TSTP Solution File: PUZ064-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : PUZ064-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 : Mon Jul 18 18:24:00 EDT 2022
% Result : Unsatisfiable 2.63s 2.95s
% Output : Refutation 2.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : PUZ064-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat May 28 22:42:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.63/2.95 ============================== Prover9 ===============================
% 2.63/2.95 Prover9 (32) version 2009-11A, November 2009.
% 2.63/2.95 Process 27019 was started by sandbox2 on n029.cluster.edu,
% 2.63/2.95 Sat May 28 22:42:43 2022
% 2.63/2.95 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_26866_n029.cluster.edu".
% 2.63/2.95 ============================== end of head ===========================
% 2.63/2.95
% 2.63/2.95 ============================== INPUT =================================
% 2.63/2.95
% 2.63/2.95 % Reading from file /tmp/Prover9_26866_n029.cluster.edu
% 2.63/2.95
% 2.63/2.95 set(prolog_style_variables).
% 2.63/2.95 set(auto2).
% 2.63/2.95 % set(auto2) -> set(auto).
% 2.63/2.95 % set(auto) -> set(auto_inference).
% 2.63/2.95 % set(auto) -> set(auto_setup).
% 2.63/2.95 % set(auto_setup) -> set(predicate_elim).
% 2.63/2.95 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.63/2.95 % set(auto) -> set(auto_limits).
% 2.63/2.95 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.63/2.95 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.63/2.95 % set(auto) -> set(auto_denials).
% 2.63/2.95 % set(auto) -> set(auto_process).
% 2.63/2.95 % set(auto2) -> assign(new_constants, 1).
% 2.63/2.95 % set(auto2) -> assign(fold_denial_max, 3).
% 2.63/2.95 % set(auto2) -> assign(max_weight, "200.000").
% 2.63/2.95 % set(auto2) -> assign(max_hours, 1).
% 2.63/2.95 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.63/2.95 % set(auto2) -> assign(max_seconds, 0).
% 2.63/2.95 % set(auto2) -> assign(max_minutes, 5).
% 2.63/2.95 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.63/2.95 % set(auto2) -> set(sort_initial_sos).
% 2.63/2.95 % set(auto2) -> assign(sos_limit, -1).
% 2.63/2.95 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.63/2.95 % set(auto2) -> assign(max_megs, 400).
% 2.63/2.95 % set(auto2) -> assign(stats, some).
% 2.63/2.95 % set(auto2) -> clear(echo_input).
% 2.63/2.95 % set(auto2) -> set(quiet).
% 2.63/2.95 % set(auto2) -> clear(print_initial_clauses).
% 2.63/2.95 % set(auto2) -> clear(print_given).
% 2.63/2.95 assign(lrs_ticks,-1).
% 2.63/2.95 assign(sos_limit,10000).
% 2.63/2.95 assign(order,kbo).
% 2.63/2.95 set(lex_order_vars).
% 2.63/2.95 clear(print_given).
% 2.63/2.95
% 2.63/2.95 % formulas(sos). % not echoed (29 formulas)
% 2.63/2.95
% 2.63/2.95 ============================== end of input ==========================
% 2.63/2.95
% 2.63/2.95 % From the command line: assign(max_seconds, 300).
% 2.63/2.95
% 2.63/2.95 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.63/2.95
% 2.63/2.95 % Formulas that are not ordinary clauses:
% 2.63/2.95
% 2.63/2.95 ============================== end of process non-clausal formulas ===
% 2.63/2.95
% 2.63/2.95 ============================== PROCESS INITIAL CLAUSES ===============
% 2.63/2.95
% 2.63/2.95 ============================== PREDICATE ELIMINATION =================
% 2.63/2.95
% 2.63/2.95 ============================== end predicate elimination =============
% 2.63/2.95
% 2.63/2.95 Auto_denials: (non-Horn, no changes).
% 2.63/2.95
% 2.63/2.95 Term ordering decisions:
% 2.63/2.95
% 2.63/2.95 % Assigning unary symbol tc_set kb_weight 0 and highest precedence (19).
% 2.63/2.95 Function symbol KB weights: t_a=1. c_emptyset=1. v_u=1. c_UNIV=1. v_A=1. v_t=1. v_a=1. c_uminus=1. c_Mutil_Otiling=1. c_Relation_Odiag=1. c_union=1. c_inter=1. c_minus=1. c_Main_OsubsetI__1=1. c_Relation_OImage=1. tc_set=0.
% 2.63/2.95
% 2.63/2.95 ============================== end of process initial clauses ========
% 2.63/2.95
% 2.63/2.95 ============================== CLAUSES FOR SEARCH ====================
% 2.63/2.95
% 2.63/2.95 ============================== end of clauses for search =============
% 2.63/2.95
% 2.63/2.95 ============================== SEARCH ================================
% 2.63/2.95
% 2.63/2.95 % Starting search at 0.01 seconds.
