TSTP Solution File: GRP209-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP209-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 : Sat Jul 16 11:18:10 EDT 2022
% Result : Unsatisfiable 36.10s 36.41s
% Output : Refutation 36.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP209-1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Tue Jun 14 07:00:42 EDT 2022
% 0.11/0.31 % CPUTime :
% 32.70/33.00 ============================== Prover9 ===============================
% 32.70/33.00 Prover9 (32) version 2009-11A, November 2009.
% 32.70/33.00 Process 2252 was started by sandbox on n032.cluster.edu,
% 32.70/33.00 Tue Jun 14 07:00:43 2022
% 32.70/33.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_2093_n032.cluster.edu".
% 32.70/33.00 ============================== end of head ===========================
% 32.70/33.00
% 32.70/33.00 ============================== INPUT =================================
% 32.70/33.00
% 32.70/33.00 % Reading from file /tmp/Prover9_2093_n032.cluster.edu
% 32.70/33.00
% 32.70/33.00 set(prolog_style_variables).
% 32.70/33.00 set(auto2).
% 32.70/33.00 % set(auto2) -> set(auto).
% 32.70/33.00 % set(auto) -> set(auto_inference).
% 32.70/33.00 % set(auto) -> set(auto_setup).
% 32.70/33.00 % set(auto_setup) -> set(predicate_elim).
% 32.70/33.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 32.70/33.00 % set(auto) -> set(auto_limits).
% 32.70/33.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 32.70/33.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 32.70/33.00 % set(auto) -> set(auto_denials).
% 32.70/33.00 % set(auto) -> set(auto_process).
% 32.70/33.00 % set(auto2) -> assign(new_constants, 1).
% 32.70/33.00 % set(auto2) -> assign(fold_denial_max, 3).
% 32.70/33.00 % set(auto2) -> assign(max_weight, "200.000").
% 32.70/33.00 % set(auto2) -> assign(max_hours, 1).
% 32.70/33.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 32.70/33.00 % set(auto2) -> assign(max_seconds, 0).
% 32.70/33.00 % set(auto2) -> assign(max_minutes, 5).
% 32.70/33.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 32.70/33.00 % set(auto2) -> set(sort_initial_sos).
% 32.70/33.00 % set(auto2) -> assign(sos_limit, -1).
% 32.70/33.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 32.70/33.00 % set(auto2) -> assign(max_megs, 400).
% 32.70/33.00 % set(auto2) -> assign(stats, some).
% 32.70/33.00 % set(auto2) -> clear(echo_input).
% 32.70/33.00 % set(auto2) -> set(quiet).
% 32.70/33.00 % set(auto2) -> clear(print_initial_clauses).
% 32.70/33.00 % set(auto2) -> clear(print_given).
% 32.70/33.00 assign(lrs_ticks,-1).
% 32.70/33.00 assign(sos_limit,10000).
% 32.70/33.00 assign(order,kbo).
% 32.70/33.00 set(lex_order_vars).
% 32.70/33.00 clear(print_given).
% 32.70/33.00
% 32.70/33.00 % formulas(sos). % not echoed (46 formulas)
% 32.70/33.00
% 32.70/33.00 ============================== end of input ==========================
% 32.70/33.00
% 32.70/33.00 % From the command line: assign(max_seconds, 300).
% 32.70/33.00
% 32.70/33.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 32.70/33.00
% 32.70/33.00 % Formulas that are not ordinary clauses:
% 32.70/33.00
% 32.70/33.00 ============================== end of process non-clausal formulas ===
% 32.70/33.00
% 32.70/33.00 ============================== PROCESS INITIAL CLAUSES ===============
% 32.70/33.00
% 32.70/33.00 ============================== PREDICATE ELIMINATION =================
% 32.70/33.00
% 32.70/33.00 ============================== end predicate elimination =============
% 32.70/33.00
% 32.70/33.00 Auto_denials: (non-Horn, no changes).
% 32.70/33.00
% 32.70/33.00 Term ordering decisions:
% 32.70/33.00
% 32.70/33.00 % Assigning unary symbol inverse kb_weight 0 and highest precedence (14).
% 32.70/33.00 Function symbol KB weights: sk_c10=1. sk_c9=1. sk_c2=1. sk_c8=1. sk_c1=1. sk_c3=1. sk_c4=1. sk_c5=1. sk_c6=1. sk_c7=1. identity=1. multiply=1. inverse=0.
