TSTP Solution File: LCL787-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL787-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 13:50:11 EDT 2022
% Result : Unsatisfiable 6.04s 6.37s
% Output : Refutation 6.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LCL787-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.33 % Computer : n026.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sat Jul 2 17:58:05 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.81/1.11 ============================== Prover9 ===============================
% 0.81/1.11 Prover9 (32) version 2009-11A, November 2009.
% 0.81/1.11 Process 3726 was started by sandbox on n026.cluster.edu,
% 0.81/1.11 Sat Jul 2 17:58:06 2022
% 0.81/1.11 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3570_n026.cluster.edu".
% 0.81/1.11 ============================== end of head ===========================
% 0.81/1.11
% 0.81/1.11 ============================== INPUT =================================
% 0.81/1.11
% 0.81/1.11 % Reading from file /tmp/Prover9_3570_n026.cluster.edu
% 0.81/1.11
% 0.81/1.11 set(prolog_style_variables).
% 0.81/1.11 set(auto2).
% 0.81/1.11 % set(auto2) -> set(auto).
% 0.81/1.11 % set(auto) -> set(auto_inference).
% 0.81/1.11 % set(auto) -> set(auto_setup).
% 0.81/1.11 % set(auto_setup) -> set(predicate_elim).
% 0.81/1.11 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.81/1.11 % set(auto) -> set(auto_limits).
% 0.81/1.11 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.81/1.11 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.81/1.11 % set(auto) -> set(auto_denials).
% 0.81/1.11 % set(auto) -> set(auto_process).
% 0.81/1.11 % set(auto2) -> assign(new_constants, 1).
% 0.81/1.11 % set(auto2) -> assign(fold_denial_max, 3).
% 0.81/1.11 % set(auto2) -> assign(max_weight, "200.000").
% 0.81/1.11 % set(auto2) -> assign(max_hours, 1).
% 0.81/1.11 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.81/1.11 % set(auto2) -> assign(max_seconds, 0).
% 0.81/1.11 % set(auto2) -> assign(max_minutes, 5).
% 0.81/1.11 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.81/1.11 % set(auto2) -> set(sort_initial_sos).
% 0.81/1.11 % set(auto2) -> assign(sos_limit, -1).
% 0.81/1.11 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.81/1.11 % set(auto2) -> assign(max_megs, 400).
% 0.81/1.11 % set(auto2) -> assign(stats, some).
% 0.81/1.11 % set(auto2) -> clear(echo_input).
% 0.81/1.11 % set(auto2) -> set(quiet).
% 0.81/1.11 % set(auto2) -> clear(print_initial_clauses).
% 0.81/1.11 % set(auto2) -> clear(print_given).
% 0.81/1.11 assign(lrs_ticks,-1).
% 0.81/1.11 assign(sos_limit,10000).
% 0.81/1.11 assign(order,kbo).
% 0.81/1.11 set(lex_order_vars).
% 0.81/1.11 clear(print_given).
% 0.81/1.11
% 0.81/1.11 % formulas(sos). % not echoed (378 formulas)
% 0.81/1.11
% 0.81/1.11 ============================== end of input ==========================
% 0.81/1.11
% 0.81/1.11 % From the command line: assign(max_seconds, 300).
% 0.81/1.11
% 0.81/1.11 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.81/1.11
% 0.81/1.11 % Formulas that are not ordinary clauses:
% 0.81/1.11
% 0.81/1.11 ============================== end of process non-clausal formulas ===
% 0.81/1.11
% 0.81/1.11 ============================== PROCESS INITIAL CLAUSES ===============
% 0.81/1.11
% 0.81/1.11 ============================== PREDICATE ELIMINATION =================
% 0.81/1.11 1 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 0.81/1.11 2 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Oadd__a_0) # label(axiom). [assumption].
% 0.81/1.11 3 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 0.81/1.11 4 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 0.81/1.11 5 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 0.81/1.11 6 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 0.81/1.11 7 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 0.81/1.13 8 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom). [assumption].
