P_c_Nat_Osemiring__1__class_Oof__nat-{F}(V2,V0,V3), c_HOL_Oord__class_Oless-{F}(V3,V1,V0) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #1: input, references = 3, size of lhs = 6:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Nat_Osemiring__1__class_Oof__nat-{F}(V1,V2,V3), P_c_HOL_Ozero__class_Ozero-{F}(V2,V4), class_Ring__and__Field_Osemiring__1-{F}(V2), V3 == V4 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #2: input, references = 3, size of lhs = 6:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Nat_Osemiring__1__class_Oof__nat-{F}(V2,V4,V6), P_c_Nat_Osemiring__1__class_Oof__nat-{F}(V3,V4,V6), class_Nat_Osemiring__char__0-{F}(V4), V2 == V3 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #3: input, references = 3, size of lhs = 6:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), c_HOL_Oord__class_Oless-{F}(V2,V3,V0), P_c_Nat_Osemiring__1__class_Oof__nat-{F}(V2,V4,V5), P_c_Nat_Osemiring__1__class_Oof__nat-{F}(V3,V4,V6), class_Ring__and__Field_Oordered__semidom-{F}(V4) | c_HOL_Oord__class_Oless-{T}(V5,V6,V4)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #4: input, references = 3, size of lhs = 6:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Nat_Osemiring__1__class_Oof__nat-{F}(V2,V4,V5), P_c_Nat_Osemiring__1__class_Oof__nat-{F}(V3,V4,V6), class_Ring__and__Field_Oordered__semidom-{F}(V4), c_HOL_Oord__class_Oless-{F}(V5,V6,V4) | c_HOL_Oord__class_Oless-{T}(V2,V3,V0)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #5: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), class_Orderings_Opreorder-{F}(V2), c_HOL_Oord__class_Oless-{F}(V4,V3,V2), c_HOL_Oord__class_Oless-{F}(V3,V4,V2) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #6: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), class_Orderings_Opreorder-{F}(V2), c_HOL_Oord__class_Oless-{F}(V4,V3,V2), c_HOL_Oord__class_Oless-{F}(V3,V4,V2) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #7: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), class_Orderings_Olinorder-{F}(V2), c_HOL_Oord__class_Oless-{F}(V3,V4,V2), c_HOL_Oord__class_Oless-{F}(V4,V3,V2) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #8: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), class_Orderings_Oorder-{F}(V2), c_HOL_Oord__class_Oless-{F}(V3,V4,V2), c_HOL_Oord__class_Oless-{F}(V4,V3,V2) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #9: input, references = 3, size of lhs = 8:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_OdB_OApp-{F}(V2,V3,V6), P_c_Lambda_Osubst-{F}(V6,V4,V5,V7), P_c_Lambda_Osubst-{F}(V2,V4,V5,V8), P_c_Lambda_Osubst-{F}(V3,V4,V5,V9), P_c_Lambda_OdB_OApp-{F}(V8,V9,V10), V7 == V10 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #10: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_OdB_OVar-{F}(V3,V4), P_c_Lambda_Osubst-{F}(V4,V2,V3,V5), V5 == V2 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #11: input, references = 3, size of lhs = 6:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_OdB_OVar-{F}(V2,V4), c_HOL_Oord__class_Oless-{F}(V2,V3,V0), P_c_Lambda_Osubst-{F}(V4,V5,V3,V6), V6 == V4 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #12: input, references = 3, size of lhs = 3:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), c_HOL_Oord__class_Oless-{F}(V1,V1,V0) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #13: input, references = 3, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), #-{F} V2, V2 == V1 | c_HOL_Oord__class_Oless-{T}(V1,V2,V0)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #14: input, references = 3, size of lhs = 6:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_HOL_Ozero__class_Ozero-{F}(V3,V4), P_c_Nat_Osemiring__1__class_Oof__nat-{F}(V2,V3,V5), class_Ring__and__Field_Oordered__semidom-{F}(V3), c_HOL_Oord__class_Oless-{F}(V4,V5,V3) | c_HOL_Oord__class_Oless-{T}(V1,V2,V0)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #15: input, references = 3, size of lhs = 6:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), c_HOL_Oord__class_Oless-{F}(V1,V2,V0), P_c_HOL_Ozero__class_Ozero-{F}(V3,V4), P_c_Nat_Osemiring__1__class_Oof__nat-{F}(V2,V3,V5), class_Ring__and__Field_Oordered__semidom-{F}(V3) | c_HOL_Oord__class_Oless-{T}(V4,V5,V3)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #16: input, references = 3, size of lhs = 6:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), #-{F} V2, #-{F} V3, class_Orderings_Olinorder-{F}(V4), V3 == V2 | c_HOL_Oord__class_Oless-{T}(V3,V2,V4), c_HOL_Oord__class_Oless-{T}(V2,V3,V4)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #17: