TSTP Solution File: SET854-2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET854-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 : Tue Jul 19 04:32:52 EDT 2022
% Result : Unsatisfiable 129.44s 129.88s
% Output : Refutation 129.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SET854-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.32 % Computer : n023.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 600
% 0.10/0.32 % DateTime : Sun Jul 10 17:49:55 EDT 2022
% 0.10/0.32 % CPUTime :
% 2.61/2.91 ============================== Prover9 ===============================
% 2.61/2.91 Prover9 (32) version 2009-11A, November 2009.
% 2.61/2.91 Process 31028 was started by sandbox on n023.cluster.edu,
% 2.61/2.91 Sun Jul 10 17:49:55 2022
% 2.61/2.91 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30701_n023.cluster.edu".
% 2.61/2.91 ============================== end of head ===========================
% 2.61/2.91
% 2.61/2.91 ============================== INPUT =================================
% 2.61/2.91
% 2.61/2.91 % Reading from file /tmp/Prover9_30701_n023.cluster.edu
% 2.61/2.91
% 2.61/2.91 set(prolog_style_variables).
% 2.61/2.91 set(auto2).
% 2.61/2.91 % set(auto2) -> set(auto).
% 2.61/2.91 % set(auto) -> set(auto_inference).
% 2.61/2.91 % set(auto) -> set(auto_setup).
% 2.61/2.91 % set(auto_setup) -> set(predicate_elim).
% 2.61/2.91 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.61/2.91 % set(auto) -> set(auto_limits).
% 2.61/2.91 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.61/2.91 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.61/2.91 % set(auto) -> set(auto_denials).
% 2.61/2.91 % set(auto) -> set(auto_process).
% 2.61/2.91 % set(auto2) -> assign(new_constants, 1).
% 2.61/2.91 % set(auto2) -> assign(fold_denial_max, 3).
% 2.61/2.91 % set(auto2) -> assign(max_weight, "200.000").
% 2.61/2.91 % set(auto2) -> assign(max_hours, 1).
% 2.61/2.91 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.61/2.91 % set(auto2) -> assign(max_seconds, 0).
% 2.61/2.91 % set(auto2) -> assign(max_minutes, 5).
% 2.61/2.91 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.61/2.91 % set(auto2) -> set(sort_initial_sos).
% 2.61/2.91 % set(auto2) -> assign(sos_limit, -1).
% 2.61/2.91 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.61/2.91 % set(auto2) -> assign(max_megs, 400).
% 2.61/2.91 % set(auto2) -> assign(stats, some).
% 2.61/2.91 % set(auto2) -> clear(echo_input).
% 2.61/2.91 % set(auto2) -> set(quiet).
% 2.61/2.91 % set(auto2) -> clear(print_initial_clauses).
% 2.61/2.91 % set(auto2) -> clear(print_given).
% 2.61/2.91 assign(lrs_ticks,-1).
% 2.61/2.91 assign(sos_limit,10000).
% 2.61/2.91 assign(order,kbo).
% 2.61/2.91 set(lex_order_vars).
% 2.61/2.91 clear(print_given).
% 2.61/2.91
% 2.61/2.91 % formulas(sos). % not echoed (18 formulas)
% 2.61/2.91
% 2.61/2.91 ============================== end of input ==========================
% 2.61/2.91
% 2.61/2.91 % From the command line: assign(max_seconds, 300).
% 2.61/2.91
% 2.61/2.91 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.61/2.91
% 2.61/2.91 % Formulas that are not ordinary clauses:
% 2.61/2.91
% 2.61/2.91 ============================== end of process non-clausal formulas ===
% 2.61/2.91
% 2.61/2.91 ============================== PROCESS INITIAL CLAUSES ===============
% 2.61/2.91
% 2.61/2.91 ============================== PREDICATE ELIMINATION =================
% 2.61/2.91
% 2.61/2.91 ============================== end predicate elimination =============
% 2.61/2.91
% 2.61/2.91 Auto_denials: (non-Horn, no changes).
% 2.61/2.91
% 2.61/2.91 Term ordering decisions:
% 2.61/2.91
% 2.61/2.91 % Assigning unary symbol tc_set kb_weight 0 and highest precedence (14).
% 2.61/2.91 Function symbol KB weights: t_a=1. v_S=1. v_Y=1. v_x=1. c_Zorn_OTFin=1. c_Union=1. c_Zorn_Osucc=1. c_Zorn_OTFin__linear__lemma1__1=1. c_Main_OsubsetI__1=1. c_Zorn_OUnion__lemma0__1=1. tc_set=0.
