TSTP Solution File: GRP313-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP313-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 11:18:35 EDT 2022
% Result : Unsatisfiable 1.55s 1.88s
% Output : Refutation 1.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP313-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 11:48:37 EDT 2022
% 0.18/0.34 % CPUTime :
% 1.55/1.87 ============================== Prover9 ===============================
% 1.55/1.87 Prover9 (32) version 2009-11A, November 2009.
% 1.55/1.87 Process 11053 was started by sandbox on n028.cluster.edu,
% 1.55/1.87 Mon Jun 13 11:48:38 2022
% 1.55/1.87 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_10900_n028.cluster.edu".
% 1.55/1.87 ============================== end of head ===========================
% 1.55/1.87
% 1.55/1.87 ============================== INPUT =================================
% 1.55/1.87
% 1.55/1.87 % Reading from file /tmp/Prover9_10900_n028.cluster.edu
% 1.55/1.87
% 1.55/1.87 set(prolog_style_variables).
% 1.55/1.87 set(auto2).
% 1.55/1.87 % set(auto2) -> set(auto).
% 1.55/1.87 % set(auto) -> set(auto_inference).
% 1.55/1.87 % set(auto) -> set(auto_setup).
% 1.55/1.87 % set(auto_setup) -> set(predicate_elim).
% 1.55/1.87 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.55/1.87 % set(auto) -> set(auto_limits).
% 1.55/1.87 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.55/1.87 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.55/1.87 % set(auto) -> set(auto_denials).
% 1.55/1.87 % set(auto) -> set(auto_process).
% 1.55/1.87 % set(auto2) -> assign(new_constants, 1).
% 1.55/1.87 % set(auto2) -> assign(fold_denial_max, 3).
% 1.55/1.87 % set(auto2) -> assign(max_weight, "200.000").
% 1.55/1.87 % set(auto2) -> assign(max_hours, 1).
% 1.55/1.87 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.55/1.87 % set(auto2) -> assign(max_seconds, 0).
% 1.55/1.87 % set(auto2) -> assign(max_minutes, 5).
% 1.55/1.87 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.55/1.87 % set(auto2) -> set(sort_initial_sos).
% 1.55/1.87 % set(auto2) -> assign(sos_limit, -1).
% 1.55/1.87 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.55/1.87 % set(auto2) -> assign(max_megs, 400).
% 1.55/1.87 % set(auto2) -> assign(stats, some).
% 1.55/1.87 % set(auto2) -> clear(echo_input).
% 1.55/1.87 % set(auto2) -> set(quiet).
% 1.55/1.87 % set(auto2) -> clear(print_initial_clauses).
% 1.55/1.87 % set(auto2) -> clear(print_given).
% 1.55/1.87 assign(lrs_ticks,-1).
% 1.55/1.87 assign(sos_limit,10000).
% 1.55/1.87 assign(order,kbo).
% 1.55/1.87 set(lex_order_vars).
% 1.55/1.87 clear(print_given).
% 1.55/1.87
% 1.55/1.87 % formulas(sos). % not echoed (53 formulas)
% 1.55/1.87
% 1.55/1.87 ============================== end of input ==========================
% 1.55/1.87
% 1.55/1.87 % From the command line: assign(max_seconds, 300).
% 1.55/1.87
% 1.55/1.87 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.55/1.88
% 1.55/1.88 % Formulas that are not ordinary clauses:
% 1.55/1.88
% 1.55/1.88 ============================== end of process non-clausal formulas ===
% 1.55/1.88
% 1.55/1.88 ============================== PROCESS INITIAL CLAUSES ===============
% 1.55/1.88
% 1.55/1.88 ============================== PREDICATE ELIMINATION =================
% 1.55/1.88
% 1.55/1.88 ============================== end predicate elimination =============
% 1.55/1.88
% 1.55/1.88 Auto_denials: (non-Horn, no changes).
% 1.55/1.88
% 1.55/1.88 Term ordering decisions:
% 1.55/1.88
% 1.55/1.88 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 1.55/1.88 Function symbol KB weights: sk_c8=1. sk_c9=1. sk_c7=1. sk_c1=1. sk_c2=1. sk_c3=1. sk_c4=1. sk_c5=1. sk_c6=1. identity=1. multiply=1. inverse=0.