% 0.81/1.13 9 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_class__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 0.81/1.13 10 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 0.81/1.13 11 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 0.81/1.13 12 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Oadd__c_0) # label(axiom). [assumption].
% 0.81/1.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C). [resolve(1,a,2,a)].
% 0.81/1.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(1,a,4,a)].
% 0.81/1.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)). [resolve(1,a,5,a)].
% 0.81/1.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(1,a,6,a)].
% 0.81/1.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),D)). [resolve(1,a,7,a)].
% 0.81/1.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(1,a,8,a)].
% 0.81/1.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(1,a,9,a)].
% 0.81/1.13 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(1,a,11,a)].
% 0.81/1.13 13 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 0.81/1.13 14 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_comm__monoid__add_Omult__assoc_0) # label(axiom). [assumption].
% 0.81/1.13 15 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_comm__monoid__add_Omult__left__commute_0) # label(axiom). [assumption].
% 0.81/1.13 16 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_comm__monoid__add_Omult__1_0) # label(axiom). [assumption].
% 0.81/1.13 17 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_comm__monoid__add_Omult__1__right_0) # label(axiom). [assumption].
% 0.81/1.13 18 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_comm__monoid__add_Omult__commute_0) # label(axiom). [assumption].
% 0.81/1.16 19 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 0.81/1.16 20 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 0.81/1.16 21 -class_OrderedGroup_Oab__semigroup__add(A) | c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,C,A,A) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,B,A,A) # label(cls_foldr__conv__foldl_0) # label(axiom). [assumption].
% 0.81/1.16 Derived: c_List_Ofoldr(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),B,A,tc_nat,tc_nat). [resolve(19,a,21,a)].
% 0.81/1.16 22 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.81/1.16 23 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 0.81/1.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C) | B = C. [resolve(22,a,23,a)].
% 0.81/1.16 24 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 0.81/1.16 25 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 0.81/1.16 26 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 0.81/1.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B) | A = C. [resolve(24,a,26,a)].
% 0.81/1.16 27 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 0.81/1.16 28 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 0.81/1.16 29 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 0.81/1.16 30 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),C,A,A)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A) # label(cls_foldl__absorb0_0) # label(axiom). [assumption].
% 0.81/1.16 31 -class_OrderedGroup_Omonoid__add(A) | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A,A) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(A),A,A) # label(cls_foldl__foldr1_0) # label(axiom). [assumption].
% 0.81/1.16 32 -class_OrderedGroup_Omonoid__add(A) | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),C,c_HOL_Ozero__class_Ozero(A),A,A)) # label(cls_foldl__foldr1__lemma_0) # label(axiom). [assumption].
% 0.81/1.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat,tc_nat)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat). [resolve(27,a,30,a)].
% 0.81/1.16 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat,tc_nat) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(tc_nat),A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat,tc_nat). [resolve(27,a,31,a)].
% 0.81/1.16 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(tc_nat),B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat,tc_nat)). [resolve(27,a,32,a)].
% 0.93/1.18 33 class_OrderedGroup_Osemigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 0.93/1.18 34 -class_OrderedGroup_Osemigroup__add(A) | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,D,A,A)) # label(cls_foldl__assoc_0) # label(axiom). [assumption].
% 0.93/1.18 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat,tc_nat)). [resolve(33,a,34,a)].
% 0.93/1.18 35 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 0.93/1.18 36 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(B,A) != c_Nat_Osemiring__1__class_Oof__nat(C,A) | B = C # label(cls_of__nat__eq__iff_0) # label(axiom). [assumption].
% 0.93/1.18 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(35,a,36,a)].
% 0.93/1.18 37 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.93/1.18 38 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 0.93/1.18 39 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 0.93/1.18 40 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 0.93/1.18 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(37,a,38,a)].
% 0.93/1.18 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(37,a,39,a)].
% 0.93/1.18 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(37,a,40,a)].