% 2.61/2.91
% 2.61/2.91 ============================== end of process initial clauses ========
% 2.61/2.91
% 2.61/2.91 ============================== CLAUSES FOR SEARCH ====================
% 2.61/2.91
% 2.61/2.91 ============================== end of clauses for search =============
% 2.61/2.91
% 2.61/2.91 ============================== SEARCH ================================
% 2.61/2.91
% 2.61/2.91 % Starting search at 0.01 seconds.
% 2.61/2.91
% 2.61/2.91 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 22 (0.00 of 0.37 sec).
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=199.000, iters=3364
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=197.000, iters=3339
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=195.000, iters=3359
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=193.000, iters=3370
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=192.000, iters=3524
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=189.000, iters=3432
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=186.000, iters=3358
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=185.000, iters=3411
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=184.000, iters=3362
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=183.000, iters=3345
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=182.000, iters=3359
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=179.000, iters=3350
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=176.000, iters=3335
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=174.000, iters=3385
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=173.000, iters=3398
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=172.000, iters=3385
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=170.000, iters=3384
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=168.000, iters=3406
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=167.000, iters=3352
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=166.000, iters=3363
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=165.000, iters=3353
% 2.61/2.91
% 2.61/2.91 Low Water (keep): wt=164.000, iters=3440
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=163.000, iters=3431
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=160.000, iters=3385
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=159.000, iters=3341
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=157.000, iters=3369
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=156.000, iters=3355
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=154.000, iters=3353
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=153.000, iters=3339
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=152.000, iters=3409
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=151.000, iters=3353
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=150.000, iters=3361
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=149.000, iters=3377
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=147.000, iters=3334
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=141.000, iters=3548
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=137.000, iters=3342
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=135.000, iters=3441
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=133.000, iters=3349
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=132.000, iters=3382
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=131.000, iters=3352
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=129.000, iters=3364
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=128.000, iters=3355
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=127.000, iters=3409
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=126.000, iters=3351
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=125.000, iters=3385
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=124.000, iters=3337
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=123.000, iters=3355
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=122.000, iters=3335
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=121.000, iters=3350
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=120.000, iters=3346
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=118.000, iters=3368
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=117.000, iters=3359
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=116.000, iters=3384
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=115.000, iters=3373
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=114.000, iters=3343
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=113.000, iters=3342
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=112.000, iters=3367
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=111.000, iters=3369
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=110.000, iters=3334
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=109.000, iters=3358
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=108.000, iters=3342
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=107.000, iters=3334
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=106.000, iters=3336
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=105.000, iters=3359
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=104.000, iters=3336
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=103.000, iters=3349
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=102.000, iters=3334
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=101.000, iters=3334
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=100.000, iters=3336
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=99.000, iters=3334
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=98.000, iters=3364
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=5073, wt=200.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=5099, wt=199.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=5091, wt=198.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=5082, wt=197.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=5132, wt=196.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=5124, wt=195.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=5160, wt=194.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=5186, wt=193.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=5173, wt=192.000
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=97.000, iters=3352
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=5116, wt=191.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=16120, wt=133.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=16306, wt=131.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=14635, wt=129.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=16307, wt=128.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=16308, wt=125.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=12232, wt=122.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=11932, wt=121.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=12233, wt=119.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=11133, wt=117.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=16354, wt=116.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=16374, wt=95.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=16375, wt=92.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=16419, wt=91.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=16747, wt=89.000
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=96.000, iters=3348
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=95.000, iters=3339
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=94.000, iters=3357
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=20490, wt=88.000
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=21842, wt=87.000
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=93.000, iters=3335
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=22292, wt=86.000
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=92.000, iters=3350
% 129.44/129.88
% 129.44/129.88 Low Water (displace): id=24112, wt=85.000
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=91.000, iters=3333
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=90.000, iters=3334
% 129.44/129.88
% 129.44/129.88 Low Water (keep): wt=89.000, iters=3333
% 129.44/129.88
% 129.44/129.88 ============================== PROOF =================================
% 129.44/129.88 % SZS status Unsatisfiable
% 129.44/129.88 % SZS output start Refutation
% 129.44/129.88
% 129.44/129.88 % Proof 1 at 128.61 (+ 0.20) seconds.
% 129.44/129.88 % Length of proof is 49.
% 129.44/129.88 % Level of proof is 11.
% 129.44/129.88 % Maximum clause weight is 118.000.