% 2.63/2.95
% 2.63/2.95 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 51 (0.00 of 0.74 sec).
% 2.63/2.95
% 2.63/2.95 Low Water (keep): wt=44.000, iters=3418
% 2.63/2.95
% 2.63/2.95 Low Water (keep): wt=43.000, iters=3403
% 2.63/2.95
% 2.63/2.95 Low Water (keep): wt=40.000, iters=3389
% 2.63/2.95
% 2.63/2.95 Low Water (keep): wt=39.000, iters=3373
% 2.63/2.95
% 2.63/2.95 Low Water (keep): wt=38.000, iters=3341
% 2.63/2.95
% 2.63/2.95 Low Water (keep): wt=37.000, iters=3357
% 2.63/2.95
% 2.63/2.95 Low Water (keep): wt=36.000, iters=3334
% 2.63/2.95
% 2.63/2.95 Low Water (keep): wt=35.000, iters=3416
% 2.63/2.95
% 2.63/2.95 Low Water (keep): wt=34.000, iters=3377
% 2.63/2.95
% 2.63/2.95 Low Water (keep): wt=33.000, iters=3486
% 2.63/2.95
% 2.63/2.95 Low Water (keep): wt=32.000, iters=3370
% 2.63/2.95
% 2.63/2.95 ============================== PROOF =================================
% 2.63/2.95 % SZS status Unsatisfiable
% 2.63/2.95 % SZS output start Refutation
% 2.63/2.95
% 2.63/2.95 % Proof 1 at 1.93 (+ 0.05) seconds.
% 2.63/2.95 % Length of proof is 146.
% 2.63/2.95 % Level of proof is 24.
% 2.63/2.95 % Maximum clause weight is 39.000.
% 2.63/2.95 % Given clauses 1106.
% 2.63/2.95
% 2.63/2.95 1 c_in(v_a,v_A,tc_set(t_a)) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 2.63/2.95 2 c_lessequals(c_emptyset,A,tc_set(B)) # label(cls_Set_Oempty__subsetI_0) # label(axiom). [assumption].
% 2.63/2.95 3 c_lessequals(A,A,tc_set(B)) # label(cls_Set_Osubset__refl_0) # label(axiom). [assumption].
% 2.63/2.95 4 c_inter(v_a,v_t,t_a) = c_emptyset # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 2.63/2.95 5 c_emptyset = c_inter(v_a,v_t,t_a). [copy(4),flip(a)].
% 2.63/2.95 6 c_uminus(c_UNIV,tc_set(A)) = c_emptyset # label(cls_Set_OCompl__UNIV__eq_0) # label(axiom). [assumption].
% 2.63/2.95 7 c_uminus(c_UNIV,tc_set(A)) = c_inter(v_a,v_t,t_a). [copy(6),rewrite([5(4)])].
% 2.63/2.95 8 c_inter(c_UNIV,A,B) = A # label(cls_Set_OInt__UNIV__left_0) # label(axiom). [assumption].
% 2.63/2.95 9 c_union(c_UNIV,A,B) = c_UNIV # label(cls_Set_OUn__UNIV__left_0) # label(axiom). [assumption].
% 2.63/2.95 10 c_union(A,A,B) = A # label(cls_Set_OUn__absorb_0) # label(axiom). [assumption].
% 2.63/2.95 11 c_union(c_emptyset,A,B) = A # label(cls_Set_OUn__empty__left_0) # label(axiom). [assumption].
% 2.63/2.95 12 c_union(c_inter(v_a,v_t,t_a),A,B) = A. [copy(11),rewrite([5(1)])].
% 2.63/2.95 13 c_union(A,c_emptyset,B) = A # label(cls_Set_OUn__empty__right_0) # label(axiom). [assumption].
% 2.63/2.95 14 c_union(A,c_inter(v_a,v_t,t_a),B) = A. [copy(13),rewrite([5(1)])].
% 2.63/2.95 15 c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) # label(cls_conjecture_3) # label(negated_conjecture). [assumption].
% 2.63/2.95 16 c_inter(c_union(v_a,v_t,t_a),v_u,t_a) = c_emptyset # label(cls_conjecture_4) # label(negated_conjecture). [assumption].
% 2.63/2.95 17 c_inter(c_union(v_a,v_t,t_a),v_u,t_a) = c_inter(v_a,v_t,t_a). [copy(16),rewrite([5(8)])].
% 2.63/2.95 18 c_uminus(c_uminus(A,tc_set(B)),tc_set(B)) = A # label(cls_Set_Odouble__complement_0) # label(axiom). [assumption].
