TSTP Solution File: SET831-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET831-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 04:32:30 EDT 2022
% Result : Unsatisfiable 0.89s 1.16s
% Output : Refutation 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET831-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n007.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 : Mon Jul 11 02:28:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.89/1.16 ============================== Prover9 ===============================
% 0.89/1.16 Prover9 (32) version 2009-11A, November 2009.
% 0.89/1.16 Process 2458 was started by sandbox on n007.cluster.edu,
% 0.89/1.16 Mon Jul 11 02:28:33 2022
% 0.89/1.16 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_2303_n007.cluster.edu".
% 0.89/1.16 ============================== end of head ===========================
% 0.89/1.16
% 0.89/1.16 ============================== INPUT =================================
% 0.89/1.16
% 0.89/1.16 % Reading from file /tmp/Prover9_2303_n007.cluster.edu
% 0.89/1.16
% 0.89/1.16 set(prolog_style_variables).
% 0.89/1.16 set(auto2).
% 0.89/1.16 % set(auto2) -> set(auto).
% 0.89/1.16 % set(auto) -> set(auto_inference).
% 0.89/1.16 % set(auto) -> set(auto_setup).
% 0.89/1.16 % set(auto_setup) -> set(predicate_elim).
% 0.89/1.16 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.89/1.16 % set(auto) -> set(auto_limits).
% 0.89/1.16 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.89/1.16 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.89/1.16 % set(auto) -> set(auto_denials).
% 0.89/1.16 % set(auto) -> set(auto_process).
% 0.89/1.16 % set(auto2) -> assign(new_constants, 1).
% 0.89/1.16 % set(auto2) -> assign(fold_denial_max, 3).
% 0.89/1.16 % set(auto2) -> assign(max_weight, "200.000").
% 0.89/1.16 % set(auto2) -> assign(max_hours, 1).
% 0.89/1.16 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.89/1.16 % set(auto2) -> assign(max_seconds, 0).
% 0.89/1.16 % set(auto2) -> assign(max_minutes, 5).
% 0.89/1.16 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.89/1.16 % set(auto2) -> set(sort_initial_sos).
% 0.89/1.16 % set(auto2) -> assign(sos_limit, -1).
% 0.89/1.16 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.89/1.16 % set(auto2) -> assign(max_megs, 400).
% 0.89/1.16 % set(auto2) -> assign(stats, some).
% 0.89/1.16 % set(auto2) -> clear(echo_input).
% 0.89/1.16 % set(auto2) -> set(quiet).
% 0.89/1.16 % set(auto2) -> clear(print_initial_clauses).
% 0.89/1.16 % set(auto2) -> clear(print_given).
% 0.89/1.16 assign(lrs_ticks,-1).
% 0.89/1.16 assign(sos_limit,10000).
% 0.89/1.16 assign(order,kbo).
% 0.89/1.16 set(lex_order_vars).
% 0.89/1.16 clear(print_given).
% 0.89/1.16
% 0.89/1.16 % formulas(sos). % not echoed (13 formulas)
% 0.89/1.16
% 0.89/1.16 ============================== end of input ==========================
% 0.89/1.16
% 0.89/1.16 % From the command line: assign(max_seconds, 300).
% 0.89/1.16
% 0.89/1.16 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.89/1.16
% 0.89/1.16 % Formulas that are not ordinary clauses:
% 0.89/1.16
% 0.89/1.16 ============================== end of process non-clausal formulas ===
% 0.89/1.16
% 0.89/1.16 ============================== PROCESS INITIAL CLAUSES ===============
% 0.89/1.16
% 0.89/1.16 ============================== PREDICATE ELIMINATION =================
% 0.89/1.16
% 0.89/1.16 ============================== end predicate elimination =============
% 0.89/1.16
% 0.89/1.16 Auto_denials: (non-Horn, no changes).
% 0.89/1.16
% 0.89/1.16 Term ordering decisions:
% 0.89/1.16
% 0.89/1.16 % Assigning unary symbol tc_set kb_weight 0 and highest precedence (11).
% 0.89/1.16 Function symbol KB weights: t_a=1. v_X=1. v_Y=1. v_Z=1. v_x=1. c_inter=1. c_Main_OsubsetI__1=1. tc_set=0.