% 129.44/129.88 % Given clauses 13390.
% 129.44/129.88
% 129.44/129.88 1 c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 129.44/129.88 2 c_lessequals(A,c_Zorn_Osucc(B,A,C),tc_set(tc_set(C))) # label(cls_Zorn_OAbrial__axiom1_0) # label(axiom). [assumption].
% 129.44/129.88 3 c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 129.44/129.88 4 c_lessequals(v_x,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 129.44/129.88 5 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].
% 129.44/129.88 6 c_in(c_Zorn_OUnion__lemma0__1(A,B,C,D),C,tc_set(D)) | c_lessequals(B,c_Union(C,D),tc_set(D)) | c_lessequals(c_Union(C,D),A,tc_set(D)) # label(cls_Zorn_OUnion__lemma0_0) # label(axiom). [assumption].
% 129.44/129.88 7 v_x != c_Union(v_Y,tc_set(t_a)) # label(cls_conjecture_3) # label(negated_conjecture). [assumption].
% 129.44/129.88 8 c_Union(v_Y,tc_set(t_a)) != v_x. [copy(7),flip(a)].
% 129.44/129.88 9 -c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) # label(cls_conjecture_4) # label(negated_conjecture). [assumption].
% 129.44/129.88 10 -c_in(c_Main_OsubsetI__1(A,B,C),B,C) | c_lessequals(A,B,tc_set(C)) # label(cls_Set_OsubsetI_1) # label(axiom). [assumption].
% 129.44/129.88 11 -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].
% 129.44/129.88 12 -c_in(A,B,C) | -c_lessequals(B,D,tc_set(C)) | c_in(A,D,C) # label(cls_Set_OsubsetD_0) # label(axiom). [assumption].
% 129.44/129.88 13 -c_lessequals(c_Zorn_OUnion__lemma0__1(A,B,C,D),A,tc_set(D)) | c_lessequals(B,c_Union(C,D),tc_set(D)) | c_lessequals(c_Union(C,D),A,tc_set(D)) # label(cls_Zorn_OUnion__lemma0_1) # label(axiom). [assumption].
% 129.44/129.88 14 -c_lessequals(A,c_Zorn_OUnion__lemma0__1(B,A,C,D),tc_set(D)) | c_lessequals(A,c_Union(C,D),tc_set(D)) | c_lessequals(c_Union(C,D),B,tc_set(D)) # label(cls_Zorn_OUnion__lemma0_2) # label(axiom). [assumption].
% 129.44/129.88 15 c_lessequals(c_Zorn_Osucc(v_S,A,t_a),B,tc_set(tc_set(t_a))) | A = B | -c_lessequals(A,B,tc_set(tc_set(t_a))) | -c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) | -c_in(B,v_Y,tc_set(tc_set(t_a))) # label(cls_conjecture_5) # label(negated_conjecture). [assumption].
% 129.44/129.88 16 -c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C))) | -c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C))) | c_Zorn_OTFin__linear__lemma1__1(B,A,C) != A | c_lessequals(D,A,tc_set(tc_set(C))) | c_lessequals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))) # label(cls_Zorn_OTFin__linear__lemma1_2) # label(axiom). [assumption].
% 129.44/129.88 17 -c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C))) | -c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C))) | c_lessequals(D,A,tc_set(tc_set(C))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(B,A,C),A,tc_set(tc_set(C))) | c_lessequals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))) # label(cls_Zorn_OTFin__linear__lemma1_1) # label(axiom). [assumption].
% 129.44/129.88 18 -c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C))) | -c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C))) | c_in(c_Zorn_OTFin__linear__lemma1__1(B,A,C),c_Zorn_OTFin(B,C),tc_set(tc_set(C))) | c_lessequals(D,A,tc_set(tc_set(C))) | c_lessequals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))) # label(cls_Zorn_OTFin__linear__lemma1_0) # label(axiom). [assumption].
% 129.44/129.88 19 -c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C))) | -c_in(D,c_Zorn_OTFin(B,C),tc_set(tc_set(C))) | -c_lessequals(c_Zorn_Osucc(B,c_Zorn_OTFin__linear__lemma1__1(B,A,C),C),A,tc_set(tc_set(C))) | c_lessequals(D,A,tc_set(tc_set(C))) | c_lessequals(c_Zorn_Osucc(B,A,C),D,tc_set(tc_set(C))) # label(cls_Zorn_OTFin__linear__lemma1_3) # label(axiom). [assumption].