% 2.63/2.95 19 c_Relation_OImage(c_Relation_Odiag(A,B),C,B,B) = c_inter(A,C,B) # label(cls_Relation_OImage__diag_0) # label(axiom). [assumption].
% 2.63/2.95 20 c_inter(A,B,C) = c_Relation_OImage(c_Relation_Odiag(A,C),B,C,C). [copy(19),flip(a)].
% 2.63/2.95 21 c_in(c_Main_OsubsetI__1(A,B,C),A,C) | c_lessequals(A,B,tc_set(C)) # label(cls_Set_OsubsetI_0) # label(axiom). [assumption].
% 2.63/2.95 22 c_minus(A,c_uminus(B,tc_set(C)),tc_set(C)) = c_inter(A,B,C) # label(cls_Set_ODiff__Compl_0) # label(axiom). [assumption].
% 2.63/2.95 23 c_Relation_OImage(c_Relation_Odiag(A,B),C,B,B) = c_minus(A,c_uminus(C,tc_set(B)),tc_set(B)). [copy(22),rewrite([20(5)]),flip(a)].
% 2.63/2.95 24 c_union(c_minus(A,B,tc_set(C)),B,C) = c_union(A,B,C) # label(cls_Set_OUn__Diff__cancel2_0) # label(axiom). [assumption].
% 2.63/2.95 25 c_union(A,c_minus(B,A,tc_set(C)),C) = c_union(A,B,C) # label(cls_Set_OUn__Diff__cancel_0) # label(axiom). [assumption].
% 2.63/2.95 26 c_union(c_union(A,B,C),D,C) = c_union(A,c_union(B,D,C),C) # label(cls_Set_OUn__assoc_0) # label(axiom). [assumption].
% 2.63/2.95 27 c_uminus(c_minus(A,B,tc_set(C)),tc_set(C)) = c_union(c_uminus(A,tc_set(C)),B,C) # label(cls_Set_OCompl__Diff__eq_0) # label(axiom). [assumption].
% 2.63/2.95 28 c_union(c_uminus(A,tc_set(B)),C,B) = c_uminus(c_minus(A,C,tc_set(B)),tc_set(B)). [copy(27),flip(a)].
% 2.63/2.95 29 -c_in(A,c_emptyset,B) # label(cls_Set_Oempty__iff_0) # label(axiom). [assumption].
% 2.63/2.95 30 -c_in(A,c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),B). [copy(29),rewrite([5(1),20(4),23(7)])].
% 2.63/2.95 31 -c_in(c_union(c_union(v_a,v_t,t_a),v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) # label(cls_conjecture_5) # label(negated_conjecture). [assumption].
% 2.63/2.95 32 -c_in(c_union(v_a,c_union(v_t,v_u,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)). [copy(31),rewrite([26(7)])].
% 2.63/2.95 33 -c_in(A,c_inter(B,C,D),D) | c_in(A,C,D) # label(cls_Set_OInt__iff_1) # label(axiom). [assumption].
% 2.63/2.95 34 -c_in(A,c_minus(B,c_uminus(C,tc_set(D)),tc_set(D)),D) | c_in(A,C,D). [copy(33),rewrite([20(1),23(2)])].
% 2.63/2.95 35 -c_lessequals(c_union(A,B,C),D,tc_set(C)) | c_lessequals(A,D,tc_set(C)) # label(cls_Set_OUn__subset__iff_0) # label(axiom). [assumption].
% 2.63/2.95 36 -c_lessequals(c_union(A,B,C),D,tc_set(C)) | c_lessequals(B,D,tc_set(C)) # label(cls_Set_OUn__subset__iff_1) # label(axiom). [assumption].
% 2.63/2.95 37 -c_lessequals(A,B,tc_set(C)) | -c_lessequals(B,A,tc_set(C)) | B = A # label(cls_Set_Osubset__antisym_0) # label(axiom). [assumption].
% 2.63/2.95 38 -c_lessequals(A,B,tc_set(C)) | -c_lessequals(D,B,tc_set(C)) | c_lessequals(c_union(D,A,C),B,tc_set(C)) # label(cls_Set_OUn__subset__iff_2) # label(axiom). [assumption].
% 2.63/2.95 39 c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) | c_inter(v_t,v_u,t_a) != c_emptyset | -c_in(v_u,c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) # label(cls_conjecture_6) # label(negated_conjecture). [assumption].
% 2.63/2.95 40 c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) | c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) != c_minus(v_t,c_uminus(v_u,tc_set(t_a)),tc_set(t_a)). [copy(39),rewrite([20(14),23(17),5(19),20(22),23(25)]),flip(b),unit_del(c,15)].