% 1.55/1.88
% 1.55/1.88 ============================== end of process initial clauses ========
% 1.55/1.88
% 1.55/1.88 ============================== CLAUSES FOR SEARCH ====================
% 1.55/1.88
% 1.55/1.88 ============================== end of clauses for search =============
% 1.55/1.88
% 1.55/1.88 ============================== SEARCH ================================
% 1.55/1.88
% 1.55/1.88 % Starting search at 0.02 seconds.
% 1.55/1.88
% 1.55/1.88 ============================== PROOF =================================
% 1.55/1.88 % SZS status Unsatisfiable
% 1.55/1.88 % SZS output start Refutation
% 1.55/1.88
% 1.55/1.88 % Proof 1 at 0.88 (+ 0.02) seconds.
% 1.55/1.88 % Length of proof is 65.
% 1.55/1.88 % Level of proof is 21.
% 1.55/1.88 % Maximum clause weight is 64.000.
% 1.55/1.88 % Given clauses 350.
% 1.55/1.88
% 1.55/1.88 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 1.55/1.88 2 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 1.55/1.88 3 inverse(sk_c1) = sk_c9 | inverse(sk_c4) = sk_c9 # label(prove_this_16) # label(negated_conjecture). [assumption].
% 1.55/1.88 10 inverse(sk_c3) = sk_c8 | inverse(sk_c5) = sk_c8 # label(prove_this_46) # label(negated_conjecture). [assumption].
% 1.55/1.88 15 multiply(sk_c1,sk_c9) = sk_c8 | inverse(sk_c4) = sk_c9 # label(prove_this_9) # label(negated_conjecture). [assumption].
% 1.55/1.88 18 inverse(sk_c1) = sk_c9 | multiply(sk_c4,sk_c9) = sk_c8 # label(prove_this_15) # label(negated_conjecture). [assumption].
% 1.55/1.88 30 multiply(sk_c3,sk_c8) = sk_c9 | inverse(sk_c5) = sk_c8 # label(prove_this_39) # label(negated_conjecture). [assumption].
% 1.55/1.88 33 inverse(sk_c3) = sk_c8 | multiply(sk_c5,sk_c8) = sk_c7 # label(prove_this_45) # label(negated_conjecture). [assumption].
% 1.55/1.88 38 multiply(sk_c8,sk_c9) = sk_c7 | multiply(sk_c7,sk_c9) = sk_c8 # label(prove_this_5) # label(negated_conjecture). [assumption].
% 1.55/1.88 40 multiply(sk_c1,sk_c9) = sk_c8 | multiply(sk_c4,sk_c9) = sk_c8 # label(prove_this_8) # label(negated_conjecture). [assumption].
% 1.55/1.88 49 multiply(sk_c3,sk_c8) = sk_c9 | multiply(sk_c5,sk_c8) = sk_c7 # label(prove_this_38) # label(negated_conjecture). [assumption].
% 1.55/1.88 52 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 1.55/1.88 53 multiply(sk_c8,sk_c9) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(B,sk_c8) != sk_c7 | inverse(B) != sk_c8 | multiply(C,sk_c8) != sk_c9 | inverse(C) != sk_c8 | multiply(D,sk_c9) != sk_c8 | inverse(D) != sk_c9 | multiply(E,sk_c8) != sk_c7 | inverse(E) != sk_c8 | multiply(sk_c7,sk_c9) != sk_c8 | multiply(F,sk_c7) != sk_c9 | inverse(F) != sk_c7 # label(prove_this_50) # label(negated_conjecture). [assumption].
% 1.55/1.88 54 multiply(sk_c8,sk_c9) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(B,sk_c8) != sk_c7 | inverse(B) != sk_c8 | multiply(C,sk_c8) != sk_c9 | inverse(C) != sk_c8 | multiply(D,sk_c8) != sk_c7 | inverse(D) != sk_c8 | multiply(sk_c7,sk_c9) != sk_c8 | multiply(E,sk_c7) != sk_c9 | inverse(E) != sk_c7. [factor(53,b,h),merge(h)].