% 32.70/33.00
% 32.70/33.00 ============================== end of process initial clauses ========
% 32.70/33.00
% 32.70/33.00 ============================== CLAUSES FOR SEARCH ====================
% 32.70/33.00
% 32.70/33.00 ============================== end of clauses for search =============
% 32.70/33.00
% 32.70/33.00 ============================== SEARCH ================================
% 32.70/33.00
% 32.70/33.00 % Starting search at 0.25 seconds.
% 32.70/33.00
% 32.70/33.00 Low Water (keep): wt=51.000, iters=4020
% 32.70/33.00
% 32.70/33.00 Low Water (displace): id=3610, wt=68.000
% 32.70/33.00
% 32.70/33.00 Low Water (displace): id=10258, wt=67.000
% 32.70/33.00
% 32.70/33.00 Low Water (displace): id=10261, wt=66.000
% 32.70/33.00
% 32.70/33.00 Low Water (displace): id=10455, wt=46.000
% 32.70/33.00
% 32.70/33.00 Low Water (displace): id=10462, wt=45.000
% 32.70/33.00
% 32.70/33.00 Low Water (displace): id=11019, wt=42.000
% 32.70/33.00
% 32.70/33.00 Low Water (displace): id=11395, wt=41.000
% 32.70/33.00
% 32.70/33.00 Low Water (displace): id=17936, wt=40.000
% 32.70/33.00
% 32.70/33.00 Low Water (displace): id=18377, wt=38.000
% 32.70/33.00
% 32.70/33.00 Low Water (displace): id=18433, wt=37.000
% 32.70/33.00
% 32.70/33.00 Low Water (displace): id=18698, wt=36.000
% 32.70/33.00
% 32.70/33.00 Low Water (keep): wt=50.000, iters=6546
% 32.70/33.00
% 32.70/33.00 Low Water (keep): wt=46.000, iters=4200
% 32.70/33.00
% 32.70/33.00 Low Water (keep): wt=45.000, iters=3411
% 32.70/33.00
% 32.70/33.00 Low Water (displace): id=52126, wt=35.000
% 32.70/33.00
% 32.70/33.00 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 56 (0.00 of 27.70 sec).
% 32.70/33.00
% 32.70/33.00 Low Water (displace): id=67816, wt=34.000
% 32.70/33.00
% 32.70/33.00 Low Water (displace): id=67817, wt=33.000
% 32.70/33.00
% 32.70/33.00 Low Water (keep): wt=44.000, iters=3340
% 32.70/33.00
% 32.70/33.00 Low Water (displace): id=68943, wt=25.000
% 32.70/33.00
% 32.70/33.00 Low Water (displace): id=68961, wt=24.000
% 32.70/33.00
% 32.70/33.00 Low Water (keep): wt=43.000, iters=3336
% 32.70/33.00
% 32.70/33.00 Low Water (displace): id=69530, wt=17.000
% 36.10/36.41
% 36.10/36.41 Low Water (displace): id=69539, wt=15.000
% 36.10/36.41
% 36.10/36.41 Low Water (keep): wt=42.000, iters=3371
% 36.10/36.41
% 36.10/36.41 Low Water (keep): wt=41.000, iters=3493
% 36.10/36.41
% 36.10/36.41 Low Water (keep): wt=40.000, iters=3589
% 36.10/36.41
% 36.10/36.41 Low Water (keep): wt=39.000, iters=3334
% 36.10/36.41
% 36.10/36.41 Low Water (keep): wt=37.000, iters=3633
% 36.10/36.41
% 36.10/36.41 Low Water (keep): wt=36.000, iters=3550
% 36.10/36.41
% 36.10/36.41 ============================== PROOF =================================
% 36.10/36.41 % SZS status Unsatisfiable
% 36.10/36.41 % SZS output start Refutation
% 36.10/36.41
% 36.10/36.41 % Proof 1 at 35.33 (+ 0.26) seconds.
% 36.10/36.41 % Length of proof is 60.
% 36.10/36.41 % Level of proof is 16.
% 36.10/36.41 % Maximum clause weight is 60.000.
% 36.10/36.41 % Given clauses 695.
% 36.10/36.41
% 36.10/36.41 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 36.10/36.41 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 36.10/36.41 4 inverse(sk_c1) = sk_c2 | inverse(sk_c6) = sk_c9 # label(prove_this_11) # label(negated_conjecture). [assumption].
% 36.10/36.41 6 inverse(sk_c3) = sk_c10 | inverse(sk_c5) = sk_c10 # label(prove_this_36) # label(negated_conjecture). [assumption].