% 0.89/1.16
% 0.89/1.16 ============================== end of process initial clauses ========
% 0.89/1.16
% 0.89/1.16 ============================== CLAUSES FOR SEARCH ====================
% 0.89/1.16
% 0.89/1.16 ============================== end of clauses for search =============
% 0.89/1.16
% 0.89/1.16 ============================== SEARCH ================================
% 0.89/1.16
% 0.89/1.16 % Starting search at 0.01 seconds.
% 0.89/1.16
% 0.89/1.16 ============================== PROOF =================================
% 0.89/1.16 % SZS status Unsatisfiable
% 0.89/1.16 % SZS output start Refutation
% 0.89/1.16
% 0.89/1.16 % Proof 1 at 0.19 (+ 0.01) seconds.
% 0.89/1.16 % Length of proof is 108.
% 0.89/1.16 % Level of proof is 29.
% 0.89/1.16 % Maximum clause weight is 33.000.
% 0.89/1.16 % Given clauses 309.
% 0.89/1.16
% 0.89/1.16 1 v_X = c_inter(v_Y,v_Z,t_a) | c_lessequals(v_X,v_Y,tc_set(t_a)) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 0.89/1.16 2 c_inter(v_Y,v_Z,t_a) = v_X | c_lessequals(v_X,v_Y,tc_set(t_a)). [copy(1),flip(a)].
% 0.89/1.16 3 v_X = c_inter(v_Y,v_Z,t_a) | c_lessequals(v_X,v_Z,tc_set(t_a)) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 0.89/1.16 4 c_inter(v_Y,v_Z,t_a) = v_X | c_lessequals(v_X,v_Z,tc_set(t_a)). [copy(3),flip(a)].
% 0.89/1.16 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].
% 0.89/1.16 6 -c_lessequals(v_x,v_X,tc_set(t_a)) | -c_lessequals(v_X,v_Z,tc_set(t_a)) | -c_lessequals(v_X,v_Y,tc_set(t_a)) | v_X != c_inter(v_Y,v_Z,t_a) # label(cls_conjecture_4) # label(negated_conjecture). [assumption].
% 0.89/1.16 7 -c_lessequals(v_x,v_X,tc_set(t_a)) | -c_lessequals(v_X,v_Z,tc_set(t_a)) | -c_lessequals(v_X,v_Y,tc_set(t_a)) | c_inter(v_Y,v_Z,t_a) != v_X. [copy(6),flip(d)].
% 0.89/1.16 8 -c_in(A,c_inter(B,C,D),D) | c_in(A,C,D) # label(cls_Set_OIntE_0) # label(axiom). [assumption].
% 0.89/1.16 9 -c_in(A,c_inter(B,C,D),D) | c_in(A,B,D) # label(cls_Set_OIntE_1) # label(axiom). [assumption].
% 0.89/1.16 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].
% 0.89/1.16 11 -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].
% 0.89/1.16 12 -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].
% 0.89/1.16 13 -c_in(A,B,C) | -c_in(A,D,C) | c_in(A,c_inter(D,B,C),C) # label(cls_Set_OIntI_0) # label(axiom). [assumption].
% 0.89/1.16 14 c_lessequals(v_x,v_Y,tc_set(t_a)) | -c_lessequals(v_X,v_Z,tc_set(t_a)) | -c_lessequals(v_X,v_Y,tc_set(t_a)) | v_X != c_inter(v_Y,v_Z,t_a) # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 0.89/1.16 15 c_lessequals(v_x,v_Y,tc_set(t_a)) | -c_lessequals(v_X,v_Z,tc_set(t_a)) | -c_lessequals(v_X,v_Y,tc_set(t_a)) | c_inter(v_Y,v_Z,t_a) != v_X. [copy(14),flip(d)].
% 0.89/1.16 16 c_lessequals(v_x,v_Z,tc_set(t_a)) | -c_lessequals(v_X,v_Z,tc_set(t_a)) | -c_lessequals(v_X,v_Y,tc_set(t_a)) | v_X != c_inter(v_Y,v_Z,t_a) # label(cls_conjecture_3) # label(negated_conjecture). [assumption].