% 1.55/1.88 57 multiply(sk_c8,sk_c9) != sk_c7 | multiply(A,sk_c9) != sk_c8 | inverse(A) != sk_c9 | multiply(B,sk_c8) != sk_c7 | inverse(B) != sk_c8 | multiply(C,sk_c8) != sk_c9 | inverse(C) != sk_c8 | multiply(sk_c7,sk_c9) != sk_c8 | multiply(D,sk_c7) != sk_c9 | inverse(D) != sk_c7. [factor(54,d,h),merge(h)].
% 1.55/1.88 68 inverse(sk_c3) = sk_c8 | multiply(sk_c8,sk_c5) = identity. [para(10(b,1),2(a,1,1))].
% 1.55/1.88 70 multiply(inverse(A),multiply(A,B)) = B. [para(2(a,1),52(a,1,1)),rewrite([1(2)]),flip(a)].
% 1.55/1.88 185 multiply(sk_c8,sk_c9) != sk_c7 | identity != sk_c8 | inverse(inverse(sk_c9)) != sk_c9 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(B,sk_c8) != sk_c9 | inverse(B) != sk_c8 | multiply(sk_c7,sk_c9) != sk_c8 | multiply(C,sk_c7) != sk_c9 | inverse(C) != sk_c7. [para(2(a,1),57(b,1))].
% 1.55/1.88 376 multiply(inverse(inverse(A)),identity) = A. [para(2(a,1),70(a,1,2))].
% 1.55/1.88 411 multiply(sk_c8,sk_c9) = sk_c7 | multiply(inverse(sk_c7),sk_c8) = sk_c9. [para(38(b,1),70(a,1,2))].
% 1.55/1.88 427 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(70(a,1),70(a,1,2))].
% 1.55/1.88 428 multiply(A,identity) = A. [back_rewrite(376),rewrite([427(4)])].
% 1.55/1.88 431 inverse(identity) = identity. [para(428(a,1),2(a,1))].
% 1.55/1.88 556 inverse(sk_c3) = sk_c8 | inverse(sk_c8) = sk_c5. [para(68(b,1),70(a,1,2)),rewrite([428(8)])].
% 1.55/1.88 557 inverse(sk_c8) = sk_c5 | multiply(sk_c8,sk_c3) = identity. [para(556(a,1),2(a,1,1))].
% 1.55/1.88 611 multiply(A,inverse(A)) = identity. [para(427(a,1),2(a,1))].
% 1.55/1.88 634 multiply(A,multiply(inverse(A),B)) = B. [para(427(a,1),70(a,1))].
% 1.55/1.88 635 inverse(inverse(A)) = A. [para(427(a,1),428(a,1)),rewrite([428(2)]),flip(a)].
% 1.55/1.88 683 multiply(sk_c8,sk_c9) != sk_c7 | identity != sk_c8 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(B,sk_c8) != sk_c9 | inverse(B) != sk_c8 | multiply(sk_c7,sk_c9) != sk_c8 | multiply(C,sk_c7) != sk_c9 | inverse(C) != sk_c7. [back_rewrite(185),rewrite([635(11)]),xx(c)].
% 1.55/1.88 693 inverse(sk_c1) = sk_c9 | multiply(sk_c4,sk_c9) = identity. [para(3(b,1),611(a,1,2))].
% 1.55/1.88 1468 inverse(sk_c1) = sk_c9 | identity = sk_c8. [para(693(b,1),18(b,1)),merge(b)].
% 1.55/1.88 1640 identity = sk_c8 | multiply(sk_c1,sk_c9) = identity. [para(1468(a,1),611(a,1,2))].
% 1.55/1.88 1665 identity = sk_c8 | inverse(sk_c4) = sk_c9. [para(1640(b,1),15(a,1)),merge(b)].
% 1.55/1.88 1917 identity = sk_c8 | multiply(sk_c4,sk_c9) = identity. [para(1665(b,1),611(a,1,2))].
% 1.55/1.88 2183 identity = sk_c8 | multiply(sk_c1,sk_c9) = sk_c8. [para(1917(b,1),40(b,1)),merge(c)].
