TSTP Solution File: SWV835-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV835-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 : Wed Jul 20 21:14:59 EDT 2022
% Result : Unsatisfiable 0.93s 1.41s
% Output : Refutation 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV835-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 19:23:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.93/1.28 ============================== Prover9 ===============================
% 0.93/1.28 Prover9 (32) version 2009-11A, November 2009.
% 0.93/1.28 Process 709 was started by sandbox on n025.cluster.edu,
% 0.93/1.28 Tue Jun 14 19:23:40 2022
% 0.93/1.28 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_530_n025.cluster.edu".
% 0.93/1.28 ============================== end of head ===========================
% 0.93/1.28
% 0.93/1.28 ============================== INPUT =================================
% 0.93/1.28
% 0.93/1.28 % Reading from file /tmp/Prover9_530_n025.cluster.edu
% 0.93/1.28
% 0.93/1.28 set(prolog_style_variables).
% 0.93/1.28 set(auto2).
% 0.93/1.28 % set(auto2) -> set(auto).
% 0.93/1.28 % set(auto) -> set(auto_inference).
% 0.93/1.28 % set(auto) -> set(auto_setup).
% 0.93/1.28 % set(auto_setup) -> set(predicate_elim).
% 0.93/1.28 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.93/1.28 % set(auto) -> set(auto_limits).
% 0.93/1.28 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.93/1.28 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.93/1.28 % set(auto) -> set(auto_denials).
% 0.93/1.28 % set(auto) -> set(auto_process).
% 0.93/1.28 % set(auto2) -> assign(new_constants, 1).
% 0.93/1.28 % set(auto2) -> assign(fold_denial_max, 3).
% 0.93/1.28 % set(auto2) -> assign(max_weight, "200.000").
% 0.93/1.28 % set(auto2) -> assign(max_hours, 1).
% 0.93/1.28 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.93/1.28 % set(auto2) -> assign(max_seconds, 0).
% 0.93/1.28 % set(auto2) -> assign(max_minutes, 5).
% 0.93/1.28 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.93/1.28 % set(auto2) -> set(sort_initial_sos).
% 0.93/1.28 % set(auto2) -> assign(sos_limit, -1).
% 0.93/1.28 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.93/1.28 % set(auto2) -> assign(max_megs, 400).
% 0.93/1.28 % set(auto2) -> assign(stats, some).
% 0.93/1.28 % set(auto2) -> clear(echo_input).
% 0.93/1.28 % set(auto2) -> set(quiet).
% 0.93/1.28 % set(auto2) -> clear(print_initial_clauses).
% 0.93/1.28 % set(auto2) -> clear(print_given).
% 0.93/1.28 assign(lrs_ticks,-1).
% 0.93/1.28 assign(sos_limit,10000).
% 0.93/1.28 assign(order,kbo).
% 0.93/1.28 set(lex_order_vars).
% 0.93/1.28 clear(print_given).
% 0.93/1.28
% 0.93/1.28 % formulas(sos). % not echoed (608 formulas)
% 0.93/1.28
% 0.93/1.28 ============================== end of input ==========================
% 0.93/1.28
% 0.93/1.28 % From the command line: assign(max_seconds, 300).
% 0.93/1.28
% 0.93/1.28 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.93/1.28
% 0.93/1.28 % Formulas that are not ordinary clauses:
% 0.93/1.28
% 0.93/1.28 ============================== end of process non-clausal formulas ===
% 0.93/1.28
% 0.93/1.28 ============================== PROCESS INITIAL CLAUSES ===============
% 0.93/1.28
% 0.93/1.28 ============================== PREDICATE ELIMINATION =================
% 0.93/1.28 1 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.93/1.28 2 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 0.93/1.28 3 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 0.93/1.28 4 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 0.93/1.28 5 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),B)) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 0.93/1.28 6 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),C)) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 0.93/1.28 7 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__infI_0) # label(axiom). [assumption].
% 0.93/1.28 8 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 0.93/1.28 9 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 0.93/1.28 10 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 0.93/1.28 11 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 0.93/1.28 12 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 0.93/1.28 13 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) # label(cls_le__infE_0) # label(axiom). [assumption].
% 0.93/1.28 14 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(D,C,A))) # label(cls_le__infE_1) # label(axiom). [assumption].
% 0.93/1.28 15 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 0.93/1.28 16 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 0.93/1.28 17 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 0.93/1.28 18 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(D,C,A))) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 0.93/1.28 19 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 0.93/1.28 20 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 0.93/1.28 21 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,C,A) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 0.93/1.28 22 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_fun(D,A)). [resolve(1,a,2,a)].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(1,a,3,a)].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(1,a,4,a)].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),C)). [resolve(1,a,5,a)].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),D)). [resolve(1,a,6,a)].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Olower__semilattice__class_Oinf(D,E,tc_fun(B,A)))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(1,a,7,a)].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),B),C)). [resolve(1,a,10,a)].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) != B | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),B),C)). [resolve(1,a,11,a)].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = C | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),C),B)). [resolve(1,a,12,a)].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Olower__semilattice__class_Oinf(D,E,tc_fun(B,A)))). [resolve(1,a,13,a)].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Olower__semilattice__class_Oinf(E,D,tc_fun(B,A)))). [resolve(1,a,14,a)].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)). [resolve(1,a,15,a)].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),E)). [resolve(1,a,16,a)].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_HOL_Oord__class_Oless(C,E,tc_fun(D,A)). [resolve(1,a,19,a)].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_HOL_Oord__class_Oless(B,E,tc_fun(D,A)). [resolve(1,a,20,a)].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)). [resolve(1,a,21,a)].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(1,a,22,a)].