% 2.63/2.95 41 -c_in(A,B,tc_set(C)) | -c_in(D,c_Mutil_Otiling(B,C),tc_set(C)) | c_inter(A,D,C) != c_emptyset | c_in(c_union(A,D,C),c_Mutil_Otiling(B,C),tc_set(C)) # label(cls_Mutil_Otiling_OUn_0) # label(axiom). [assumption].
% 2.63/2.95 42 -c_in(A,B,tc_set(C)) | -c_in(D,c_Mutil_Otiling(B,C),tc_set(C)) | c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) != c_minus(A,c_uminus(D,tc_set(C)),tc_set(C)) | c_in(c_union(A,D,C),c_Mutil_Otiling(B,C),tc_set(C)). [copy(41),rewrite([20(6),23(7),5(10),20(13),23(16)]),flip(c)].
% 2.63/2.95 43 c_lessequals(c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),A,tc_set(B)). [back_rewrite(2),rewrite([5(1),20(4),23(7)])].
% 2.63/2.95 44 c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)). [back_rewrite(17),rewrite([20(7),23(10),20(15),23(18)])].
% 2.63/2.95 45 c_union(A,c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),B) = A. [back_rewrite(14),rewrite([20(4),23(7)])].
% 2.63/2.95 46 c_union(c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),A,B) = A. [back_rewrite(12),rewrite([20(4),23(7)])].
% 2.63/2.95 47 c_minus(c_UNIV,c_uminus(A,tc_set(B)),tc_set(B)) = A. [back_rewrite(8),rewrite([20(2),23(3)])].
% 2.63/2.95 48 c_uminus(c_UNIV,tc_set(A)) = c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)). [back_rewrite(7),rewrite([20(7),23(10)])].
% 2.63/2.95 52 c_union(A,c_union(A,B,C),C) = c_union(A,B,C). [para(10(a,1),26(a,1,1)),flip(a)].
% 2.63/2.95 53 c_union(c_minus(A,B,tc_set(C)),c_union(B,D,C),C) = c_union(A,c_union(B,D,C),C). [para(24(a,1),26(a,1,1)),rewrite([26(2)]),flip(a)].
% 2.63/2.95 54 c_union(A,c_union(B,c_minus(C,c_union(A,B,D),tc_set(D)),D),D) = c_union(A,c_union(B,C,D),D). [para(26(a,1),25(a,1)),rewrite([26(7)])].
% 2.63/2.95 55 c_union(A,c_union(c_minus(B,A,tc_set(C)),D,C),C) = c_union(A,c_union(B,D,C),C). [para(25(a,1),26(a,1,1)),rewrite([26(2)]),flip(a)].
% 2.63/2.95 57 c_uminus(c_minus(c_uminus(A,tc_set(B)),C,tc_set(B)),tc_set(B)) = c_union(A,C,B). [para(18(a,1),28(a,1,1)),flip(a)].
% 2.63/2.95 58 c_uminus(c_minus(A,c_minus(B,c_uminus(A,tc_set(C)),tc_set(C)),tc_set(C)),tc_set(C)) = c_uminus(c_minus(A,B,tc_set(C)),tc_set(C)). [para(28(a,1),25(a,1)),rewrite([28(11)])].
% 2.63/2.95 59 c_uminus(c_minus(c_minus(A,B,tc_set(C)),D,tc_set(C)),tc_set(C)) = c_uminus(c_minus(A,c_union(B,D,C),tc_set(C)),tc_set(C)). [para(28(a,1),26(a,1,1)),rewrite([28(5),28(10)])].
% 2.63/2.95 62 -c_in(A,c_minus(B,c_uminus(c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(C)),tc_set(C)),C). [ur(34,b,30,a)].
% 2.63/2.95 64 c_lessequals(A,c_union(A,B,C),tc_set(C)). [resolve(35,a,3,a)].
% 2.63/2.95 68 c_lessequals(A,c_union(B,A,C),tc_set(C)). [resolve(36,a,3,a)].
% 2.63/2.95 73 -c_lessequals(A,B,tc_set(C)) | c_lessequals(c_union(A,B,C),B,tc_set(C)). [resolve(38,a,3,a)].
% 2.63/2.95 80 -c_lessequals(A,c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(B)) | c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) = A. [resolve(43,a,37,b)].
% 2.63/2.95 83 c_minus(A,c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(B)) = A. [para(45(a,1),24(a,1)),rewrite([45(19)])].
% 2.63/2.95 86 c_minus(c_UNIV,A,tc_set(B)) = c_uminus(A,tc_set(B)). [para(18(a,1),47(a,1,2))].
% 2.63/2.95 88 c_uminus(c_minus(A,c_UNIV,tc_set(B)),tc_set(B)) = c_uminus(c_minus(A,A,tc_set(B)),tc_set(B)). [para(47(a,1),25(a,1,2)),rewrite([28(3),28(8)]),flip(a)].
