TSTP Solution File: SEU406+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU406+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 13:31:36 EDT 2022
% Result : Theorem 3.45s 3.74s
% Output : Refutation 3.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SEU406+1 : TPTP v8.1.0. Released v3.4.0.
% 0.09/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n003.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 : Sun Jun 19 16:44:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.67/0.98 ============================== Prover9 ===============================
% 0.67/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.67/0.98 Process 25877 was started by sandbox on n003.cluster.edu,
% 0.67/0.98 Sun Jun 19 16:44:44 2022
% 0.67/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25724_n003.cluster.edu".
% 0.67/0.98 ============================== end of head ===========================
% 0.67/0.98
% 0.67/0.98 ============================== INPUT =================================
% 0.67/0.98
% 0.67/0.98 % Reading from file /tmp/Prover9_25724_n003.cluster.edu
% 0.67/0.98
% 0.67/0.98 set(prolog_style_variables).
% 0.67/0.98 set(auto2).
% 0.67/0.98 % set(auto2) -> set(auto).
% 0.67/0.98 % set(auto) -> set(auto_inference).
% 0.67/0.98 % set(auto) -> set(auto_setup).
% 0.67/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.67/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.67/0.98 % set(auto) -> set(auto_limits).
% 0.67/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.67/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.67/0.98 % set(auto) -> set(auto_denials).
% 0.67/0.98 % set(auto) -> set(auto_process).
% 0.67/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.67/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.67/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.67/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.67/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.67/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.67/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.67/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.67/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.67/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.67/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.67/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.67/0.98 % set(auto2) -> assign(stats, some).
% 0.67/0.98 % set(auto2) -> clear(echo_input).
% 0.67/0.98 % set(auto2) -> set(quiet).
% 0.67/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.67/0.98 % set(auto2) -> clear(print_given).
% 0.67/0.98 assign(lrs_ticks,-1).
% 0.67/0.98 assign(sos_limit,10000).
% 0.67/0.98 assign(order,kbo).
% 0.67/0.98 set(lex_order_vars).
% 0.67/0.98 clear(print_given).
% 0.67/0.98
% 0.67/0.98 % formulas(sos). % not echoed (24 formulas)
% 0.67/0.98
% 0.67/0.98 ============================== end of input ==========================
% 0.67/0.98
% 0.67/0.98 % From the command line: assign(max_seconds, 300).
% 0.67/0.98
% 0.67/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.67/0.98
% 0.67/0.98 % Formulas that are not ordinary clauses:
% 0.67/0.98 1 (all A all B (r2_hidden(A,B) -> -r2_hidden(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 2 (all A all B k2_xboole_0(A,B) = k2_xboole_0(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 3 (all A all B all C (C = k2_xboole_0(A,B) <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,A) | r2_hidden(D,B))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 4 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 5 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 6 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 7 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 8 (all A exists B m1_subset_1(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 9 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 10 (all A all B (-v1_xboole_0(A) -> -v1_xboole_0(k2_xboole_0(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 11 (all A all B k2_xboole_0(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 12 (exists A v1_xboole_0(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 13 (exists A -v1_xboole_0(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 14 (all A k2_xboole_0(A,k1_xboole_0) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 15 (all A all B (r2_hidden(A,B) -> m1_subset_1(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 16 (all A all B (m1_subset_1(A,B) -> v1_xboole_0(B) | r2_hidden(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.98 17 (all A all B k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B)) # label(t39_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 3.45/3.74 18 (all A k4_xboole_0(A,k1_xboole_0) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 3.45/3.74 19 (all A k4_xboole_0(k1_xboole_0,A) = k1_xboole_0) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 3.45/3.74 20 (all A (v1_xboole_0(A) -> A = k1_xboole_0)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 3.45/3.74 21 (all A all B -(r2_hidden(A,B) & v1_xboole_0(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 3.45/3.74 22 (all A all B -(v1_xboole_0(A) & A != B & v1_xboole_0(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 3.45/3.74 23 -(all A all B all C all D -(r2_hidden(A,k2_xboole_0(C,D)) & r2_hidden(B,k2_xboole_0(C,D)) & -(r2_hidden(A,k4_xboole_0(C,D)) & r2_hidden(B,k4_xboole_0(C,D))) & -(r2_hidden(A,D) & r2_hidden(B,D)) & -(r2_hidden(A,k4_xboole_0(C,D)) & r2_hidden(B,D)) & -(r2_hidden(A,D) & r2_hidden(B,k4_xboole_0(C,D))))) # label(t1_latsum_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.45/3.74
% 3.45/3.74 ============================== end of process non-clausal formulas ===
% 3.45/3.74
% 3.45/3.74 ============================== PROCESS INITIAL CLAUSES ===============
% 3.45/3.74
% 3.45/3.74 ============================== PREDICATE ELIMINATION =================
% 3.45/3.74 24 -m1_subset_1(A,B) | v1_xboole_0(B) | r2_hidden(A,B) # label(t2_subset) # label(axiom). [clausify(16)].