% 129.44/129.88 28 c_lessequals(A,A,tc_set(B)). [resolve(10,a,5,a),merge(b)].
% 129.44/129.88 30 -c_lessequals(c_Union(v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a))). [resolve(11,a,4,a),unit_del(b,8)].
% 129.44/129.88 33 -c_lessequals(A,B,tc_set(tc_set(C))) | c_in(c_Zorn_OUnion__lemma0__1(D,E,A,C),B,tc_set(C)) | c_lessequals(E,c_Union(A,C),tc_set(C)) | c_lessequals(c_Union(A,C),D,tc_set(C)). [resolve(12,a,6,a)].
% 129.44/129.88 34 -c_lessequals(A,B,tc_set(C)) | c_in(c_Main_OsubsetI__1(A,D,C),B,C) | c_lessequals(A,D,tc_set(C)). [resolve(12,a,5,a)].
% 129.44/129.88 38 c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),A,tc_set(tc_set(t_a))) | v_x = A | -c_lessequals(v_x,A,tc_set(tc_set(t_a))) | -c_in(A,v_Y,tc_set(tc_set(t_a))). [resolve(15,d,1,a)].
% 129.44/129.88 39 c_lessequals(c_Zorn_Osucc(v_S,A,t_a),c_Zorn_OUnion__lemma0__1(B,C,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_Zorn_OUnion__lemma0__1(B,C,v_Y,tc_set(t_a)) = A | -c_lessequals(A,c_Zorn_OUnion__lemma0__1(B,C,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | -c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) | c_lessequals(C,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Union(v_Y,tc_set(t_a)),B,tc_set(tc_set(t_a))). [resolve(15,e,6,a),flip(b)].
% 129.44/129.88 47 -c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) | c_Zorn_OTFin__linear__lemma1__1(v_S,A,t_a) != A | c_lessequals(v_x,A,tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S,A,t_a),v_x,tc_set(tc_set(t_a))). [resolve(16,b,1,a)].
% 129.44/129.88 53 -c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) | c_lessequals(v_x,A,tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,A,t_a),A,tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S,A,t_a),v_x,tc_set(tc_set(t_a))). [resolve(17,b,1,a)].
% 129.44/129.88 63 -c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) | c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,A,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) | c_lessequals(v_x,A,tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S,A,t_a),v_x,tc_set(tc_set(t_a))). [resolve(18,b,1,a)].
% 129.44/129.88 69 -c_in(A,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) | -c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,A,t_a),t_a),A,tc_set(tc_set(t_a))) | c_lessequals(v_x,A,tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S,A,t_a),v_x,tc_set(tc_set(t_a))). [resolve(19,b,1,a)].
% 129.44/129.88 70 -c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))). [ur(14,b,9,a,c,30,a)].
% 129.44/129.88 71 -c_lessequals(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a))). [ur(13,b,9,a,c,30,a)].
% 129.44/129.88 73 -c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(t_a)),v_x,tc_set(t_a)). [ur(10,b,71,a)].
% 129.44/129.88 80 c_in(c_Main_OsubsetI__1(A,B,tc_set(C)),c_Zorn_Osucc(D,A,C),tc_set(C)) | c_lessequals(A,B,tc_set(tc_set(C))). [resolve(34,a,2,a)].
% 129.44/129.88 83 c_lessequals(A,B,tc_set(tc_set(C))) | -c_lessequals(c_Zorn_Osucc(D,A,C),E,tc_set(tc_set(C))) | c_in(c_Main_OsubsetI__1(A,B,tc_set(C)),E,tc_set(C)). [resolve(80,a,12,a)].
% 129.44/129.88 86 c_in(c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) | c_lessequals(B,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Union(v_Y,tc_set(t_a)),A,tc_set(tc_set(t_a))). [resolve(33,a,3,a)].
% 129.44/129.88 108 c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)) = v_x | -c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(B,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Union(v_Y,tc_set(t_a)),A,tc_set(tc_set(t_a))). [resolve(38,d,6,a),flip(b)].
% 129.44/129.88 119 -c_lessequals(c_Zorn_Osucc(A,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a),v_x,tc_set(tc_set(t_a))). [ur(83,a,71,a,c,73,a)].
% 129.44/129.88 270 c_lessequals(A,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Union(v_Y,tc_set(t_a)),B,tc_set(tc_set(t_a))) | c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(B,A,v_Y,tc_set(t_a)),t_a) != c_Zorn_OUnion__lemma0__1(B,A,v_Y,tc_set(t_a)) | c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(B,A,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(B,A,v_Y,tc_set(t_a)),t_a),v_x,tc_set(tc_set(t_a))). [resolve(86,a,47,a)].