% 0.89/1.16 17 c_lessequals(v_x,v_Z,tc_set(t_a)) | -c_lessequals(v_X,v_Z,tc_set(t_a)) | -c_lessequals(v_X,v_Y,tc_set(t_a)) | c_inter(v_Y,v_Z,t_a) != v_X. [copy(16),flip(d)].
% 0.89/1.16 18 v_X = c_inter(v_Y,v_Z,t_a) | c_lessequals(A,v_X,tc_set(t_a)) | -c_lessequals(A,v_Z,tc_set(t_a)) | -c_lessequals(A,v_Y,tc_set(t_a)) # label(cls_conjecture_5) # label(negated_conjecture). [assumption].
% 0.89/1.16 19 c_inter(v_Y,v_Z,t_a) = v_X | c_lessequals(A,v_X,tc_set(t_a)) | -c_lessequals(A,v_Z,tc_set(t_a)) | -c_lessequals(A,v_Y,tc_set(t_a)). [copy(18),flip(a)].
% 0.89/1.16 20 -c_in(A,B,C) | c_in(A,c_inter(B,B,C),C). [factor(13,a,b)].
% 0.89/1.16 21 c_in(c_Main_OsubsetI__1(c_inter(A,B,C),D,C),B,C) | c_lessequals(c_inter(A,B,C),D,tc_set(C)). [resolve(8,a,5,a)].
% 0.89/1.16 22 c_in(c_Main_OsubsetI__1(c_inter(A,B,C),D,C),A,C) | c_lessequals(c_inter(A,B,C),D,tc_set(C)). [resolve(9,a,5,a)].
% 0.89/1.16 24 -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(11,a,5,a)].
% 0.89/1.16 27 -c_in(c_Main_OsubsetI__1(A,B,C),D,C) | c_in(c_Main_OsubsetI__1(A,B,C),c_inter(D,A,C),C) | c_lessequals(A,B,tc_set(C)). [resolve(13,a,5,a)].
% 0.89/1.16 28 -c_in(c_Main_OsubsetI__1(A,B,C),D,C) | c_in(c_Main_OsubsetI__1(A,B,C),c_inter(A,D,C),C) | c_lessequals(A,B,tc_set(C)). [resolve(13,b,5,a)].
% 0.89/1.16 29 c_in(c_Main_OsubsetI__1(A,B,C),c_inter(A,A,C),C) | c_lessequals(A,B,tc_set(C)). [resolve(20,a,5,a)].
% 0.89/1.16 31 c_lessequals(c_inter(A,B,C),D,tc_set(C)) | -c_in(c_Main_OsubsetI__1(c_inter(A,B,C),D,C),E,C) | c_in(c_Main_OsubsetI__1(c_inter(A,B,C),D,C),c_inter(B,E,C),C). [resolve(21,a,13,b)].
% 0.89/1.16 34 c_lessequals(c_inter(A,B,C),B,tc_set(C)). [resolve(21,a,10,a),merge(b)].
% 0.89/1.16 35 c_lessequals(c_inter(A,c_inter(B,C,D),D),E,tc_set(D)) | c_in(c_Main_OsubsetI__1(c_inter(A,c_inter(B,C,D),D),E,D),B,D). [resolve(21,a,9,a)].
% 0.89/1.16 36 c_lessequals(c_inter(A,c_inter(B,C,D),D),E,tc_set(D)) | c_in(c_Main_OsubsetI__1(c_inter(A,c_inter(B,C,D),D),E,D),C,D). [resolve(21,a,8,a)].
% 0.89/1.16 38 c_inter(v_Y,v_Z,t_a) = v_X | c_lessequals(c_inter(A,v_Z,t_a),v_X,tc_set(t_a)) | -c_lessequals(c_inter(A,v_Z,t_a),v_Y,tc_set(t_a)). [resolve(34,a,19,c)].
% 0.89/1.16 39 -c_lessequals(A,c_inter(B,A,C),tc_set(C)) | c_inter(B,A,C) = A. [resolve(34,a,12,b)].
% 0.89/1.16 41 c_lessequals(c_inter(A,B,C),D,tc_set(C)) | -c_in(c_Main_OsubsetI__1(c_inter(A,B,C),D,C),E,C) | c_in(c_Main_OsubsetI__1(c_inter(A,B,C),D,C),c_inter(A,E,C),C). [resolve(22,a,13,b)].