% 2.63/2.95 89 c_uminus(c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)),tc_set(A)) = c_UNIV. [para(48(a,1),18(a,1,1))].
% 2.63/2.95 90 c_minus(A,c_uminus(c_UNIV,tc_set(B)),tc_set(B)) = A. [para(48(a,1),23(a,2,2)),rewrite([23(3),83(15)])].
% 2.63/2.95 96 c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) | c_uminus(c_UNIV,tc_set(A)) != c_minus(v_t,c_uminus(v_u,tc_set(t_a)),tc_set(t_a)). [para(48(a,2),40(b,1))].
% 2.63/2.95 97 c_lessequals(c_uminus(c_UNIV,tc_set(A)),B,tc_set(C)). [para(48(a,2),43(a,1))].
% 2.63/2.95 98 c_union(A,c_uminus(c_UNIV,tc_set(B)),C) = A. [para(48(a,2),45(a,1,2))].
% 2.63/2.95 99 c_union(c_uminus(c_UNIV,tc_set(A)),B,C) = B. [para(48(a,2),46(a,1,1))].
% 2.63/2.95 100 c_uminus(c_UNIV,tc_set(A)) = c_uminus(c_UNIV,tc_set(B)). [para(48(a,2),48(a,2))].
% 2.63/2.95 101 -c_in(A,c_minus(B,c_UNIV,tc_set(C)),C). [back_rewrite(62),rewrite([89(10)])].
% 2.63/2.95 102 c_uminus(c_UNIV,tc_set(A)) = c_0. [new_symbol(100)].
% 2.63/2.95 103 c_union(c_0,A,B) = A. [back_rewrite(99),rewrite([102(3)])].
% 2.63/2.95 104 c_union(A,c_0,B) = A. [back_rewrite(98),rewrite([102(3)])].
% 2.63/2.95 105 c_lessequals(c_0,A,tc_set(B)). [back_rewrite(97),rewrite([102(3)])].
% 2.63/2.95 106 c_in(c_union(v_t,v_u,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) | c_minus(v_t,c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) != c_0. [back_rewrite(96),rewrite([102(13)]),flip(b)].
% 2.63/2.95 110 c_minus(A,c_0,tc_set(B)) = A. [back_rewrite(90),rewrite([102(3)])].
% 2.63/2.95 111 c_minus(v_a,c_uminus(v_t,tc_set(t_a)),tc_set(t_a)) = c_0. [back_rewrite(48),rewrite([102(3)]),flip(a)].
% 2.63/2.95 112 c_uminus(c_0,tc_set(A)) = c_UNIV. [back_rewrite(89),rewrite([111(8)])].
% 2.63/2.95 113 -c_lessequals(A,c_0,tc_set(B)) | c_0 = A. [back_rewrite(80),rewrite([111(8),111(11)])].
% 2.63/2.95 120 c_minus(c_union(v_a,v_t,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_0. [back_rewrite(44),rewrite([111(19)])].
% 2.63/2.95 121 -c_in(A,B,tc_set(C)) | -c_in(D,c_Mutil_Otiling(B,C),tc_set(C)) | c_minus(A,c_uminus(D,tc_set(C)),tc_set(C)) != c_0 | c_in(c_union(A,D,C),c_Mutil_Otiling(B,C),tc_set(C)). [back_rewrite(42),rewrite([111(13)]),flip(c)].
% 2.63/2.95 127 c_lessequals(c_minus(A,c_UNIV,tc_set(B)),C,tc_set(B)). [resolve(101,a,21,a)].
% 2.63/2.95 141 c_uminus(c_minus(c_0,A,tc_set(B)),tc_set(B)) = c_UNIV. [para(112(a,1),28(a,1,1)),rewrite([9(2)]),flip(a)].
% 2.63/2.95 143 -c_lessequals(A,c_union(B,C,D),tc_set(D)) | c_lessequals(c_union(A,B,D),c_union(B,C,D),tc_set(D)). [resolve(64,a,38,a)].
% 2.63/2.95 146 c_lessequals(c_minus(A,B,tc_set(C)),c_union(A,B,C),tc_set(C)). [para(24(a,1),64(a,2))].
% 2.63/2.95 149 c_uminus(c_minus(A,c_union(A,B,C),tc_set(C)),tc_set(C)) = c_UNIV. [para(9(a,1),53(a,2)),rewrite([86(3),28(4)])].
% 2.63/2.95 165 -c_lessequals(c_union(A,B,C),B,tc_set(C)) | c_union(A,B,C) = B. [resolve(68,a,37,b),flip(b)].
% 2.63/2.95 167 c_lessequals(A,c_UNIV,tc_set(B)). [para(9(a,1),68(a,2))].