% 0.93/1.28 23 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.93/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(23,a,2,a)].
% 0.93/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_bool),tc_bool). [resolve(23,a,3,a)].
% 0.93/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(23,a,4,a)].
% 0.93/1.28 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),A)). [resolve(23,a,5,a)].
% 0.93/1.28 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),B)). [resolve(23,a,6,a)].
% 0.93/1.28 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(23,a,7,a)].
% 0.93/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(23,a,10,a)].
% 0.93/1.30 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(23,a,11,a)].
% 0.93/1.30 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),A)). [resolve(23,a,12,a)].
% 0.93/1.30 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool))). [resolve(23,a,13,a)].
% 0.93/1.30 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool))). [resolve(23,a,14,a)].
% 0.93/1.30 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)). [resolve(23,a,15,a)].
% 0.93/1.30 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),C)). [resolve(23,a,16,a)].
% 0.93/1.30 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_HOL_Oord__class_Oless(B,C,tc_bool). [resolve(23,a,19,a)].
% 0.93/1.30 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(23,a,20,a)].
% 0.93/1.30 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool). [resolve(23,a,21,a)].
% 0.93/1.30 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(23,a,22,a)].
% 0.93/1.30 24 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.93/1.30 25 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 0.93/1.30 26 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 0.93/1.30 27 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.93/1.30 28 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_Lattices_Oupper__semilattice__class_Osup(C,B,A) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 0.93/1.30 29 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(B,C,A) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 0.93/1.30 30 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__supI1_0) # label(axiom). [assumption].
% 0.93/1.30 31 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 0.93/1.30 32 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Oupper__semilattice__class_Osup(B,D,A)),C)) # label(cls_le__supE_0) # label(axiom). [assumption].
% 0.93/1.30 33 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Oupper__semilattice__class_Osup(D,B,A)),C)) # label(cls_le__supE_1) # label(axiom). [assumption].
% 0.93/1.30 34 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 0.93/1.30 35 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 0.93/1.30 36 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Oupper__semilattice__class_Osup(B,D,A)),C)) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 0.93/1.30 37 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Oupper__semilattice__class_Osup(D,B,A)),C)) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 0.93/1.30 38 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = C | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 0.93/1.30 39 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) != C | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 0.93/1.30 40 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = B | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 0.93/1.30 41 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__supI_0) # label(axiom). [assumption].
% 0.93/1.30 42 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Oupper__semilattice__class_Osup(B,C,A))) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 0.93/1.30 43 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Oupper__semilattice__class_Osup(C,B,A))) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 0.93/1.30 44 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_sup__least_0) # label(axiom). [assumption].
% 0.93/1.30 45 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 0.93/1.30 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(24,a,25,a)].
% 0.93/1.30 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(24,a,26,a)].
% 0.93/1.30 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(24,a,27,a)].
% 0.93/1.30 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)). [resolve(24,a,28,a)].
% 0.93/1.30 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)). [resolve(24,a,29,a)].
% 0.93/1.30 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_HOL_Oord__class_Oless(B,C,tc_fun(E,A)). [resolve(24,a,30,a)].
% 0.93/1.30 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_HOL_Oord__class_Oless(B,D,tc_fun(E,A)). [resolve(24,a,31,a)].
% 0.93/1.30 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Oupper__semilattice__class_Osup(C,E,tc_fun(B,A))),D)). [resolve(24,a,32,a)].
% 0.93/1.30 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Oupper__semilattice__class_Osup(E,C,tc_fun(B,A))),D)). [resolve(24,a,33,a)].
% 0.93/1.30 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(B,A)))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(24,a,34,a)].
% 0.93/1.30 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(B,A)))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)). [resolve(24,a,35,a)].
% 0.93/1.30 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = C | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),B),C)). [resolve(24,a,38,a)].
% 0.93/1.30 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) != C | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),B),C)). [resolve(24,a,39,a)].
% 0.93/1.30 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),C),B)). [resolve(24,a,40,a)].
% 0.93/1.30 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(B,A))),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)). [resolve(24,a,41,a)].
% 0.93/1.30 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(B,A)))). [resolve(24,a,42,a)].
% 0.93/1.30 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Oupper__semilattice__class_Osup(D,C,tc_fun(B,A)))). [resolve(24,a,43,a)].
% 0.93/1.30 46 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.93/1.30 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),tc_bool). [resolve(46,a,25,a)].