input, references = 3, size of lhs = 6:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), #-{F} V2, #-{F} V3, class_Orderings_Olinorder-{F}(V4), V3 == V2 | c_HOL_Oord__class_Oless-{T}(V2,V3,V4), c_HOL_Oord__class_Oless-{T}(V3,V2,V4)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #18: input, references = 3, size of lhs = 6:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), #-{F} V2, #-{F} V3, class_Orderings_Olinorder-{F}(V4), V3 == V2 | c_HOL_Oord__class_Oless-{T}(V2,V3,V4), c_HOL_Oord__class_Oless-{T}(V3,V2,V4)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #19: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), #-{F} V2, #-{F} V3, V3 == V2 | c_HOL_Oord__class_Oless-{T}(V2,V3,V0), c_HOL_Oord__class_Oless-{T}(V3,V2,V0)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #20: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), #-{F} V2, #-{F} V3, V2 == V3 | c_HOL_Oord__class_Oless-{T}(V3,V2,V0), c_HOL_Oord__class_Oless-{T}(V2,V3,V0)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #21: input, references = 3, size of lhs = 6:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), #-{F} V2, #-{F} V3, class_Orderings_Olinorder-{F}(V4), V3 == V2 | c_HOL_Oord__class_Oless-{T}(V2,V3,V4), c_HOL_Oord__class_Oless-{T}(V3,V2,V4)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #22: input, references = 3, size of lhs = 6:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), #-{F} V2, #-{F} V3, class_Ring__and__Field_Oordered__idom-{F}(V4), V3 == V2 | c_HOL_Oord__class_Oless-{T}(V2,V3,V4), c_HOL_Oord__class_Oless-{T}(V3,V2,V4)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #23: input, references = 3, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), class_Orderings_Opreorder-{F}(V2), c_HOL_Oord__class_Oless-{F}(V3,V3,V2) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #24: input, references = 3, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), class_Orderings_Olinorder-{F}(V2), c_HOL_Oord__class_Oless-{F}(V3,V3,V2) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #25: input, references = 3, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), class_Orderings_Oorder-{F}(V2), c_HOL_Oord__class_Oless-{F}(V3,V3,V2) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #26: input, references = 3, size of lhs = 3:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), c_HOL_Oord__class_Oless-{F}(V2,V2,V0) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #27: input, references = 3, size of lhs = 3:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), c_HOL_Oord__class_Oless-{F}(V2,V2,V0) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #28: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), c_Lambda_Obeta-{F}(V3,V2), P_c_Lambda_Osubst-{F}(V3,V5,V4,V6), P_c_Lambda_Osubst-{F}(V2,V5,V4,V7) | c_Lambda_Obeta-{T}(V6,V7)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #29: input, references = 3, size of lhs = 6:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_OdB_OVar-{F}(V3,V4), P_c_Lambda_Osubst-{F}(V4,V5,V2,V6), V3 == V2, V6 == V4 | c_HOL_Oord__class_Oless-{T}(V2,V3,V0)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #30: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), class_Orderings_Opreorder-{F}(V2), c_HOL_Oord__class_Oless-{F}(V5,V3,V2), c_HOL_Oord__class_Oless-{F}(V4,V5,V2) | c_HOL_Oord__class_Oless-{T}(V4,V3,V2)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #31: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), class_Orderings_Oorder-{F}(V2), c_HOL_Oord__class_Oless-{F}(V3,V5,V2), c_HOL_Oord__class_Oless-{F}(V5,V4,V2) | c_HOL_Oord__class_Oless-{T}(V3,V4,V2)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #32: input, references = 3, size of lhs = 3:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), c_HOL_Oord__class_Oless-{F}(V2,V1,V0) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #33: input, references = 3, size of lhs = 3:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), c_HOL_Oord__class_Oless-{F}(V2,V1,V0) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #34: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_OdB_OVar-{F}(V2,V3), P_c_Lambda_Osubst-{F}(V3,V4,V2,V5), V5 == V4 | c_HOL_Oord__class_Oless-{T}(V2,V2,V0)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #35: input, references = 4, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_Olift-{F}(V2,V4,V5), P_c_Lambda_Osubst-{F}(V5,V3,V4,V6), V6 == V2 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #36: input, references = 3, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_OdB_OApp-{F}(V2,V3,V6), P_c_Lambda_OdB_OVar-{F}(V4,V6) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #37: input, references = 3, size of lhs = 7:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_Osko__Lambda__Xbeta__cases__2__1-{F}(V3,V2,V4), P_c_Lambda_OdB_OAbs-{F}(V4,V5), P_c_Lambda_OdB_OAbs-{F}(V3,V6), c_Lambda_Obeta-{F}(V6,V2), V2 == V5 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #38: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), c_InductTermi_OIT-{F}(V2), P_c_Lambda_OdB_OVar-{F}(V3,V4), P_c_Lambda_OdB_OApp-{F}(V2,V4,V5) | c_InductTermi_OIT-{T}(V5)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #39: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), c_Lambda_Obeta-{F}(V3,V2), P_c_Lambda_Olift-{F}(V3,V4,V5), P_c_Lambda_Olift-{F}(V2,V4,V6) | c_Lambda_Obeta-{T}(V5,V6)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #40: input, references = 3, size of lhs = 6:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_OdB_OVar-{F}(V3,V4), P_c_Lambda_Olift-{F}(V4,V2,V5), c_HOL_Oord__class_Oless-{F}(V3,V2,V0), V5 == V4 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #41: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), c_Lambda_Obeta-{F}(V3,V2), P_c_Lambda_OdB_OApp-{F}(V3,V4,V5), P_c_Lambda_OdB_OApp-{F}(V2,V4,V6) | c_Lambda_Obeta-{T}(V5,V6)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #42: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), c_Lambda_Obeta-{F}(V3,V2), P_c_Lambda_OdB_OApp-{F}(V4,V3,V5), P_c_Lambda_OdB_OApp-{F}(V4,V2,V6) | c_Lambda_Obeta-{T}(V5,V6)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #43: input, references = 3, size of lhs = 8:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_OdB_OApp-{F}(V3,V2,V5), P_c_Lambda_Olift-{F}(V5,V4,V6), P_c_Lambda_Olift-{F}(V3,V4,V7), P_c_Lambda_Olift-{F}(V2,V4,V8), P_c_Lambda_OdB_OApp-{F}(V7,V8,V9), V6 == V9 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #44: input, references = 3, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_OdB_OVar-{F}(V4,V6), P_c_Lambda_OdB_OApp-{F}(V2,V3,V6) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #45: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_OdB_OAbs-{F}(V3,V4), P_c_Lambda_OdB_OApp-{F}(V4,V2,V5), P_c_Lambda_Osubst-{F}(V3,V2,V1,V6) | c_Lambda_Obeta-{T}(V5,V6)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #46: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_OdB_OApp-{F}(V4,V3,V7), P_c_Lambda_OdB_OApp-{F}(V5,V2,V7), V3 == V2 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #47: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_OdB_OApp-{F}(V3,V4,V7), P_c_Lambda_OdB_OApp-{F}(V2,V5,V7), V3 == V2 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #48: input, references = 3, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_OdB_OVar-{F}(V3,V4), c_Lambda_Obeta-{F}(V4,V2) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #49: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_Osko__Lambda__Xbeta__cases__2__1-{F}(V3,V2,V4), P_c_Lambda_OdB_OAbs-{F}(V3,V5), c_Lambda_Obeta-{F}(V5,V2) | c_Lambda_Obeta-{T}(V3,V4)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #50: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), c_InductTermi_OIT-{F}(V2), P_c_Lambda_OdB_OVar-{F}(V3,V5), P_c_Lambda_Osubst-{F}(V2,V5,V4,V6) | c_InductTermi_OIT-{T}(V6)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #51: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_OdB_OVar-{F}(V2,V5), P_c_Lambda_OdB_OVar-{F}(V3,V5), V2 == V3 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #52: input, references = 3, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_OdB_OAbs-{F}(V3,V5), P_c_Lambda_OdB_OVar-{F}(V2,V5) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #53: input, references = 4, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_OdB_OApp-{F}(V2,V3,V6), P_c_Lambda_OdB_OAbs-{F}(V4,V6) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #54: input, references = 3, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_Lambda_OdB_OAbs-{F}(V4,V6), P_c_Lambda_OdB_OApp-{F}(V2,V3,V6) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #55: input, references = 4, size of lhs = 3:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_v_ta______-{F}(V2) | c_InductTermi_OIT-{T}(V2)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #56: input, references = 3, size of lhs = 6:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_v_ta______-{F}(V2), P_c_Lambda_OdB_OAbs-{F}(V4,V6), P_c_Lambda_OdB_OAbs-{F}(V3,V6), V4 == V3 