% 2.63/2.95 171 -c_lessequals(c_UNIV,A,tc_set(B)) | c_UNIV = A. [resolve(167,a,37,b),flip(b)].
% 2.63/2.95 178 c_uminus(c_minus(A,c_union(B,c_minus(C,c_uminus(c_minus(A,B,tc_set(D)),tc_set(D)),tc_set(D)),D),tc_set(D)),tc_set(D)) = c_uminus(c_minus(A,c_union(B,C,D),tc_set(D)),tc_set(D)). [para(54(a,1),28(a,1)),rewrite([28(4),28(8)]),flip(a)].
% 2.63/2.95 188 c_union(A,c_UNIV,B) = c_UNIV. [resolve(171,a,68,a),flip(a)].
% 2.63/2.95 189 c_uminus(c_minus(A,c_UNIV,tc_set(B)),tc_set(B)) = c_UNIV. [para(188(a,1),28(a,1)),flip(a)].
% 2.63/2.95 191 c_uminus(c_minus(A,A,tc_set(B)),tc_set(B)) = c_UNIV. [back_rewrite(88),rewrite([189(5)]),flip(a)].
% 2.63/2.95 206 c_minus(A,c_UNIV,tc_set(B)) = c_0. [resolve(127,a,113,a),flip(a)].
% 2.63/2.95 214 c_minus(c_0,A,tc_set(B)) = c_0. [para(141(a,1),18(a,1,1)),rewrite([102(3)]),flip(a)].
% 2.63/2.95 215 c_minus(c_uminus(A,tc_set(B)),C,tc_set(B)) = c_uminus(c_union(A,C,B),tc_set(B)). [para(57(a,1),18(a,1,1)),flip(a)].
% 2.63/2.95 314 c_minus(A,A,tc_set(B)) = c_0. [para(191(a,1),18(a,1,1)),rewrite([102(3)]),flip(a)].
% 2.63/2.95 325 c_minus(A,c_minus(B,c_uminus(A,tc_set(C)),tc_set(C)),tc_set(C)) = c_minus(A,B,tc_set(C)). [para(58(a,1),18(a,1,1)),rewrite([18(6)]),flip(a)].
% 2.63/2.95 326 c_uminus(c_minus(v_a,c_uminus(c_union(v_t,c_uminus(v_a,tc_set(t_a)),t_a),tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_UNIV. [para(111(a,1),58(a,2,1)),rewrite([215(12),112(21)])].
% 2.63/2.95 359 c_minus(c_minus(A,B,tc_set(C)),D,tc_set(C)) = c_minus(A,c_union(B,D,C),tc_set(C)). [para(59(a,1),18(a,1,1)),rewrite([18(7)]),flip(a)].
% 2.63/2.95 435 c_minus(A,c_union(A,B,C),tc_set(C)) = c_0. [para(149(a,1),18(a,1,1)),rewrite([102(3)]),flip(a)].
% 2.63/2.95 439 c_minus(A,c_union(B,c_union(A,B,C),C),tc_set(C)) = c_0. [para(24(a,1),435(a,1,2)),rewrite([359(5)])].
% 2.63/2.95 440 c_union(A,c_union(B,A,C),C) = c_union(A,B,C). [para(435(a,1),25(a,1,2)),rewrite([104(3),26(3)]),flip(a)].
% 2.63/2.95 442 c_minus(A,c_union(B,c_union(A,c_union(B,C,D),D),D),tc_set(D)) = c_0. [para(53(a,1),435(a,1,2)),rewrite([359(6)])].
% 2.63/2.95 443 c_union(A,c_union(B,c_union(A,C,D),D),D) = c_union(A,c_union(B,C,D),D). [para(435(a,1),55(a,1,2,1)),rewrite([103(3),26(2),26(5)]),flip(a)].
% 2.63/2.95 445 c_minus(A,c_union(B,A,C),tc_set(C)) = c_0. [back_rewrite(439),rewrite([440(2)])].
% 2.63/2.95 452 c_minus(A,c_union(B,c_union(A,C,D),D),tc_set(D)) = c_0. [back_rewrite(442),rewrite([443(3)])].
% 2.63/2.95 471 c_union(A,B,C) = c_union(B,A,C). [para(445(a,1),24(a,1,1)),rewrite([103(3),440(3)])].
% 2.63/2.95 472 c_minus(A,c_uminus(c_minus(B,A,tc_set(C)),tc_set(C)),tc_set(C)) = c_0. [para(28(a,1),445(a,1,2))].
% 2.63/2.95 475 c_union(A,c_union(B,C,D),D) = c_union(C,c_union(A,B,D),D). [para(445(a,1),55(a,1,2,1)),rewrite([471(3),104(3),471(2),26(5),52(4)]),flip(a)].