% 36.10/36.41 10 multiply(sk_c1,sk_c2) = sk_c10 | inverse(sk_c6) = sk_c9 # label(prove_this_4) # label(negated_conjecture). [assumption].
% 36.10/36.41 13 inverse(sk_c1) = sk_c2 | multiply(sk_c6,sk_c9) = sk_c10 # label(prove_this_10) # label(negated_conjecture). [assumption].
% 36.10/36.41 19 multiply(sk_c10,sk_c4) = sk_c9 | inverse(sk_c5) = sk_c10 # label(prove_this_22) # label(negated_conjecture). [assumption].
% 36.10/36.41 22 multiply(sk_c3,sk_c10) = sk_c4 | inverse(sk_c5) = sk_c10 # label(prove_this_29) # label(negated_conjecture). [assumption].
% 36.10/36.41 25 inverse(sk_c3) = sk_c10 | multiply(sk_c5,sk_c9) = sk_c10 # label(prove_this_37) # label(negated_conjecture). [assumption].
% 36.10/36.41 30 multiply(sk_c1,sk_c2) = sk_c10 | multiply(sk_c6,sk_c9) = sk_c10 # label(prove_this_3) # label(negated_conjecture). [assumption].
% 36.10/36.41 37 multiply(sk_c10,sk_c4) = sk_c9 | multiply(sk_c5,sk_c9) = sk_c10 # label(prove_this_23) # label(negated_conjecture). [assumption].
% 36.10/36.41 41 multiply(sk_c3,sk_c10) = sk_c4 | multiply(sk_c5,sk_c9) = sk_c10 # label(prove_this_30) # label(negated_conjecture). [assumption].
% 36.10/36.41 45 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 36.10/36.41 46 multiply(A,B) != sk_c10 | inverse(A) != B | multiply(B,sk_c9) != sk_c10 | multiply(sk_c10,C) != sk_c9 | multiply(D,sk_c10) != C | inverse(D) != sk_c10 | inverse(E) != sk_c10 | multiply(E,sk_c9) != sk_c10 | multiply(F,sk_c9) != sk_c10 | inverse(F) != sk_c9 | multiply(V6,V7) != sk_c9 | inverse(V6) != V7 | multiply(V7,sk_c10) != sk_c9 # label(prove_this_43) # label(negated_conjecture). [assumption].
% 36.10/36.41 486 inverse(sk_c3) = sk_c10 | multiply(sk_c10,sk_c5) = identity. [para(6(b,1),2(a,1,1))].
% 36.10/36.41 489 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),45(a,1,1)),rewrite([1(2)]),flip(a)].
% 36.10/36.41 647 multiply(A,B) != sk_c10 | inverse(A) != B | multiply(B,sk_c9) != sk_c10 | multiply(sk_c10,C) != sk_c9 | sk_c10 != C | inverse(identity) != sk_c10 | inverse(D) != sk_c10 | multiply(D,sk_c9) != sk_c10 | multiply(E,sk_c9) != sk_c10 | inverse(E) != sk_c9 | multiply(F,V6) != sk_c9 | inverse(F) != V6 | multiply(V6,sk_c10) != sk_c9. [para(1(a,1),46(e,1))].
% 36.10/36.41 1847 multiply(A,B) != sk_c10 | inverse(A) != B | multiply(B,sk_c9) != sk_c10 | multiply(sk_c10,C) != sk_c9 | sk_c10 != C | inverse(identity) != sk_c10 | inverse(D) != sk_c10 | multiply(D,sk_c9) != sk_c10 | multiply(E,sk_c9) != sk_c10 | inverse(E) != sk_c9 | multiply(A,B) != sk_c9 | multiply(B,sk_c10) != sk_c9. [factor(647,b,l)].
% 36.10/36.41 6228 multiply(A,B) != sk_c10 | inverse(A) != B | multiply(B,sk_c9) != sk_c10 | multiply(sk_c10,C) != sk_c9 | sk_c10 != C | inverse(identity) != sk_c10 | inverse(B) != sk_c10 | multiply(D,sk_c9) != sk_c10 | inverse(D) != sk_c9 | multiply(A,B) != sk_c9 | multiply(B,sk_c10) != sk_c9. [factor(1847,c,h)].
% 36.10/36.41 13354 multiply(A,B) != sk_c10 | inverse(A) != B | multiply(B,sk_c9) != sk_c10 | multiply(sk_c10,C) != sk_c9 | sk_c10 != C | inverse(identity) != sk_c10 | inverse(B) != sk_c10 | inverse(B) != sk_c9 | multiply(A,B) != sk_c9 | multiply(B,sk_c10) != sk_c9. [factor(6228,c,h)].
