TSTP Solution File: PUZ062-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : PUZ062-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 18:23:58 EDT 2022
% Result : Unsatisfiable 0.81s 1.08s
% Output : Refutation 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PUZ062-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat May 28 23:04:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.81/1.08 ============================== Prover9 ===============================
% 0.81/1.08 Prover9 (32) version 2009-11A, November 2009.
% 0.81/1.08 Process 26356 was started by sandbox2 on n027.cluster.edu,
% 0.81/1.08 Sat May 28 23:05:00 2022
% 0.81/1.08 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_26202_n027.cluster.edu".
% 0.81/1.08 ============================== end of head ===========================
% 0.81/1.08
% 0.81/1.08 ============================== INPUT =================================
% 0.81/1.08
% 0.81/1.08 % Reading from file /tmp/Prover9_26202_n027.cluster.edu
% 0.81/1.08
% 0.81/1.08 set(prolog_style_variables).
% 0.81/1.08 set(auto2).
% 0.81/1.08 % set(auto2) -> set(auto).
% 0.81/1.08 % set(auto) -> set(auto_inference).
% 0.81/1.08 % set(auto) -> set(auto_setup).
% 0.81/1.08 % set(auto_setup) -> set(predicate_elim).
% 0.81/1.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.81/1.08 % set(auto) -> set(auto_limits).
% 0.81/1.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.81/1.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.81/1.08 % set(auto) -> set(auto_denials).
% 0.81/1.08 % set(auto) -> set(auto_process).
% 0.81/1.08 % set(auto2) -> assign(new_constants, 1).
% 0.81/1.08 % set(auto2) -> assign(fold_denial_max, 3).
% 0.81/1.08 % set(auto2) -> assign(max_weight, "200.000").
% 0.81/1.08 % set(auto2) -> assign(max_hours, 1).
% 0.81/1.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.81/1.08 % set(auto2) -> assign(max_seconds, 0).
% 0.81/1.08 % set(auto2) -> assign(max_minutes, 5).
% 0.81/1.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.81/1.08 % set(auto2) -> set(sort_initial_sos).
% 0.81/1.08 % set(auto2) -> assign(sos_limit, -1).
% 0.81/1.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.81/1.08 % set(auto2) -> assign(max_megs, 400).
% 0.81/1.08 % set(auto2) -> assign(stats, some).
% 0.81/1.08 % set(auto2) -> clear(echo_input).
% 0.81/1.08 % set(auto2) -> set(quiet).
% 0.81/1.08 % set(auto2) -> clear(print_initial_clauses).
% 0.81/1.08 % set(auto2) -> clear(print_given).
% 0.81/1.08 assign(lrs_ticks,-1).
% 0.81/1.08 assign(sos_limit,10000).
% 0.81/1.08 assign(order,kbo).
% 0.81/1.08 set(lex_order_vars).
% 0.81/1.08 clear(print_given).
% 0.81/1.08
% 0.81/1.08 % formulas(sos). % not echoed (13 formulas)
% 0.81/1.08
% 0.81/1.08 ============================== end of input ==========================
% 0.81/1.08
% 0.81/1.08 % From the command line: assign(max_seconds, 300).
% 0.81/1.08
% 0.81/1.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.81/1.08
% 0.81/1.08 % Formulas that are not ordinary clauses:
% 0.81/1.08
% 0.81/1.08 ============================== end of process non-clausal formulas ===
% 0.81/1.08
% 0.81/1.08 ============================== PROCESS INITIAL CLAUSES ===============
% 0.81/1.08
% 0.81/1.08 ============================== PREDICATE ELIMINATION =================
% 0.81/1.08
% 0.81/1.08 ============================== end predicate elimination =============
% 0.81/1.08
% 0.81/1.08 Auto_denials: (non-Horn, no changes).
% 0.81/1.08
% 0.81/1.08 Term ordering decisions:
% 0.81/1.08 Function symbol KB weights: tc_nat=1. c_0=1. c_Finite__Set_OFinites=1. v_t=1. c_emptyset=1. v_a=1. c_Mutil_Odomino=1. v_i=1. v_j=1. v_m=1. v_n=1. tc_prod=1. c_Finite__Set_Ocard=1. c_Mutil_Otiling=1. tc_set=1. c_Mutil_Ocoloured=1. c_Suc=1. c_inter=1. c_insert=1. c_Pair=1.
% 0.81/1.08
% 0.81/1.08 ============================== end of process initial clauses ========
% 0.81/1.08
% 0.81/1.08 ============================== CLAUSES FOR SEARCH ====================
% 0.81/1.08
% 0.81/1.08 ============================== end of clauses for search =============
% 0.81/1.08
% 0.81/1.08 ============================== SEARCH ================================
% 0.81/1.08
% 0.81/1.08 % Starting search at 0.01 seconds.
% 0.81/1.08
% 0.81/1.08 ============================== PROOF =================================
% 0.81/1.08 % SZS status Unsatisfiable
% 0.81/1.08 % SZS output start Refutation
% 0.81/1.08
% 0.81/1.08 % Proof 1 at 0.09 (+ 0.00) seconds.
% 0.81/1.08 % Length of proof is 33.
% 0.81/1.08 % Level of proof is 8.