% 0.93/1.18 41 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 0.93/1.18 42 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 0.93/1.18 43 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 0.93/1.18 44 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 0.93/1.18 45 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 0.93/1.19 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(41,a,43,a)].
% 0.93/1.19 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat). [resolve(41,a,45,a)].
% 0.93/1.19 46 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.93/1.19 47 -class_Ring__and__Field_Oordered__semidom(A) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_of__nat__less__0__iff_0) # label(axiom). [assumption].
% 0.93/1.19 48 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 0.93/1.19 49 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -c_HOL_Oord__class_Oless(B,C,tc_nat) # label(cls_of__nat__less__iff_1) # label(axiom). [assumption].
% 0.93/1.19 50 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__less__iff_0) # label(axiom). [assumption].
% 0.93/1.19 51 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__0__less__iff_0) # label(axiom). [assumption].
% 0.93/1.19 52 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) # label(cls_of__nat__0__less__iff_1) # label(axiom). [assumption].
% 0.93/1.19 Derived: -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(46,a,47,a)].
% 0.93/1.19 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(46,a,48,a)].
% 0.93/1.19 Derived: c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(46,a,49,a)].
% 0.93/1.19 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(46,a,50,a)].
% 0.93/1.19 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(46,a,51,a)].
% 0.93/1.19 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(46,a,52,a)].
% 0.93/1.19 53 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 0.93/1.19 54 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 0.93/1.19 55 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 0.96/1.23 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(53,a,54,a)].
% 0.96/1.23 56 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 0.96/1.23 57 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__nat__0_0) # label(axiom). [assumption].
% 0.96/1.23 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(56,a,57,a)].
% 0.96/1.23 58 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.96/1.23 59 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.96/1.23 60 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 0.96/1.23 61 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 0.96/1.23 62 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 0.96/1.23 63 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 0.96/1.23 64 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 0.96/1.23 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(58,a,59,a)].
% 0.96/1.23 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(58,a,60,a)].
% 0.96/1.23 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(58,a,64,a)].
% 0.96/1.23
% 0.96/1.23 ============================== end predicate elimination =============
% 0.96/1.23
% 0.96/1.23 Auto_denials: (non-Horn, no changes).
% 0.96/1.23
% 0.96/1.23 Term ordering decisions:
% 0.96/1.23 Function symbol KB weights: tc_nat=1. tc_Lambda_OdB=1. c_Lambda_OdB_OApp=1. c_Lambda_Obeta=1. tc_Type_Otype=1. c_Type_Otype_OFun=1. c_InductTermi_OIT=1. v_T____=1. t_a=1. v_e____=1. v_i____=1. v_n____=1. v_T_H____=1. v_Ts____=1. v_a____=1. v_rs____=1. tc_bool=1. v_as____=1. v_ea______=1. v_u____=1. v_ua______=1. v_T_Ha______=1. v_ia______=1. hAPP=1. c_Transitive__Closure_Ortranclp=1. c_List_Orev=1. c_Lambda_Olift=1. c_List_Obutlast=1. c_List_Olast=1. c_Nat_Osize__class_Osize=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_List_Orotate1=1. tc_fun=1. c_List_Olist_ONil=1. c_HOL_Oplus__class_Oplus=1. c_Lambda_OdB_OVar=1. c_HOL_Ozero__class_Ozero=1. c_Lambda_OdB_OAbs=1. tc_List_Olist=1. c_Type_Otype_OAtom=1. c_fequal=1. c_Type_Osko__Type__Xtype__induct__1__1=1. c_List_Oappend=1. c_List_Olist_OCons=1. c_Lambda_Osubst=1. c_List_Oreplicate=1. c_Predicate_Oconversep=1. c_List_Otake=1. c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1=1. c_Type_Osko__Type__Xtyping__elims__3__1=1. c_Type_Osko__Type__Xtyping__elims__3__2=1. c_Type_Oshift=1. c_Type_Otype_Otype__case=1. c_Type_Otype_Otype__rec=1. c_Type_Osko__Type__Xlist__app__typeD__1__1=1. c_Type_Osko__Type__Xlist__app__typeE__1__1=1. c_Type_Osko__Type__Xtyping__elims__2__1=1. c_Type_Osko__Type__Xvar__app__typesE__1__1=1. c_Type_Osko__Type__Xvar__app__types__1__1=1. c_List_Ofoldl=1. c_List_Ofoldr=1. c_Lambda_OdB_OdB__case=1. c_Lambda_OdB_OdB__rec=1. c_List_Osko__List__XCons__eq__append__conv__1__1=1. c_List_Osko__List__Xappend__eq__Cons__conv__1__1=1.