% 36.10/36.41 19280 multiply(A,identity) != sk_c10 | inverse(A) != identity | sk_c9 != sk_c10 | multiply(sk_c10,B) != sk_c9 | sk_c10 != B | inverse(identity) != sk_c10 | inverse(identity) != sk_c9 | multiply(A,identity) != sk_c9. [factor(13354,f,g),rewrite([1(10),1(31)]),flip(i),merge(i)].
% 36.10/36.41 59199 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),489(a,1,2))].
% 36.10/36.41 59215 inverse(sk_c5) = sk_c10 | multiply(inverse(sk_c10),sk_c9) = sk_c4. [para(19(a,1),489(a,1,2))].
% 36.10/36.41 59218 inverse(sk_c5) = sk_c10 | multiply(inverse(sk_c3),sk_c4) = sk_c10. [para(22(a,1),489(a,1,2))].
% 36.10/36.41 59233 multiply(sk_c10,sk_c4) = sk_c9 | multiply(inverse(sk_c5),sk_c10) = sk_c9. [para(37(b,1),489(a,1,2))].
% 36.10/36.41 59237 multiply(sk_c3,sk_c10) = sk_c4 | multiply(inverse(sk_c5),sk_c10) = sk_c9. [para(41(b,1),489(a,1,2))].
% 36.10/36.41 59479 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(489(a,1),489(a,1,2))].
% 36.10/36.41 60085 multiply(A,identity) = A. [back_rewrite(59199),rewrite([59479(4)])].
% 36.10/36.41 60552 sk_c10 != A | inverse(A) != identity | sk_c9 != sk_c10 | multiply(sk_c10,B) != sk_c9 | sk_c10 != B | inverse(identity) != sk_c10 | inverse(identity) != sk_c9 | sk_c9 != A. [back_rewrite(19280),rewrite([60085(2),60085(24)]),flip(a),flip(h)].
% 36.10/36.41 60676 sk_c10 != A | inverse(A) != identity | sk_c9 != sk_c10 | multiply(sk_c10,A) != sk_c9 | inverse(identity) != sk_c10 | inverse(identity) != sk_c9 | sk_c9 != A. [factor(60552,a,e)].
% 36.10/36.41 60985 inverse(identity) = identity. [para(60085(a,1),2(a,1))].
% 36.10/36.41 61559 sk_c10 != A | inverse(A) != identity | sk_c9 != sk_c10 | multiply(sk_c10,A) != sk_c9 | identity != sk_c10 | identity != sk_c9 | sk_c9 != A. [back_rewrite(60676),rewrite([60985(14),60985(17)])].
% 36.10/36.41 62184 inverse(sk_c3) = sk_c10 | inverse(sk_c10) = sk_c5. [para(486(b,1),489(a,1,2)),rewrite([60085(8)])].
% 36.10/36.41 62254 inverse(sk_c10) = sk_c5 | multiply(sk_c10,sk_c3) = identity. [para(62184(a,1),2(a,1,1))].
% 36.10/36.41 62644 multiply(A,inverse(A)) = identity. [para(59479(a,1),2(a,1))].
% 36.10/36.41 63782 inverse(inverse(A)) = A. [para(59479(a,1),60085(a,1)),rewrite([60085(2)]),flip(a)].
% 36.10/36.41 64827 inverse(sk_c1) = sk_c2 | multiply(sk_c6,sk_c9) = identity. [para(4(b,1),62644(a,1,2))].
% 36.10/36.41 68663 inverse(sk_c1) = sk_c2 | identity = sk_c10. [para(64827(b,1),13(b,1)),merge(b)].
% 36.10/36.41 68736 identity = sk_c10 | multiply(sk_c1,sk_c2) = identity. [para(68663(a,1),62644(a,1,2))].
% 36.10/36.41 68766 identity != sk_c10 | sk_c9 != sk_c10 | identity != sk_c9. [para(60085(a,1),61559(d,1)),rewrite([60985(5)]),flip(a),flip(d),flip(g),xx(b),merge(c),merge(d),merge(f)].
% 36.10/36.41 68790 identity = sk_c10 | inverse(sk_c6) = sk_c9. [para(68736(b,1),10(a,1)),merge(b)].