% 2.63/2.95 659 c_minus(c_union(v_t,v_a,t_a),c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_0. [back_rewrite(120),rewrite([471(4)])].
% 2.63/2.95 663 c_in(c_union(v_u,v_t,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)) | c_minus(v_t,c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) != c_0. [back_rewrite(106),rewrite([471(4)])].
% 2.63/2.95 668 -c_in(c_union(v_a,c_union(v_u,v_t,t_a),t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)). [back_rewrite(32),rewrite([471(5)])].
% 2.63/2.95 669 c_union(A,c_uminus(B,tc_set(C)),C) = c_uminus(c_minus(B,A,tc_set(C)),tc_set(C)). [back_rewrite(28),rewrite([471(3)])].
% 2.63/2.95 692 c_uminus(c_minus(v_a,c_minus(v_a,v_t,tc_set(t_a)),tc_set(t_a)),tc_set(t_a)) = c_UNIV. [back_rewrite(326),rewrite([669(8),18(12)])].
% 2.63/2.95 703 c_union(c_uminus(v_u,tc_set(t_a)),c_union(v_t,v_a,t_a),t_a) = c_uminus(v_u,tc_set(t_a)). [para(659(a,1),25(a,1,2)),rewrite([471(7),669(7),110(5)]),flip(a)].
% 2.63/2.95 725 c_minus(v_a,c_minus(v_a,v_t,tc_set(t_a)),tc_set(t_a)) = c_0. [para(692(a,1),18(a,1,1)),rewrite([102(4)]),flip(a)].
% 2.63/2.95 726 c_union(c_0,c_minus(v_a,v_t,tc_set(t_a)),t_a) = c_union(v_a,c_minus(v_a,v_t,tc_set(t_a)),t_a). [para(725(a,1),25(a,1,2)),rewrite([471(8),471(16)])].
% 2.63/2.95 727 c_union(c_0,c_union(A,c_minus(v_a,v_t,tc_set(t_a)),t_a),t_a) = c_union(v_a,c_union(A,c_minus(v_a,v_t,tc_set(t_a)),t_a),t_a). [para(725(a,1),53(a,1,1)),rewrite([471(8),471(18)])].
% 2.63/2.95 827 c_lessequals(c_union(A,c_minus(A,B,tc_set(C)),C),c_union(A,B,C),tc_set(C)). [resolve(143,a,146,a),rewrite([471(3)])].
% 2.63/2.95 841 c_union(c_0,c_union(A,B,C),C) = c_union(A,B,C). [para(104(a,1),475(a,1,2)),flip(a)].
% 2.63/2.95 853 c_union(A,c_union(B,C,D),D) = c_union(C,c_union(B,A,D),D). [para(475(a,1),471(a,2)),rewrite([471(2),471(3)])].
% 2.63/2.95 966 c_union(v_a,c_union(A,c_minus(v_a,v_t,tc_set(t_a)),t_a),t_a) = c_union(A,c_minus(v_a,v_t,tc_set(t_a)),t_a). [back_rewrite(727),rewrite([841(10)]),flip(a)].
% 2.63/2.95 1112 c_minus(v_t,c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_0. [para(703(a,1),452(a,1,2))].
% 2.63/2.95 1132 c_in(c_union(v_u,v_t,t_a),c_Mutil_Otiling(v_A,t_a),tc_set(t_a)). [back_rewrite(663),rewrite([1112(18)]),xx(b)].
% 2.63/2.95 1145 c_uminus(c_minus(v_u,v_t,tc_set(t_a)),tc_set(t_a)) = c_uminus(v_u,tc_set(t_a)). [para(1112(a,1),25(a,1,2)),rewrite([471(7),669(7),110(5),471(11),669(11)]),flip(a)].
% 2.63/2.95 1151 c_minus(v_a,c_uminus(c_union(v_u,v_t,t_a),tc_set(t_a)),tc_set(t_a)) != c_0. [ur(121,a,1,a,b,1132,a,d,668,a)].
% 2.63/2.95 1195 -c_lessequals(c_minus(v_a,c_uminus(c_union(v_u,v_t,t_a),tc_set(t_a)),tc_set(t_a)),c_0,tc_set(A)). [ur(37,a,105,a,c,1151,a)].
% 2.63/2.95 1201 -c_lessequals(c_union(A,c_minus(v_a,c_uminus(c_union(v_u,v_t,t_a),tc_set(t_a)),tc_set(t_a)),B),c_0,tc_set(B)). [ur(36,b,1195,a)].
% 2.63/2.95 1219 c_uminus(c_minus(v_a,c_union(A,c_minus(v_a,v_t,tc_set(t_a)),t_a),tc_set(t_a)),tc_set(t_a)) = c_UNIV. [para(725(a,1),178(a,1,1,2,2,2,1)),rewrite([112(10),206(10),471(9),726(9),435(12),112(4),471(9)]),flip(a)].