% 0.89/1.16 44 c_lessequals(c_inter(A,B,C),A,tc_set(C)). [resolve(22,a,10,a),merge(b)].
% 0.89/1.16 48 -c_lessequals(A,c_inter(A,B,C),tc_set(C)) | c_inter(A,B,C) = A. [resolve(44,a,12,b)].
% 0.89/1.16 53 c_lessequals(A,c_inter(A,A,B),tc_set(B)). [resolve(29,a,10,a),merge(b)].
% 0.89/1.16 54 c_in(c_Main_OsubsetI__1(v_X,A,t_a),v_Z,t_a) | c_lessequals(v_X,A,tc_set(t_a)) | c_inter(v_Y,v_Z,t_a) = v_X. [resolve(24,a,4,b)].
% 0.89/1.16 55 c_in(c_Main_OsubsetI__1(v_X,A,t_a),v_Y,t_a) | c_lessequals(v_X,A,tc_set(t_a)) | c_inter(v_Y,v_Z,t_a) = v_X. [resolve(24,a,2,b)].
% 0.89/1.16 56 c_inter(A,A,B) = A. [resolve(53,a,48,a)].
% 0.89/1.16 61 c_in(c_Main_OsubsetI__1(c_inter(A,B,C),D,C),c_inter(A,c_inter(A,B,C),C),C) | c_lessequals(c_inter(A,B,C),D,tc_set(C)). [resolve(27,a,22,a),merge(c)].
% 0.89/1.16 62 c_in(c_Main_OsubsetI__1(c_inter(A,B,C),D,C),c_inter(B,c_inter(A,B,C),C),C) | c_lessequals(c_inter(A,B,C),D,tc_set(C)). [resolve(27,a,21,a),merge(c)].
% 0.89/1.16 63 c_lessequals(v_X,A,tc_set(t_a)) | c_inter(v_Y,v_Z,t_a) = v_X | c_in(c_Main_OsubsetI__1(v_X,A,t_a),c_inter(v_Y,v_X,t_a),t_a). [resolve(55,a,27,a),merge(d)].
% 0.89/1.16 79 c_in(c_Main_OsubsetI__1(v_X,A,t_a),c_inter(v_X,v_Z,t_a),t_a) | c_lessequals(v_X,A,tc_set(t_a)) | c_inter(v_Y,v_Z,t_a) = v_X. [resolve(28,a,54,a),merge(c)].
% 0.89/1.16 80 c_in(c_Main_OsubsetI__1(c_inter(A,B,C),D,C),c_inter(c_inter(A,B,C),A,C),C) | c_lessequals(c_inter(A,B,C),D,tc_set(C)). [resolve(28,a,22,a),merge(c)].
% 0.89/1.16 89 c_lessequals(v_X,c_inter(v_Y,v_X,t_a),tc_set(t_a)) | c_inter(v_Y,v_Z,t_a) = v_X. [resolve(63,c,10,a),merge(c)].
% 0.89/1.16 90 c_inter(v_Y,v_Z,t_a) = v_X | c_inter(v_Y,v_X,t_a) = v_X. [resolve(89,a,39,a)].
% 0.89/1.16 91 c_lessequals(c_inter(A,B,C),D,tc_set(C)) | c_in(c_Main_OsubsetI__1(c_inter(A,B,C),D,C),c_inter(B,A,C),C). [resolve(31,b,22,a),merge(c)].
% 0.89/1.16 135 c_lessequals(c_inter(A,c_inter(B,C,D),D),E,tc_set(D)) | c_in(c_Main_OsubsetI__1(c_inter(A,c_inter(B,C,D),D),E,D),c_inter(c_inter(A,c_inter(B,C,D),D),B,D),D). [resolve(35,b,28,a),merge(c)].
% 0.89/1.16 172 c_inter(v_Y,v_Z,t_a) = v_X | c_lessequals(c_inter(v_Y,v_Z,t_a),v_X,tc_set(t_a)). [resolve(38,c,44,a)].
% 0.89/1.16 175 c_inter(v_Y,v_Z,t_a) = v_X | -c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a)). [resolve(172,b,12,b),merge(c)].