% 3.45/3.74 25 m1_subset_1(f2(A),A) # label(existence_m1_subset_1) # label(axiom). [clausify(8)].
% 3.45/3.74 26 -r2_hidden(A,B) | m1_subset_1(A,B) # label(t1_subset) # label(axiom). [clausify(15)].
% 3.45/3.74 Derived: v1_xboole_0(A) | r2_hidden(f2(A),A). [resolve(24,a,25,a)].
% 3.45/3.74
% 3.45/3.74 ============================== end predicate elimination =============
% 3.45/3.74
% 3.45/3.74 Auto_denials: (non-Horn, no changes).
% 3.45/3.74
% 3.45/3.74 Term ordering decisions:
% 3.45/3.74
% 3.45/3.74 % Assigning unary symbol f2 kb_weight 0 and highest precedence (14).
% 3.45/3.74 Function symbol KB weights: k1_xboole_0=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. k2_xboole_0=1. k4_xboole_0=1. f1=1. f2=0.
% 3.45/3.74
% 3.45/3.74 ============================== end of process initial clauses ========
% 3.45/3.74
% 3.45/3.74 ============================== CLAUSES FOR SEARCH ====================
% 3.45/3.74
% 3.45/3.74 ============================== end of clauses for search =============
% 3.45/3.74
% 3.45/3.74 ============================== SEARCH ================================
% 3.45/3.74
% 3.45/3.74 % Starting search at 0.01 seconds.
% 3.45/3.74
% 3.45/3.74 Low Water (keep): wt=25.000, iters=3488
% 3.45/3.74
% 3.45/3.74 Low Water (keep): wt=23.000, iters=3470
% 3.45/3.74
% 3.45/3.74 Low Water (keep): wt=19.000, iters=3400
% 3.45/3.74
% 3.45/3.74 Low Water (keep): wt=17.000, iters=3398
% 3.45/3.74
% 3.45/3.74 Low Water (keep): wt=16.000, iters=3388
% 3.45/3.74
% 3.45/3.74 Low Water (keep): wt=15.000, iters=3364
% 3.45/3.74
% 3.45/3.74 Low Water (keep): wt=14.000, iters=3367
% 3.45/3.74
% 3.45/3.74 Low Water (keep): wt=13.000, iters=3353
% 3.45/3.74
% 3.45/3.74 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 37 (0.00 of 1.38 sec).
% 3.45/3.74
% 3.45/3.74 ============================== PROOF =================================
% 3.45/3.74 % SZS status Theorem
% 3.45/3.74 % SZS output start Refutation
% 3.45/3.74
% 3.45/3.74 % Proof 1 at 2.67 (+ 0.11) seconds.
% 3.45/3.74 % Length of proof is 33.
% 3.45/3.74 % Level of proof is 16.
% 3.45/3.74 % Maximum clause weight is 15.000.
% 3.45/3.74 % Given clauses 790.
% 3.45/3.74
% 3.45/3.74 2 (all A all B k2_xboole_0(A,B) = k2_xboole_0(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 3.45/3.74 3 (all A all B all C (C = k2_xboole_0(A,B) <-> (all D (r2_hidden(D,C) <-> r2_hidden(D,A) | r2_hidden(D,B))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 3.45/3.74 17 (all A all B k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B)) # label(t39_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 3.45/3.74 23 -(all A all B all C all D -(r2_hidden(A,k2_xboole_0(C,D)) & r2_hidden(B,k2_xboole_0(C,D)) & -(r2_hidden(A,k4_xboole_0(C,D)) & r2_hidden(B,k4_xboole_0(C,D))) & -(r2_hidden(A,D) & r2_hidden(B,D)) & -(r2_hidden(A,k4_xboole_0(C,D)) & r2_hidden(B,D)) & -(r2_hidden(A,D) & r2_hidden(B,k4_xboole_0(C,D))))) # label(t1_latsum_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.45/3.74 33 r2_hidden(c3,k2_xboole_0(c5,c6)) # label(t1_latsum_1) # label(negated_conjecture). [clausify(23)].
% 3.45/3.74 34 r2_hidden(c4,k2_xboole_0(c5,c6)) # label(t1_latsum_1) # label(negated_conjecture). [clausify(23)].
% 3.45/3.74 35 k2_xboole_0(A,B) = k2_xboole_0(B,A) # label(commutativity_k2_xboole_0) # label(axiom). [clausify(2)].
% 3.45/3.74 36 k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B) # label(t39_xboole_1) # label(axiom). [clausify(17)].
% 3.45/3.74 41 -r2_hidden(c3,c6) | -r2_hidden(c4,c6) # label(t1_latsum_1) # label(negated_conjecture). [clausify(23)].
% 3.45/3.74 42 -r2_hidden(c3,k4_xboole_0(c5,c6)) | -r2_hidden(c4,c6) # label(t1_latsum_1) # label(negated_conjecture). [clausify(23)].
% 3.45/3.74 43 -r2_hidden(c3,c6) | -r2_hidden(c4,k4_xboole_0(c5,c6)) # label(t1_latsum_1) # label(negated_conjecture). [clausify(23)].