% 36.10/36.41 68820 identity = sk_c10 | multiply(sk_c6,sk_c9) = identity. [para(68790(b,1),62644(a,1,2))].
% 36.10/36.41 69486 identity = sk_c10 | multiply(sk_c1,sk_c2) = sk_c10. [para(68820(b,1),30(b,1)),merge(c)].
% 36.10/36.41 69684 identity = sk_c10. [para(69486(b,1),68736(b,1)),flip(c),merge(b),merge(c)].
% 36.10/36.41 69712 sk_c9 != sk_c10. [back_rewrite(68766),rewrite([69684(1),69684(7)]),flip(c),xx(a),merge(b)].
% 36.10/36.41 69806 inverse(sk_c10) = sk_c5 | multiply(sk_c10,sk_c3) = sk_c10. [back_rewrite(62254),rewrite([69684(8)])].
% 36.10/36.41 69826 inverse(sk_c10) = sk_c10. [back_rewrite(60985),rewrite([69684(1),69684(3)])].
% 36.10/36.41 69827 multiply(A,sk_c10) = A. [back_rewrite(60085),rewrite([69684(1)])].
% 36.10/36.41 69835 multiply(sk_c10,A) = A. [back_rewrite(1),rewrite([69684(1)])].
% 36.10/36.41 69837 sk_c5 = sk_c10 | sk_c3 = sk_c10. [back_rewrite(69806),rewrite([69826(2),69835(6)]),flip(a)].
% 36.10/36.41 69878 inverse(sk_c5) = sk_c10 | sk_c4 = sk_c9. [back_rewrite(59215),rewrite([69826(6),69835(7)]),flip(b)].
% 36.10/36.41 70545 sk_c4 = sk_c3 | inverse(sk_c5) = sk_c9. [back_rewrite(59237),rewrite([69827(3),69827(7)]),flip(a)].
% 36.10/36.41 70546 sk_c4 = sk_c9 | inverse(sk_c5) = sk_c9. [back_rewrite(59233),rewrite([69835(3),69827(7)])].
% 36.10/36.41 77914 sk_c3 = sk_c10 | inverse(sk_c3) = sk_c10. [para(69837(a,1),25(b,1,1)),rewrite([69835(10)]),unit_del(c,69712)].
% 36.10/36.41 78353 sk_c4 = sk_c9. [para(70546(b,1),69878(a,1)),merge(c),unit_del(b,69712)].
% 36.10/36.41 78789 sk_c3 = sk_c9 | inverse(sk_c5) = sk_c9. [back_rewrite(70545),rewrite([78353(1)]),flip(a)].
% 36.10/36.41 78804 inverse(sk_c5) = sk_c10 | multiply(inverse(sk_c3),sk_c9) = sk_c10. [back_rewrite(59218),rewrite([78353(7)])].
% 36.10/36.41 79723 sk_c3 = sk_c10. [para(77914(b,1),63782(a,1,1)),rewrite([69826(5)]),flip(b),merge(b)].
% 36.10/36.41 79759 inverse(sk_c5) = sk_c10. [back_rewrite(78804),rewrite([79723(5),69826(6),69835(7)]),unit_del(b,69712)].
% 36.12/36.41 79761 $F. [back_rewrite(78789),rewrite([79723(1),79759(5)]),flip(a),flip(b),merge(b),unit_del(a,69712)].
% 36.12/36.41
% 36.12/36.41 % SZS output end Refutation
% 36.12/36.41 ============================== end of proof ==========================
% 36.12/36.41
% 36.12/36.41 ============================== STATISTICS ============================
% 36.12/36.41
% 36.12/36.41 Given=695. Generated=386003. Kept=79760. proofs=1.
% 36.12/36.41 Usable=85. Sos=4503. Demods=23. Limbo=38, Disabled=75180. Hints=0.
% 36.12/36.41 Megabytes=94.75.
% 36.12/36.41 User_CPU=35.33, System_CPU=0.26, Wall_clock=35.
% 36.12/36.41
% 36.12/36.41 ============================== end of statistics =====================
% 36.12/36.41
% 36.12/36.41 ============================== end of search =========================
% 36.12/36.41
% 36.12/36.41 THEOREM PROVED
% 36.12/36.41 % SZS status Unsatisfiable
% 36.12/36.41
% 36.12/36.41 Exiting with 1 proof.
% 36.12/36.41
% 36.12/36.41 Process 2252 exit (max_proofs) Tue Jun 14 07:01:18 2022
% 36.12/36.41 Prover9 interrupted
%------------------------------------------------------------------------------