% 129.44/129.88 311 c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),t_a),c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),t_a),v_x,tc_set(tc_set(t_a))) | c_lessequals(B,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Union(v_Y,tc_set(t_a)),A,tc_set(tc_set(t_a))). [resolve(53,a,86,a)].
% 129.44/129.88 374 c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) | c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),t_a),v_x,tc_set(tc_set(t_a))) | c_lessequals(B,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Union(v_Y,tc_set(t_a)),A,tc_set(tc_set(t_a))). [resolve(63,a,86,a)].
% 129.44/129.88 382 -c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),t_a),t_a),c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),t_a),v_x,tc_set(tc_set(t_a))) | c_lessequals(B,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Union(v_Y,tc_set(t_a)),A,tc_set(tc_set(t_a))). [resolve(69,a,86,a)].
% 129.44/129.88 2920 c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),t_a),v_x,tc_set(tc_set(t_a))) | c_lessequals(B,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Union(v_Y,tc_set(t_a)),A,tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),t_a),t_a),c_Zorn_OUnion__lemma0__1(C,D,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_Zorn_OUnion__lemma0__1(C,D,v_Y,tc_set(t_a)) = c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),t_a) | -c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),t_a),c_Zorn_OUnion__lemma0__1(C,D,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(D,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Union(v_Y,tc_set(t_a)),C,tc_set(tc_set(t_a))). [resolve(374,a,39,d)].
% 129.44/129.88 29672 c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),t_a),v_x,tc_set(tc_set(t_a))) | c_lessequals(B,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Union(v_Y,tc_set(t_a)),A,tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),t_a),t_a),c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),t_a) = c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)). [resolve(2920,g,311,b),flip(f),merge(g),merge(h),merge(i),merge(j),merge(k),merge(l)].
% 129.44/129.88 40108 c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),t_a),v_x,tc_set(tc_set(t_a))) | c_lessequals(B,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_lessequals(c_Union(v_Y,tc_set(t_a)),A,tc_set(tc_set(t_a))) | c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)),t_a) = c_Zorn_OUnion__lemma0__1(A,B,v_Y,tc_set(t_a)). [resolve(29672,e,382,a),merge(f),merge(g),merge(h),merge(i)].
% 129.44/129.88 40115 c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) | c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a) = c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)). [resolve(40108,b,119,a),unit_del(b,9),unit_del(c,30)].
% 129.44/129.88 40127 c_Zorn_OTFin__linear__lemma1__1(v_S,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),t_a) = c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)) | c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)) = v_x. [resolve(40115,a,108,c),unit_del(b,70),unit_del(d,9),unit_del(e,30)].
% 129.44/129.88 40145 c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)) = v_x | c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))). [resolve(40127,a,270,c),unit_del(b,9),unit_del(c,30),unit_del(e,119)].
% 129.44/129.88 40188 c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)) = v_x. [resolve(40145,b,108,c),merge(c),unit_del(b,70),unit_del(c,9),unit_del(d,30)].
% 129.44/129.88 40320 $F. [back_rewrite(71),rewrite([40188(9)]),unit_del(a,28)].
% 129.44/129.88
% 129.44/129.88 % SZS output end Refutation
% 129.44/129.88 ============================== end of proof ==========================
% 129.44/129.88
% 129.44/129.88 ============================== STATISTICS ============================
% 129.44/129.88
% 129.44/129.88 Given=13390. Generated=255489. Kept=40318. proofs=1.
% 129.44/129.88 Usable=12617. Sos=9701. Demods=1. Limbo=132, Disabled=17886. Hints=0.
% 129.44/129.88 Megabytes=113.84.
% 129.44/129.88 User_CPU=128.61, System_CPU=0.20, Wall_clock=129.
% 129.44/129.88
% 129.44/129.88 ============================== end of statistics =====================
% 129.44/129.88
% 129.44/129.88 ============================== end of search =========================
% 129.44/129.88
% 129.44/129.88 THEOREM PROVED
% 129.44/129.88 % SZS status Unsatisfiable
% 129.44/129.88
% 129.44/129.88 Exiting with 1 proof.
% 129.44/129.88
% 129.44/129.88 Process 31028 exit (max_proofs) Sun Jul 10 17:52:04 2022
% 129.44/129.88 Prover9 interrupted
%------------------------------------------------------------------------------