% 0.89/1.16 178 c_lessequals(c_inter(A,c_inter(B,C,D),D),E,tc_set(D)) | c_in(c_Main_OsubsetI__1(c_inter(A,c_inter(B,C,D),D),E,D),c_inter(A,C,D),D). [resolve(41,b,36,b),merge(c)].
% 0.89/1.16 348 c_lessequals(c_inter(A,B,C),c_inter(A,c_inter(A,B,C),C),tc_set(C)). [resolve(61,a,10,a),merge(b)].
% 0.89/1.16 354 c_inter(A,c_inter(A,B,C),C) = c_inter(A,B,C). [resolve(348,a,39,a)].
% 0.89/1.16 362 c_inter(v_Y,v_X,t_a) = v_X | c_inter(v_Y,v_Z,t_a) = c_inter(v_Y,v_X,t_a). [para(90(a,1),354(a,1,2)),flip(b)].
% 0.89/1.16 378 c_lessequals(c_inter(A,B,C),c_inter(B,c_inter(A,B,C),C),tc_set(C)). [resolve(62,a,10,a),merge(b)].
% 0.89/1.16 384 c_inter(A,c_inter(B,A,C),C) = c_inter(B,A,C). [resolve(378,a,39,a)].
% 0.89/1.16 395 c_inter(v_Y,v_X,t_a) = v_X. [para(362(b,1),90(a,1)),merge(b),merge(c)].
% 0.89/1.16 399 c_in(c_Main_OsubsetI__1(v_X,A,t_a),v_Y,t_a) | c_lessequals(v_X,A,tc_set(t_a)). [para(395(a,1),22(a,1,1)),rewrite([395(10)])].
% 0.89/1.16 400 c_lessequals(v_X,v_Y,tc_set(t_a)). [para(395(a,1),44(a,1))].
% 0.89/1.16 412 c_lessequals(v_x,v_Z,tc_set(t_a)) | -c_lessequals(v_X,v_Z,tc_set(t_a)) | c_inter(v_Y,v_Z,t_a) != v_X. [back_unit_del(17),unit_del(c,400)].
% 0.89/1.16 413 c_lessequals(v_x,v_Y,tc_set(t_a)) | -c_lessequals(v_X,v_Z,tc_set(t_a)) | c_inter(v_Y,v_Z,t_a) != v_X. [back_unit_del(15),unit_del(c,400)].
% 0.89/1.16 414 -c_lessequals(v_x,v_X,tc_set(t_a)) | -c_lessequals(v_X,v_Z,tc_set(t_a)) | c_inter(v_Y,v_Z,t_a) != v_X. [back_unit_del(7),unit_del(c,400)].
% 0.89/1.16 427 c_lessequals(v_X,A,tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_X,A,t_a),c_inter(v_X,v_Y,t_a),t_a). [resolve(399,a,28,a),merge(c)].
% 0.89/1.16 476 c_lessequals(v_X,c_inter(v_X,v_Y,t_a),tc_set(t_a)). [resolve(427,b,10,a),merge(b)].
% 0.89/1.16 480 c_inter(v_X,v_Y,t_a) = v_X. [resolve(476,a,48,a)].
% 0.89/1.16 512 c_lessequals(v_X,c_inter(v_X,v_Z,t_a),tc_set(t_a)) | c_inter(v_Y,v_Z,t_a) = v_X. [resolve(79,a,10,a),merge(c)].
% 0.89/1.16 513 c_inter(v_Y,v_Z,t_a) = v_X | c_inter(v_X,v_Z,t_a) = v_X. [resolve(512,a,48,a)].
% 0.89/1.16 554 c_lessequals(c_inter(A,B,C),c_inter(c_inter(A,B,C),A,C),tc_set(C)). [resolve(80,a,10,a),merge(b)].
% 0.89/1.16 561 c_inter(c_inter(A,B,C),A,C) = c_inter(A,B,C). [resolve(554,a,48,a)].
% 0.89/1.16 579 c_inter(c_inter(A,B,C),B,C) = c_inter(A,B,C). [para(384(a,1),561(a,1,1)),rewrite([384(4)])].