% 6.04/6.36
% 6.04/6.36 ============================== end of process initial clauses ========
% 6.04/6.36
% 6.04/6.36 ============================== CLAUSES FOR SEARCH ====================
% 6.04/6.36
% 6.04/6.36 ============================== end of clauses for search =============
% 6.04/6.36
% 6.04/6.36 ============================== SEARCH ================================
% 6.04/6.36
% 6.04/6.36 % Starting search at 0.16 seconds.
% 6.04/6.36
% 6.04/6.36 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 121 (0.00 of 0.38 sec).
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=50.000, iters=3710
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=44.000, iters=3578
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=39.000, iters=3465
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=38.000, iters=3413
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=37.000, iters=3373
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=36.000, iters=3366
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=35.000, iters=3483
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=34.000, iters=3412
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=33.000, iters=3363
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=32.000, iters=3334
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=31.000, iters=3333
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=30.000, iters=3445
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=29.000, iters=3350
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=28.000, iters=3477
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=27.000, iters=3396
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=26.000, iters=3494
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=25.000, iters=3378
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=24.000, iters=3432
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=23.000, iters=3441
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=22.000, iters=3339
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=21.000, iters=3344
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=20.000, iters=3460
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=19.000, iters=3613
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=18.000, iters=3333
% 6.04/6.36
% 6.04/6.36 Low Water (keep): wt=17.000, iters=3364
% 6.04/6.36
% 6.04/6.36 Low Water (displace): id=8901, wt=87.000
% 6.04/6.36
% 6.04/6.36 Low Water (displace): id=8934, wt=74.000
% 6.04/6.36
% 6.04/6.36 Low Water (displace): id=11717, wt=64.000
% 6.04/6.36
% 6.04/6.36 Low Water (displace): id=12904, wt=63.000
% 6.04/6.36
% 6.04/6.36 Low Water (displace): id=11642, wt=57.000
% 6.04/6.36
% 6.04/6.36 Low Water (displace): id=12921, wt=49.000
% 6.04/6.36
% 6.04/6.36 Low Water (displace): id=13125, wt=46.000
% 6.04/6.36
% 6.04/6.36 Low Water (displace): id=13604, wt=45.000
% 6.04/6.36
% 6.04/6.36 Low Water (displace): id=12089, wt=43.000
% 6.04/6.36
% 6.04/6.36 Low Water (displace): id=12003, wt=41.000
% 6.04/6.36
% 6.04/6.36 Low Water (displace): id=7937, wt=40.000
% 6.04/6.36
% 6.04/6.36 Low Water (displace): id=7205, wt=39.000
% 6.04/6.36
% 6.04/6.36 Low Water (displace): id=11680, wt=38.000
% 6.04/6.36
% 6.04/6.36 Low Water (displace): id=13615, wt=37.000
% 6.04/6.37
% 6.04/6.37 Low Water (displace): id=13744, wt=36.000
% 6.04/6.37
% 6.04/6.37 Low Water (displace): id=13762, wt=35.000
% 6.04/6.37
% 6.04/6.37 Low Water (displace): id=13754, wt=34.000
% 6.04/6.37
% 6.04/6.37 Low Water (displace): id=13729, wt=33.000
% 6.04/6.37
% 6.04/6.37 Low Water (displace): id=13756, wt=32.000
% 6.04/6.37
% 6.04/6.37 Low Water (displace): id=14148, wt=31.000
% 6.04/6.37
% 6.04/6.37 Low Water (displace): id=13925, wt=30.000
% 6.04/6.37
% 6.04/6.37 Low Water (displace): id=14193, wt=29.000
% 6.04/6.37
% 6.04/6.37 Low Water (displace): id=14172, wt=28.000
% 6.04/6.37
% 6.04/6.37 Low Water (displace): id=14273, wt=27.000
% 6.04/6.37
% 6.04/6.37 Low Water (displace): id=14420, wt=26.000
% 6.04/6.37
% 6.04/6.37 Low Water (displace): id=15003, wt=25.000
% 6.04/6.37
% 6.04/6.37 Low Water (displace): id=15492, wt=24.000
% 6.04/6.37
% 6.04/6.37 ============================== PROOF =================================
% 6.04/6.37 % SZS status Unsatisfiable
% 6.04/6.37 % SZS output start Refutation
% 6.04/6.37
% 6.04/6.37 % Proof 1 at 5.23 (+ 0.07) seconds.