% 3.45/3.74 44 -r2_hidden(c3,k4_xboole_0(c5,c6)) | -r2_hidden(c4,k4_xboole_0(c5,c6)) # label(t1_latsum_1) # label(negated_conjecture). [clausify(23)].
% 3.45/3.74 50 k2_xboole_0(A,B) != C | r2_hidden(D,C) | -r2_hidden(D,B) # label(d2_xboole_0) # label(axiom). [clausify(3)].
% 3.45/3.74 51 k2_xboole_0(A,B) != C | -r2_hidden(D,C) | r2_hidden(D,A) | r2_hidden(D,B) # label(d2_xboole_0) # label(axiom). [clausify(3)].
% 3.45/3.74 116 k2_xboole_0(c5,c6) != k2_xboole_0(A,B) | r2_hidden(c4,A) | r2_hidden(c4,B). [resolve(51,b,34,a),flip(a)].
% 3.45/3.74 117 k2_xboole_0(c5,c6) != k2_xboole_0(A,B) | r2_hidden(c3,A) | r2_hidden(c3,B). [resolve(51,b,33,a),flip(a)].
% 3.45/3.74 778 k2_xboole_0(c5,c6) != k2_xboole_0(A,B) | r2_hidden(c4,A) | r2_hidden(c4,k4_xboole_0(B,A)). [para(36(a,1),116(a,2))].
% 3.45/3.74 1873 r2_hidden(c3,c6) | r2_hidden(c3,c5). [resolve(117,a,35,a)].
% 3.45/3.74 6802 r2_hidden(c4,c6) | r2_hidden(c4,k4_xboole_0(c5,c6)). [resolve(778,a,35,a)].
% 3.45/3.74 6809 r2_hidden(c4,c6) | -r2_hidden(c3,k4_xboole_0(c5,c6)). [resolve(6802,b,44,b)].
% 3.45/3.74 6810 r2_hidden(c4,c6) | -r2_hidden(c3,c6). [resolve(6802,b,43,b)].
% 3.45/3.74 6832 r2_hidden(c4,c6) | r2_hidden(c3,c5). [resolve(6810,b,1873,a)].
% 3.45/3.74 6836 r2_hidden(c3,c5) | -r2_hidden(c3,c6). [resolve(6832,a,41,b)].
% 3.45/3.74 6838 r2_hidden(c3,c5). [resolve(6836,b,1873,a),merge(b)].
% 3.45/3.74 6841 k2_xboole_0(A,c5) != B | r2_hidden(c3,B). [resolve(6838,a,50,c)].
% 3.45/3.74 6977 r2_hidden(c3,k2_xboole_0(A,c5)). [resolve(6841,a,35,a),rewrite([35(3)])].
% 3.45/3.74 7012 k2_xboole_0(A,c5) != k2_xboole_0(B,C) | r2_hidden(c3,B) | r2_hidden(c3,C). [resolve(6977,a,51,b),flip(a)].
% 3.45/3.74 7729 r2_hidden(c3,A) | r2_hidden(c3,k4_xboole_0(c5,A)). [resolve(7012,a,36,a(flip))].
% 3.45/3.74 7811 r2_hidden(c3,c6) | r2_hidden(c4,c6). [resolve(7729,b,6809,b)].
% 3.45/3.74 7815 r2_hidden(c3,c6) | -r2_hidden(c4,c6). [resolve(7729,b,42,a)].
% 3.45/3.74 7826 r2_hidden(c3,c6). [resolve(7815,b,7811,b),merge(b)].
% 3.45/3.74 7827 r2_hidden(c4,c6). [back_unit_del(6810),unit_del(b,7826)].
% 3.45/3.74 7830 $F. [back_unit_del(41),unit_del(a,7826),unit_del(b,7827)].
% 3.45/3.74
% 3.45/3.74 % SZS output end Refutation
% 3.45/3.74 ============================== end of proof ==========================
% 3.45/3.74
% 3.45/3.74 ============================== STATISTICS ============================
% 3.45/3.74
% 3.45/3.74 Given=790. Generated=206224. Kept=7802. proofs=1.
% 3.45/3.74 Usable=740. Sos=6884. Demods=7. Limbo=4, Disabled=205. Hints=0.
% 3.45/3.74 Megabytes=5.96.
% 3.45/3.74 User_CPU=2.67, System_CPU=0.11, Wall_clock=3.
% 3.45/3.74
% 3.45/3.74 ============================== end of statistics =====================
% 3.45/3.74
% 3.45/3.74 ============================== end of search =========================
% 3.45/3.74
% 3.45/3.74 THEOREM PROVED
% 3.45/3.74 % SZS status Theorem
% 3.45/3.74
% 3.45/3.74 Exiting with 1 proof.
% 3.45/3.74
% 3.45/3.74 Process 25877 exit (max_proofs) Sun Jun 19 16:44:47 2022
% 3.45/3.74 Prover9 interrupted
%------------------------------------------------------------------------------