% 2.63/2.95 1238 c_minus(v_u,v_t,tc_set(t_a)) = v_u. [para(1145(a,1),18(a,1,1)),rewrite([18(7)]),flip(a)].
% 2.63/2.95 1528 c_uminus(c_minus(v_u,v_a,tc_set(t_a)),tc_set(t_a)) = c_uminus(v_u,tc_set(t_a)). [para(853(a,1),703(a,1)),rewrite([669(8),1238(6),669(7)])].
% 2.63/2.95 1536 c_minus(v_a,c_uminus(v_u,tc_set(t_a)),tc_set(t_a)) = c_0. [para(1528(a,1),472(a,1,2))].
% 2.63/2.95 1551 c_minus(A,c_minus(A,B,tc_set(C)),tc_set(C)) = c_minus(A,c_uminus(B,tc_set(C)),tc_set(C)). [para(215(a,1),325(a,1,2)),rewrite([669(3),18(6)])].
% 2.63/2.95 1680 c_minus(A,c_union(B,A,C),tc_set(C)) = c_0. [para(314(a,1),359(a,1,1)),rewrite([214(3),471(2)]),flip(a)].
% 2.63/2.95 3518 c_minus(v_a,c_union(A,c_minus(v_a,v_t,tc_set(t_a)),t_a),tc_set(t_a)) = c_0. [para(1219(a,1),18(a,1,1)),rewrite([102(4)]),flip(a)].
% 2.63/2.95 3628 c_lessequals(v_a,c_union(A,c_minus(v_a,v_t,tc_set(t_a)),t_a),tc_set(t_a)). [para(3518(a,1),827(a,1,2)),rewrite([104(4),966(11)])].
% 2.63/2.95 3634 c_lessequals(v_a,c_minus(v_a,v_t,tc_set(t_a)),tc_set(t_a)). [para(10(a,1),3628(a,2))].
% 2.63/2.95 3635 c_lessequals(c_union(v_a,c_minus(v_a,v_t,tc_set(t_a)),t_a),c_minus(v_a,v_t,tc_set(t_a)),tc_set(t_a)). [resolve(3634,a,73,a)].
% 2.63/2.95 3692 c_union(v_a,c_minus(v_a,v_t,tc_set(t_a)),t_a) = c_minus(v_a,v_t,tc_set(t_a)). [resolve(3635,a,165,a)].
% 2.63/2.95 3697 c_minus(v_a,v_t,tc_set(t_a)) = v_a. [para(3692(a,1),25(a,2)),rewrite([359(10),1680(9),104(4)]),flip(a)].
% 2.63/2.95 3724 c_minus(v_a,c_union(A,v_t,t_a),tc_set(t_a)) = c_minus(v_a,A,tc_set(t_a)). [para(3697(a,1),359(a,1,1)),rewrite([471(8)]),flip(a)].
% 2.63/2.95 6782 c_minus(v_a,c_uminus(c_union(A,v_t,t_a),tc_set(t_a)),tc_set(t_a)) = c_minus(v_a,c_uminus(A,tc_set(t_a)),tc_set(t_a)). [para(3724(a,1),1551(a,1,2)),rewrite([1551(8)]),flip(a)].
% 2.63/2.95 6903 -c_lessequals(A,c_0,tc_set(B)). [back_rewrite(1201),rewrite([6782(11),1536(8),104(2)])].
% 2.63/2.95 6904 $F. [resolve(6903,a,105,a)].
% 2.63/2.95
% 2.63/2.95 % SZS output end Refutation
% 2.63/2.95 ============================== end of proof ==========================
% 2.63/2.95
% 2.63/2.95 ============================== STATISTICS ============================
% 2.63/2.95
% 2.63/2.95 Given=1106. Generated=73930. Kept=6890. proofs=1.
% 2.63/2.95 Usable=741. Sos=4017. Demods=643. Limbo=121, Disabled=2039. Hints=0.
% 2.63/2.95 Megabytes=9.45.
% 2.63/2.95 User_CPU=1.93, System_CPU=0.05, Wall_clock=2.
% 2.63/2.95
% 2.63/2.95 ============================== end of statistics =====================
% 2.63/2.95
% 2.63/2.95 ============================== end of search =========================
% 2.63/2.95
% 2.63/2.95 THEOREM PROVED
% 2.63/2.95 % SZS status Unsatisfiable
% 2.63/2.95
% 2.63/2.95 Exiting with 1 proof.
% 2.63/2.95
% 2.63/2.95 Process 27019 exit (max_proofs) Sat May 28 22:42:45 2022
% 2.63/2.95 Prover9 interrupted
%------------------------------------------------------------------------------