% 0.89/1.16 586 c_inter(v_X,v_Z,t_a) = v_X | c_inter(v_Y,v_Z,t_a) = c_inter(v_X,v_Z,t_a). [para(513(a,1),579(a,1,1)),flip(b)].
% 0.89/1.16 675 c_inter(v_X,v_Z,t_a) = v_X. [para(586(b,1),513(a,1)),merge(b),merge(c)].
% 0.89/1.16 685 c_lessequals(v_X,v_Z,tc_set(t_a)). [para(675(a,1),34(a,1))].
% 0.89/1.16 696 -c_lessequals(v_x,v_X,tc_set(t_a)) | c_inter(v_Y,v_Z,t_a) != v_X. [back_unit_del(414),unit_del(b,685)].
% 0.89/1.16 697 c_lessequals(v_x,v_Y,tc_set(t_a)) | c_inter(v_Y,v_Z,t_a) != v_X. [back_unit_del(413),unit_del(b,685)].
% 0.89/1.16 698 c_lessequals(v_x,v_Z,tc_set(t_a)) | c_inter(v_Y,v_Z,t_a) != v_X. [back_unit_del(412),unit_del(b,685)].
% 0.89/1.16 708 c_lessequals(c_inter(A,B,C),c_inter(B,A,C),tc_set(C)). [resolve(91,b,10,a),merge(b)].
% 0.89/1.16 716 c_lessequals(c_inter(A,c_inter(B,C,D),D),c_inter(c_inter(A,c_inter(B,C,D),D),B,D),tc_set(D)). [resolve(135,b,10,a),merge(b)].
% 0.89/1.16 721 c_inter(A,B,C) = c_inter(B,A,C). [resolve(708,a,12,b),unit_del(a,708)].
% 0.89/1.16 724 c_lessequals(c_inter(A,c_inter(B,C,D),D),c_inter(B,c_inter(A,c_inter(B,C,D),D),D),tc_set(D)). [back_rewrite(716),rewrite([721(5)])].
% 0.89/1.16 743 c_lessequals(c_inter(A,c_inter(B,C,D),D),c_inter(C,c_inter(A,c_inter(B,C,D),D),D),tc_set(D)). [para(721(a,1),724(a,1,2)),rewrite([721(3)])].
% 0.89/1.16 810 c_lessequals(c_inter(A,v_X,t_a),c_inter(v_Y,c_inter(A,v_X,t_a),t_a),tc_set(t_a)). [para(480(a,1),743(a,1,2)),rewrite([480(8)])].
% 0.89/1.16 811 c_lessequals(c_inter(A,v_X,t_a),c_inter(v_Z,c_inter(A,v_X,t_a),t_a),tc_set(t_a)). [para(675(a,1),743(a,1,2)),rewrite([675(8)])].
% 0.89/1.16 819 c_inter(v_Y,c_inter(A,v_X,t_a),t_a) = c_inter(A,v_X,t_a). [resolve(810,a,12,b),flip(b),unit_del(a,34)].
% 0.89/1.16 826 c_inter(v_Z,c_inter(A,v_X,t_a),t_a) = c_inter(A,v_X,t_a). [resolve(811,a,12,b),flip(b),unit_del(a,34)].
% 0.89/1.16 871 c_lessequals(c_inter(A,c_inter(B,C,D),D),c_inter(A,C,D),tc_set(D)). [resolve(178,b,10,a),merge(b)].
% 0.89/1.16 876 c_lessequals(c_inter(A,c_inter(B,C,D),D),c_inter(A,B,D),tc_set(D)). [para(721(a,1),871(a,1,2))].
% 0.89/1.16 885 c_lessequals(c_inter(A,c_inter(B,C,D),D),c_inter(B,A,D),tc_set(D)). [para(721(a,1),876(a,1)),rewrite([721(2),721(3)])].
% 0.89/1.16 888 c_lessequals(c_inter(A,c_inter(B,v_X,t_a),t_a),c_inter(A,v_Y,t_a),tc_set(t_a)). [para(819(a,1),876(a,1,2))].
% 0.89/1.16 907 c_lessequals(c_inter(A,v_X,t_a),c_inter(v_Y,v_Z,t_a),tc_set(t_a)). [para(826(a,1),888(a,1)),rewrite([721(7)])].