% 1.55/1.88 3625 identity = sk_c8. [para(2183(b,1),1640(b,1)),flip(c),merge(b),merge(c)].
% 1.55/1.88 5728 multiply(sk_c8,sk_c9) != sk_c7 | multiply(A,sk_c8) != sk_c7 | inverse(A) != sk_c8 | multiply(B,sk_c8) != sk_c9 | inverse(B) != sk_c8 | multiply(sk_c7,sk_c9) != sk_c8 | multiply(C,sk_c7) != sk_c9 | inverse(C) != sk_c7. [back_rewrite(683),rewrite([3625(6)]),xx(b)].
% 1.55/1.88 5737 inverse(sk_c8) = sk_c5 | multiply(sk_c8,sk_c3) = sk_c8. [back_rewrite(557),rewrite([3625(8)])].
% 1.55/1.88 5747 inverse(sk_c8) = sk_c8. [back_rewrite(431),rewrite([3625(1),3625(3)])].
% 1.55/1.88 5748 multiply(A,sk_c8) = A. [back_rewrite(428),rewrite([3625(1)])].
% 1.55/1.88 5758 multiply(inverse(A),A) = sk_c8. [back_rewrite(2),rewrite([3625(3)])].
% 1.55/1.88 5759 multiply(sk_c8,A) = A. [back_rewrite(1),rewrite([3625(1)])].
% 1.55/1.88 5803 sk_c7 != sk_c9 | sk_c7 != A | inverse(A) != sk_c8 | sk_c9 != A | multiply(sk_c7,sk_c9) != sk_c8 | multiply(B,sk_c7) != sk_c9 | inverse(B) != sk_c7. [factor(5728,c,e),rewrite([5759(3),5748(5),5748(10)]),flip(a),flip(b),flip(d)].
% 1.55/1.88 5814 sk_c5 = sk_c8 | sk_c3 = sk_c8. [back_rewrite(5737),rewrite([5747(2),5759(6)]),flip(a)].
% 1.55/1.88 6263 sk_c7 = sk_c9 | inverse(sk_c7) = sk_c9. [back_rewrite(411),rewrite([5759(3),5748(7)]),flip(a)].
% 1.55/1.88 6448 sk_c3 = sk_c9 | sk_c5 = sk_c7. [back_rewrite(49),rewrite([5748(3),5748(6)])].
% 1.55/1.88 6456 inverse(sk_c3) = sk_c8 | sk_c5 = sk_c7. [back_rewrite(33),rewrite([5748(7)])].
% 1.55/1.88 6458 sk_c3 = sk_c9 | inverse(sk_c5) = sk_c8. [back_rewrite(30),rewrite([5748(3)])].
% 1.55/1.88 6671 sk_c7 != sk_c9 | inverse(sk_c9) != sk_c8 | multiply(sk_c7,sk_c9) != sk_c8 | multiply(A,sk_c7) != sk_c9 | inverse(A) != sk_c7. [factor(5803,a,b),xx(c)].
% 1.55/1.88 6737 sk_c7 != sk_c9 | inverse(sk_c9) != sk_c8 | multiply(sk_c7,sk_c9) != sk_c8 | multiply(A,multiply(B,sk_c7)) != sk_c9 | inverse(multiply(A,B)) != sk_c7. [para(52(a,1),6671(d,1))].
% 1.55/1.88 6816 sk_c7 != sk_c9 | inverse(sk_c9) != sk_c8 | multiply(sk_c7,sk_c9) != sk_c8 | sk_c9 != A | inverse(multiply(A,inverse(sk_c7))) != sk_c7. [para(5758(a,1),6737(d,1,2)),rewrite([5748(14)]),flip(d)].
% 1.55/1.88 6844 sk_c7 != sk_c9 | inverse(sk_c9) != sk_c8 | multiply(sk_c7,sk_c9) != sk_c8 | multiply(A,B) != sk_c9 | inverse(multiply(A,multiply(B,inverse(sk_c7)))) != sk_c7. [para(52(a,1),6816(e,1,1)),flip(d)].