% 6.04/6.37 % Length of proof is 12.
% 6.04/6.37 % Level of proof is 3.
% 6.04/6.37 % Maximum clause weight is 32.000.
% 6.04/6.37 % Given clauses 5889.
% 6.04/6.37
% 6.04/6.37 266 c_Type_Otyping(A,B,c_Type_Osko__Type__Xtyping__elims__2__1(C,A,D,B)) | -c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,D),B),C) # label(cls_typing__elims_I2_J_1) # label(axiom). [assumption].
% 6.04/6.37 380 v_n____ = v_i____ # label(cls_True_0) # label(axiom). [assumption].
% 6.04/6.37 387 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) # label(cls_headT_0) # label(axiom). [assumption].
% 6.04/6.37 388 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)). [copy(387),rewrite([380(7)])].
% 6.04/6.37 401 v_thesis____ | -c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,A) | -c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,A),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) # label(cls_that_0) # label(axiom). [assumption].
% 6.04/6.37 402 v_thesis____ | -c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,A) | -c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,A),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))). [copy(401),rewrite([380(14)])].
% 6.04/6.37 408 c_Type_Otyping(A,B,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(C,A,B,D)),C)) | -c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),D),C) # label(cls_typing__elims_I2_J_0) # label(axiom). [assumption].
% 6.04/6.37 411 -v_thesis____ # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 6.04/6.37 470 -c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,A) | -c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,A),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))). [back_unit_del(402),unit_del(a,411)].
% 6.04/6.37 1086 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),v_a____)). [resolve(388,a,266,b)].
% 6.04/6.37 1191 c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype),c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))). [resolve(408,b,388,a)].
% 6.04/6.37 17569 $F. [resolve(1191,a,470,b),unit_del(a,1086)].
% 6.04/6.37
% 6.04/6.37 % SZS output end Refutation
% 6.04/6.37 ============================== end of proof ==========================
% 6.04/6.37
% 6.04/6.37 ============================== STATISTICS ============================
% 6.04/6.37
% 6.04/6.37 Given=5889. Generated=135718. Kept=17386. proofs=1.
% 6.04/6.37 Usable=5855. Sos=9985. Demods=341. Limbo=0, Disabled=1956. Hints=0.
% 6.04/6.37 Megabytes=27.16.
% 6.04/6.37 User_CPU=5.23, System_CPU=0.07, Wall_clock=5.
% 6.04/6.37
% 6.04/6.37 ============================== end of statistics =====================
% 6.04/6.37
% 6.04/6.37 ============================== end of search =========================
% 6.04/6.37
% 6.04/6.37 THEOREM PROVED
% 6.04/6.37 % SZS status Unsatisfiable
% 6.04/6.37
% 6.04/6.37 Exiting with 1 proof.
% 6.04/6.37
% 6.04/6.37 Process 3726 exit (max_proofs) Sat Jul 2 17:58:11 2022
% 6.04/6.37 Prover9 interrupted
%------------------------------------------------------------------------------