% 0.89/1.16 912 c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a)). [para(56(a,1),907(a,1))].
% 0.89/1.16 913 c_inter(v_Y,v_Z,t_a) = v_X. [back_unit_del(175),unit_del(b,912)].
% 0.89/1.16 914 c_lessequals(v_x,v_Z,tc_set(t_a)). [back_rewrite(698),rewrite([913(9)]),xx(b)].
% 0.89/1.16 915 c_lessequals(v_x,v_Y,tc_set(t_a)). [back_rewrite(697),rewrite([913(9)]),xx(b)].
% 0.89/1.16 916 -c_lessequals(v_x,v_X,tc_set(t_a)). [back_rewrite(696),rewrite([913(9)]),xx(b)].
% 0.89/1.16 917 -c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),v_X,t_a). [ur(10,b,916,a)].
% 0.89/1.16 928 c_in(c_Main_OsubsetI__1(v_x,A,t_a),v_Z,t_a) | c_lessequals(v_x,A,tc_set(t_a)). [resolve(914,a,24,a)].
% 0.89/1.16 932 c_in(c_Main_OsubsetI__1(v_x,A,t_a),v_Y,t_a) | c_lessequals(v_x,A,tc_set(t_a)). [resolve(915,a,24,a)].
% 0.89/1.16 958 c_lessequals(v_x,A,tc_set(t_a)) | c_in(c_Main_OsubsetI__1(v_x,A,t_a),c_inter(v_Z,v_x,t_a),t_a). [resolve(928,a,28,a),rewrite([721(11)]),merge(c)].
% 0.89/1.16 990 c_lessequals(v_x,c_inter(v_Z,v_x,t_a),tc_set(t_a)). [resolve(958,b,10,a),merge(b)].
% 0.89/1.16 993 c_inter(v_Z,v_x,t_a) = v_x. [resolve(990,a,12,b),flip(b),unit_del(a,34)].
% 0.89/1.16 1020 c_lessequals(c_inter(A,v_x,t_a),c_inter(A,v_Z,t_a),tc_set(t_a)). [para(993(a,1),876(a,1,2))].
% 0.89/1.16 1046 c_lessequals(c_inter(v_Y,v_x,t_a),v_X,tc_set(t_a)). [para(913(a,1),1020(a,2))].
% 0.89/1.16 1052 -c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),c_inter(v_Y,v_x,t_a),t_a). [ur(11,b,1046,a,c,917,a)].
% 0.89/1.16 1064 -c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),c_inter(v_x,c_inter(A,v_Y,t_a),t_a),t_a). [ur(11,b,885,a,c,1052,a),rewrite([721(8)])].
% 0.89/1.16 1085 -c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),c_inter(A,v_Y,t_a),t_a). [ur(28,b,1064,a,c,916,a)].
% 0.89/1.16 1093 -c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),v_Y,t_a). [ur(28,b,1085,a,c,916,a)].
% 0.89/1.16 1097 $F. [resolve(1093,a,932,a),unit_del(a,916)].
% 0.89/1.16
% 0.89/1.16 % SZS output end Refutation
% 0.89/1.16 ============================== end of proof ==========================
% 0.89/1.16
% 0.89/1.16 ============================== STATISTICS ============================
% 0.89/1.16
% 0.89/1.16 Given=309. Generated=4988. Kept=1090. proofs=1.
% 0.89/1.16 Usable=148. Sos=220. Demods=20. Limbo=0, Disabled=735. Hints=0.
% 0.89/1.16 Megabytes=0.98.
% 0.89/1.16 User_CPU=0.19, System_CPU=0.01, Wall_clock=0.
% 0.89/1.16
% 0.89/1.16 ============================== end of statistics =====================
% 0.89/1.16
% 0.89/1.16 ============================== end of search =========================
% 0.89/1.16
% 0.89/1.16 THEOREM PROVED
% 0.89/1.16 % SZS status Unsatisfiable
% 0.89/1.16
% 0.89/1.16 Exiting with 1 proof.
% 0.89/1.16
% 0.89/1.16 Process 2458 exit (max_proofs) Mon Jul 11 02:28:33 2022
% 0.89/1.16 Prover9 interrupted
%------------------------------------------------------------------------------