% 0.81/1.08 % Maximum clause weight is 42.000.
% 0.81/1.08 % Given clauses 105.
% 0.81/1.08
% 0.81/1.08 1 c_in(A,c_insert(A,B,C),C) # label(cls_Set_Oinsert__iff_1) # label(axiom). [assumption].
% 0.81/1.08 2 c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)) = c_emptyset # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 0.81/1.08 3 c_emptyset = c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)). [copy(2),flip(a)].
% 0.81/1.08 4 c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 0.81/1.08 5 c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)) # label(cls_conjecture_3) # label(negated_conjecture). [assumption].
% 0.81/1.08 6 c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)). [copy(5),rewrite([3(13)]),flip(a)].
% 0.81/1.08 7 c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)) # label(cls_conjecture_4) # label(negated_conjecture). [assumption].
% 0.81/1.08 8 c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)). [copy(7),rewrite([3(14)]),flip(a)].
% 0.81/1.08 9 c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 0.81/1.08 10 c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)). [copy(9),flip(a)].
% 0.81/1.08 11 -c_in(A,c_emptyset,B) # label(cls_Set_Oempty__iff_0) # label(axiom). [assumption].
% 0.81/1.08 12 -c_in(A,c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)),B). [copy(11),rewrite([3(1)])].
% 0.81/1.08 13 c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) # label(cls_conjecture_5) # label(negated_conjecture). [assumption].
% 0.81/1.08 14 c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)). [copy(13),flip(a)].
% 0.81/1.08 15 -c_in(A,c_inter(B,C,D),D) | c_in(A,C,D) # label(cls_Set_OInt__iff_1) # label(axiom). [assumption].
% 0.81/1.08 16 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(c_inter(C,A,B),c_Finite__Set_OFinites,tc_set(B)) # label(cls_Finite__Set_Ofinite__Int_1) # label(axiom). [assumption].
% 0.81/1.08 17 -c_in(A,B,C) | -c_in(A,D,C) | c_in(A,c_inter(D,B,C),C) # label(cls_Set_OInt__iff_2) # label(axiom). [assumption].
% 0.81/1.08 18 -c_in(A,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))) | c_in(A,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) # label(cls_Mutil_Otiling__domino__finite_0) # label(axiom). [assumption].
% 0.81/1.08 19 -c_in(A,c_Finite__Set_OFinites,tc_set(B)) | c_in(C,A,B) | c_Finite__Set_Ocard(c_insert(C,A,B),B) = c_Suc(c_Finite__Set_Ocard(A,B)) # label(cls_Finite__Set_Ocard__insert__disjoint_0) # label(axiom). [assumption].
% 0.81/1.08 21 c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)). [para(6(a,1),1(a,2))].
% 0.81/1.08 22 c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)). [para(8(a,1),1(a,2))].
% 0.81/1.08 28 c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))). [resolve(18,a,4,a)].
% 0.81/1.08 34 c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)). [resolve(21,a,15,a)].
% 0.81/1.08 43 c_in(c_inter(A,v_t,tc_prod(tc_nat,tc_nat)),c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))). [resolve(28,a,16,a)].
% 0.81/1.08 47 -c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)). [ur(17,b,34,a,c,12,a)].
% 0.81/1.08 49 c_in(A,c_inter(B,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) | c_Finite__Set_Ocard(c_insert(A,c_inter(B,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(B,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))). [resolve(43,a,19,a)].
% 0.81/1.08 59 c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)). [resolve(22,a,15,a)].
% 0.81/1.08 60 -c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(A,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)). [ur(15,b,47,a)].
% 0.81/1.08 67 -c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)). [ur(17,b,59,a,c,12,a)].
% 0.81/1.08 91 -c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(A,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)). [ur(15,b,67,a)].
% 0.81/1.08 446 c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(A,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(A,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))). [resolve(49,a,91,a)].
% 0.81/1.08 449 c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(A,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(A,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))). [resolve(49,a,60,a)].
% 0.81/1.08 457 $F. [back_rewrite(14),rewrite([446(21),10(12),449(32)]),xx(a)].
% 0.81/1.08
% 0.81/1.08 % SZS output end Refutation
% 0.81/1.08 ============================== end of proof ==========================
% 0.81/1.08
% 0.81/1.08 ============================== STATISTICS ============================
% 0.81/1.08
% 0.81/1.08 Given=105. Generated=1588. Kept=450. proofs=1.
% 0.81/1.08 Usable=103. Sos=329. Demods=9. Limbo=11, Disabled=20. Hints=0.
% 0.81/1.08 Megabytes=0.96.
% 0.81/1.08 User_CPU=0.09, System_CPU=0.00, Wall_clock=0.
% 0.81/1.08
% 0.81/1.08 ============================== end of statistics =====================
% 0.81/1.08
% 0.81/1.08 ============================== end of search =========================
% 0.81/1.08
% 0.81/1.08 THEOREM PROVED
% 0.81/1.08 % SZS status Unsatisfiable
% 0.81/1.08
% 0.81/1.08 Exiting with 1 proof.
% 0.81/1.08
% 0.81/1.08 Process 26356 exit (max_proofs) Sat May 28 23:05:00 2022
% 0.81/1.08 Prover9 interrupted
%------------------------------------------------------------------------------