% 0.93/1.30 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool). [resolve(46,a,26,a)].
% 0.93/1.30 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(46,a,27,a)].
% 0.93/1.30 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(46,a,28,a)].
% 0.93/1.30 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool). [resolve(46,a,29,a)].
% 0.93/1.30 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_HOL_Oord__class_Oless(A,B,tc_bool). [resolve(46,a,30,a)].
% 0.93/1.30 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(46,a,31,a)].
% 0.93/1.30 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool)),B)). [resolve(46,a,32,a)].
% 0.93/1.30 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool)),B)). [resolve(46,a,33,a)].
% 0.93/1.30 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(46,a,34,a)].
% 0.93/1.30 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)). [resolve(46,a,35,a)].
% 0.93/1.41 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(46,a,38,a)].
% 0.93/1.41 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(46,a,39,a)].
% 0.93/1.41 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),A)). [resolve(46,a,40,a)].
% 0.93/1.41 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)). [resolve(46,a,41,a)].
% 0.93/1.41 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool))). [resolve(46,a,42,a)].
% 0.93/1.41 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool))). [resolve(46,a,43,a)].
% 0.93/1.41 47 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 0.93/1.41 48 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 0.93/1.41 Derived: A = A. [resolve(47,b,48,a)].
% 0.93/1.41
% 0.93/1.41 ============================== end predicate elimination =============
% 0.93/1.41
% 0.93/1.41 Auto_denials: (non-Horn, no changes).
% 0.93/1.41
% 0.93/1.41 Term ordering decisions:
% 0.93/1.41 Function symbol KB weights: tc_bool=1. v_x=1. t_a=1. v_G=1. tc_fun=1. hAPP=1. c_HOL_Ouminus__class_Ouminus=1. c_SetInterval_Oord__class_OatLeast=1. c_SetInterval_Oord__class_OatMost=1. c_Complete__Lattice_OSup__class_OSup=1. c_SetInterval_Oord__class_OlessThan=1. c_SetInterval_Oord__class_OgreaterThan=1. c_lessequals=1. c_Orderings_Obot__class_Obot=1. c_Orderings_Otop__class_Otop=1. c_Fun_Oid=1. tc_Hoare__Mirabelle_Otriple=1. c_Option_Ooption_ONone=1. tc_Option_Ooption=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Set_Oinsert=1. c_in=1. c_HOL_Ominus__class_Ominus=1. c_SetInterval_Oord__class_OatLeastAtMost=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_SetInterval_Oord__class_OgreaterThanAtMost=1. c_SetInterval_Oord__class_OgreaterThanLessThan=1. c_ATP__Linkup_Osko__Predicate__Xpredicate1I__1__1=1. c_Set_Ovimage=1. c_Map_Orestrict__map=1. c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1=1. c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1=1. c_Fun_Ocomp=1. c_Fun_Ofcomp=1.
% 0.93/1.41
% 0.93/1.41 ============================== PROOF =================================
% 0.93/1.41 % SZS status Unsatisfiable
% 0.93/1.41 % SZS output start Refutation
% 0.93/1.41
% 0.93/1.41 % Proof 1 at 0.23 (+ 0.00) seconds.
% 0.93/1.41 % Length of proof is 3.
% 0.93/1.41 % Level of proof is 1.
% 0.93/1.41 % Maximum clause weight is 8.000.
% 0.93/1.41 % Given clauses 0.
% 0.93/1.41
% 0.93/1.41 492 c_Hoare__Mirabelle_Ohoare__derivs(A,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(B),tc_bool)),B) # label(cls_empty_0) # label(axiom). [assumption].
% 0.93/1.41 499 -c_Hoare__Mirabelle_Ohoare__derivs(v_x,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 0.93/1.41 500 $F. [copy(499),unit_del(a,492)].
% 0.93/1.41
% 0.93/1.41 % SZS output end Refutation
% 0.93/1.41 ============================== end of proof ==========================
% 0.93/1.41
% 0.93/1.41 ============================== STATISTICS ============================
% 0.93/1.41
% 0.93/1.41 Given=0. Generated=442. Kept=382. proofs=1.
% 0.93/1.41 Usable=0. Sos=0. Demods=70. Limbo=382, Disabled=581. Hints=0.
% 0.93/1.41 Megabytes=1.07.
% 0.93/1.41 User_CPU=0.23, System_CPU=0.00, Wall_clock=1.
% 0.93/1.41
% 0.93/1.41 ============================== end of statistics =====================
% 0.93/1.41
% 0.93/1.41 ============================== end of search =========================
% 0.93/1.41
% 0.93/1.41 THEOREM PROVED
% 0.93/1.41 % SZS status Unsatisfiable
% 0.93/1.41
% 0.93/1.41 Exiting with 1 proof.
% 0.93/1.41
% 0.93/1.41 Process 709 exit (max_proofs) Tue Jun 14 19:23:41 2022
% 0.93/1.41 Prover9 interrupted
%------------------------------------------------------------------------------