% 1.55/1.88 6853 sk_c7 != sk_c9 | inverse(sk_c9) != sk_c8 | multiply(sk_c7,sk_c9) != sk_c8 | multiply(A,multiply(B,C)) != sk_c9 | inverse(multiply(A,multiply(B,multiply(C,inverse(sk_c7))))) != sk_c7. [para(52(a,1),6844(e,1,1,2))].
% 1.55/1.88 7345 sk_c7 = sk_c9 | multiply(sk_c9,sk_c7) = sk_c8. [para(6263(b,1),5758(a,1,1))].
% 1.55/1.88 7413 sk_c5 = sk_c7 | sk_c3 = sk_c8. [para(6456(a,1),635(a,1,1)),rewrite([5747(5)]),flip(b)].
% 1.55/1.88 7421 sk_c3 = sk_c8 | sk_c7 = sk_c8. [para(7413(a,1),5814(a,1)),merge(c)].
% 1.55/1.88 7498 sk_c7 != sk_c9 | inverse(sk_c9) != sk_c8 | multiply(sk_c7,sk_c9) != sk_c8 | multiply(A,multiply(inverse(multiply(B,inverse(sk_c7))),B)) != sk_c9 | inverse(A) != sk_c7. [para(5758(a,1),6853(e,1,1,2)),rewrite([5748(22)])].
% 1.55/1.88 7517 sk_c3 = sk_c9 | sk_c5 = sk_c8. [para(6458(b,1),635(a,1,1)),rewrite([5747(5)]),flip(b)].
% 1.55/1.88 7520 sk_c3 = sk_c9 | sk_c7 = sk_c8. [para(7517(b,1),6448(b,1)),flip(c),merge(b)].
% 1.55/1.88 7525 sk_c7 = sk_c8 | sk_c9 = sk_c8. [para(7520(a,1),7421(a,1)),merge(c)].
% 1.55/1.88 7554 sk_c9 = sk_c8 | sk_c7 = sk_c9. [para(7525(a,1),6263(b,1,1)),rewrite([5747(8)]),flip(c),merge(c)].
% 1.55/1.88 7583 sk_c7 != sk_c9 | inverse(sk_c9) != sk_c8 | multiply(sk_c7,sk_c9) != sk_c8 | inverse(multiply(sk_c9,inverse(sk_c7))) != sk_c7. [resolve(7498,d,634,a)].
% 1.55/1.88 7684 sk_c9 = sk_c8. [para(7554(b,1),7525(a,1)),merge(b),merge(c)].
% 1.55/1.88 7707 sk_c7 != sk_c8. [back_rewrite(7583),rewrite([7684(2),7684(4),5747(5),7684(8),5748(9),7684(10),5759(13),635(12)]),xx(b),xx(d),merge(b)].
% 1.55/1.88 7720 $F. [back_rewrite(7345),rewrite([7684(2),7684(4),5759(6)]),merge(b),unit_del(a,7707)].
% 1.55/1.88
% 1.55/1.88 % SZS output end Refutation
% 1.55/1.88 ============================== end of proof ==========================
% 1.55/1.88
% 1.55/1.88 ============================== STATISTICS ============================
% 1.55/1.88
% 1.55/1.88 Given=350. Generated=14115. Kept=7719. proofs=1.
% 1.55/1.88 Usable=115. Sos=1187. Demods=15. Limbo=36, Disabled=6434. Hints=0.
% 1.55/1.88 Megabytes=8.31.
% 1.55/1.88 User_CPU=0.88, System_CPU=0.02, Wall_clock=1.
% 1.55/1.88
% 1.55/1.88 ============================== end of statistics =====================
% 1.55/1.88
% 1.55/1.88 ============================== end of search =========================
% 1.55/1.88
% 1.55/1.88 THEOREM PROVED
% 1.55/1.88 % SZS status Unsatisfiable
% 1.55/1.88
% 1.55/1.88 Exiting with 1 proof.
% 1.55/1.88
% 1.55/1.88 Process 11053 exit (max_proofs) Mon Jun 13 11:48:39 2022
% 1.55/1.88 Prover9 interrupted
%------------------------------------------------------------------------------