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #57: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_v_ta______-{F}(V2), c_InductTermi_OIT-{F}(V3), P_c_Lambda_Olift-{F}(V3,V4,V5) | c_InductTermi_OIT-{T}(V5)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #58: input, references = 3, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_v_ta______-{F}(V2), P_c_Lambda_OdB_OVar-{F}(V3,V6), P_c_Lambda_OdB_OAbs-{F}(V4,V6) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #59: input, references = 3, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_v_ta______-{F}(V2), P_c_Lambda_OdB_OVar-{F}(V3,V4) | c_InductTermi_OIT-{T}(V4)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #60: input, references = 4, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_v_ta______-{F}(V2), P_c_Lambda_OdB_OAbs-{F}(V3,V4), c_InductTermi_OIT-{F}(V3) | c_InductTermi_OIT-{T}(V4)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #61: input, references = 3, size of lhs = 6:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_v_ta______-{F}(V2), P_c_Lambda_OdB_OAbs-{F}(V4,V5), P_c_Lambda_OdB_OAbs-{F}(V3,V6), c_Lambda_Obeta-{F}(V4,V3) | c_Lambda_Obeta-{T}(V5,V6)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #62: input, references = 4, size of lhs = 5:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_v_ta______-{F}(V2), P_c_Lambda_OdB_OAbs-{F}(V2,V3), c_InductTermi_OIT-{F}(V3) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #63: input, references = 3, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_v_ta______-{F}(V2), P_c_Lambda_OdB_OAbs-{F}(V2,V3) | class_Ring__and__Field_Oordered__semidom-{T}(V0)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #64: input, references = 3, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_v_ta______-{F}(V2), P_c_Lambda_OdB_OAbs-{F}(V2,V3) | class_Ring__and__Field_Osemiring__1-{T}(V0)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #65: input, references = 3, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_v_ta______-{F}(V2), P_c_Lambda_OdB_OAbs-{F}(V2,V3) | class_Nat_Osemiring__char__0-{T}(V0)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #66: input, references = 3, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_v_ta______-{F}(V2), P_c_Lambda_OdB_OAbs-{F}(V2,V3) | class_Orderings_Opreorder-{T}(V0)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #67: input, references = 3, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_v_ta______-{F}(V2), P_c_Lambda_OdB_OAbs-{F}(V2,V3) | class_Orderings_Olinorder-{T}(V0)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #68: input, references = 3, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_v_ta______-{F}(V2), P_c_Lambda_OdB_OAbs-{F}(V2,V3) | class_Orderings_Oorder-{T}(V0)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #69: input, references = 3, size of lhs = 2:
% 0.13/0.45 #-{F} V0, #-{F} V1 | EXISTS V2: P_c_Nat_Osemiring__1__class_Oof__nat-{T}(V0,V1,V2)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #70: input, references = 5, size of lhs = 1:
% 0.13/0.45 #-{F} V0 | EXISTS V1: P_c_HOL_Ozero__class_Ozero-{T}(V0,V1)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #71: input, references = 4, size of lhs = 0:
% 0.13/0.45 FALSE | EXISTS V0: P_tc_nat-{T}(V0)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #72: input, references = 3, size of lhs = 3:
% 0.13/0.45 #-{F} V0, #-{F} V1, #-{F} V2 | EXISTS V3: P_c_Lambda_Osubst-{T}(V0,V1,V2,V3)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #73: input, references = 3, size of lhs = 2:
% 0.13/0.45 #-{F} V0, #-{F} V1 | EXISTS V2: P_c_Lambda_OdB_OApp-{T}(V0,V1,V2)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #74: input, references = 3, size of lhs = 1:
% 0.13/0.45 #-{F} V0 | EXISTS V1: P_c_Lambda_OdB_OVar-{T}(V0,V1)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #75: input, references = 3, size of lhs = 2:
% 0.13/0.45 #-{F} V0, #-{F} V1 | EXISTS V2: P_c_Lambda_Olift-{T}(V0,V1,V2)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #76: input, references = 4, size of lhs = 1:
% 0.13/0.45 #-{F} V0 | EXISTS V1: P_c_Lambda_OdB_OAbs-{T}(V0,V1)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #77: input, references = 3, size of lhs = 2:
% 0.13/0.45 #-{F} V0, #-{F} V1 | EXISTS V2: P_c_Lambda_Osko__Lambda__Xbeta__cases__2__1-{T}(V0,V1,V2)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #78: input, references = 4, size of lhs = 0:
% 0.13/0.45 FALSE | EXISTS V0: P_v_ta______-{T}(V0)
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 number of initial rules = 79
% 0.13/0.45
% 0.13/0.45 Simplifiers:
% 0.13/0.45 #79: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 class_Ring__and__Field_Oordered__semidom-{F}(V0), class_Ring__and__Field_Oordered__semidom-{F}(V1), V0 == V1 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #80: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 c_HOL_Oord__class_Oless-{F}(V0,V1,V2), c_HOL_Oord__class_Oless-{F}(V3,V4,V5), V2 == V5 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #81: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 class_Ring__and__Field_Osemiring__1-{F}(V0), class_Ring__and__Field_Osemiring__1-{F}(V1), V0 == V1 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #82: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 class_Nat_Osemiring__char__0-{F}(V0), class_Nat_Osemiring__char__0-{F}(V1), V0 == V1 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #83: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 class_Orderings_Opreorder-{F}(V0), class_Orderings_Opreorder-{F}(V1), V0 == V1 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #84: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 class_Orderings_Olinorder-{F}(V0), class_Orderings_Olinorder-{F}(V1), V0 == V1 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #85: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 class_Orderings_Oorder-{F}(V0), class_Orderings_Oorder-{F}(V1), V0 == V1 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #86: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 P_c_Nat_Osemiring__1__class_Oof__nat-{F}(V0,V1,V2), P_c_Nat_Osemiring__1__class_Oof__nat-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #87: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 P_c_HOL_Ozero__class_Ozero-{F}(V0,V1), P_c_HOL_Ozero__class_Ozero-{F}(V0,V3), V1 == V3 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #88: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 P_tc_nat-{F}(V0), P_tc_nat-{F}(V1), V0 == V1 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #89: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 P_c_Lambda_Osubst-{F}(V0,V1,V2,V3), P_c_Lambda_Osubst-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #90: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 P_c_Lambda_OdB_OApp-{F}(V0,V1,V2), P_c_Lambda_OdB_OApp-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #91: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 P_c_Lambda_OdB_OVar-{F}(V0,V1), P_c_Lambda_OdB_OVar-{F}(V0,V3), V1 == V3 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #92: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 P_c_Lambda_Olift-{F}(V0,V1,V2), P_c_Lambda_Olift-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #93: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 P_c_Lambda_OdB_OAbs-{F}(V0,V1), P_c_Lambda_OdB_OAbs-{F}(V0,V3), V1 == V3 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #94: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 P_c_Lambda_Osko__Lambda__Xbeta__cases__2__1-{F}(V0,V1,V2), P_c_Lambda_Osko__Lambda__Xbeta__cases__2__1-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #95: unsound, references = 3, size of lhs = 3:
% 0.13/0.45 P_v_ta______-{F}(V0), P_v_ta______-{F}(V1), V0 == V1 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 number of simplifiers = 17
% 0.13/0.45
% 0.13/0.45 Learnt:
% 0.13/0.45 #99: exists( #70, #53 ), references = 1, size of lhs = 3:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_Lambda_OdB_OAbs-{F}(V1,V2), P_c_Lambda_OdB_OApp-{F}(V3,V4,V2) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #100: exists( #70, #35 ), references = 1, size of lhs = 4:
% 0.13/0.45 P_tc_nat-{F}(V0), P_c_Lambda_Olift-{F}(V1,V2,V3), P_c_Lambda_Osubst-{F}(V3,V4,V2,V5), V5 == V1 | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #106: mergings( V2 == V5, V3 == V6, V4 == V0; #102 ), references = 1, size of lhs = 4:
% 0.13/0.45 c_InductTermi_OIT-{F}(V0), P_v_ta______-{F}(V0), P_tc_nat-{F}(V1), P_c_HOL_Ozero__class_Ozero-{F}(V1,V2) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #110: mergings( V2 == V3; #108 ), references = 1, size of lhs = 2:
% 0.13/0.45 P_v_ta______-{F}(V0), P_tc_nat-{F}(V1) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #112: exists( #78, #108 ), references = 1, size of lhs = 1:
% 0.13/0.45 P_tc_nat-{F}(V0) | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 #114: exists( #71, #111 ), references = 1, size of lhs = 0:
% 0.13/0.45 FALSE | FALSE
% 0.13/0.45 (used 0 times, uses = {})
% 0.13/0.45
% 0.13/0.45 number of learnt formulas = 6
% 0.13/0.45
% 0.13/0.45
% 0.13/0.45 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.45
% 0.13/0.45 randbase = 1
%------------------------------------------------------------------------------