TSTP Solution File: GRP199-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP199-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 11:18:07 EDT 2022
% Result : Unsatisfiable 7.01s 7.28s
% Output : Refutation 7.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP199-1 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n011.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 Jun 13 09:31:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 4.60/4.88 ============================== Prover9 ===============================
% 4.60/4.88 Prover9 (32) version 2009-11A, November 2009.
% 4.60/4.88 Process 3140 was started by sandbox2 on n011.cluster.edu,
% 4.60/4.88 Mon Jun 13 09:31:19 2022
% 4.60/4.88 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2987_n011.cluster.edu".
% 4.60/4.88 ============================== end of head ===========================
% 4.60/4.88
% 4.60/4.88 ============================== INPUT =================================
% 4.60/4.88
% 4.60/4.88 % Reading from file /tmp/Prover9_2987_n011.cluster.edu
% 4.60/4.88
% 4.60/4.88 set(prolog_style_variables).
% 4.60/4.88 set(auto2).
% 4.60/4.88 % set(auto2) -> set(auto).
% 4.60/4.88 % set(auto) -> set(auto_inference).
% 4.60/4.88 % set(auto) -> set(auto_setup).
% 4.60/4.88 % set(auto_setup) -> set(predicate_elim).
% 4.60/4.88 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.60/4.88 % set(auto) -> set(auto_limits).
% 4.60/4.88 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.60/4.88 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.60/4.88 % set(auto) -> set(auto_denials).
% 4.60/4.88 % set(auto) -> set(auto_process).
% 4.60/4.88 % set(auto2) -> assign(new_constants, 1).
% 4.60/4.88 % set(auto2) -> assign(fold_denial_max, 3).
% 4.60/4.88 % set(auto2) -> assign(max_weight, "200.000").
% 4.60/4.88 % set(auto2) -> assign(max_hours, 1).
% 4.60/4.88 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.60/4.88 % set(auto2) -> assign(max_seconds, 0).
% 4.60/4.88 % set(auto2) -> assign(max_minutes, 5).
% 4.60/4.88 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.60/4.88 % set(auto2) -> set(sort_initial_sos).
% 4.60/4.88 % set(auto2) -> assign(sos_limit, -1).
% 4.60/4.88 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.60/4.88 % set(auto2) -> assign(max_megs, 400).
% 4.60/4.88 % set(auto2) -> assign(stats, some).
% 4.60/4.88 % set(auto2) -> clear(echo_input).
% 4.60/4.88 % set(auto2) -> set(quiet).
% 4.60/4.88 % set(auto2) -> clear(print_initial_clauses).
% 4.60/4.88 % set(auto2) -> clear(print_given).
% 4.60/4.88 assign(lrs_ticks,-1).
% 4.60/4.88 assign(sos_limit,10000).
% 4.60/4.88 assign(order,kbo).
% 4.60/4.88 set(lex_order_vars).
% 4.60/4.88 clear(print_given).
% 4.60/4.88
% 4.60/4.88 % formulas(sos). % not echoed (8 formulas)
% 4.60/4.88
% 4.60/4.88 ============================== end of input ==========================
% 4.60/4.88
% 4.60/4.88 % From the command line: assign(max_seconds, 300).
% 4.60/4.88
% 4.60/4.88 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.60/4.88
% 4.60/4.88 % Formulas that are not ordinary clauses:
% 4.60/4.88
% 4.60/4.88 ============================== end of process non-clausal formulas ===
% 4.60/4.88
% 4.60/4.88 ============================== PROCESS INITIAL CLAUSES ===============
% 4.60/4.88
% 4.60/4.88 ============================== PREDICATE ELIMINATION =================
% 4.60/4.88
% 4.60/4.88 ============================== end predicate elimination =============
% 4.60/4.88
% 4.60/4.88 Auto_denials:
% 4.60/4.88 % copying label prove_quotient4 to answer in negative clause
% 4.60/4.88
% 4.60/4.88 Term ordering decisions:
% 4.60/4.88 Function symbol KB weights: a=1. a0=1. b=1. b0=1. c=1. c0=1. d=1. d0=1. multiply=1.
% 4.60/4.88
% 4.60/4.88 ============================== end of process initial clauses ========
% 4.60/4.88
% 4.60/4.88 ============================== CLAUSES FOR SEARCH ====================
% 4.60/4.88
% 4.60/4.88 ============================== end of clauses for search =============
% 4.60/4.88
% 4.60/4.88 ============================== SEARCH ================================
% 4.60/4.88
% 4.60/4.88 % Starting search at 0.01 seconds.
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=91.000, iters=3521
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=75.000, iters=3371
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=63.000, iters=3412
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=61.000, iters=3433
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=57.000, iters=3397
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=55.000, iters=3393
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=53.000, iters=3361
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=51.000, iters=3363
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=50.000, iters=3460
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=46.000, iters=3379
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=42.000, iters=3400
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=40.000, iters=3619
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=38.000, iters=3476
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=36.000, iters=3376
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=35.000, iters=3403
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=34.000, iters=3346
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=33.000, iters=3361
% 4.60/4.88
% 4.60/4.88 Low Water (keep): wt=32.000, iters=3371
% 4.60/4.88
% 4.60/4.88 Low Water (displace): id=1595, wt=187.000
% 4.60/4.88
% 4.60/4.88 Low Water (displace): id=2042, wt=179.000
% 4.60/4.88
% 4.60/4.88 Low Water (displace): id=1596, wt=171.000
% 4.60/4.88
% 4.60/4.88 Low Water (displace): id=2040, wt=163.000
% 4.60/4.88
% 4.60/4.88 Low Water (displace): id=2032, wt=155.000
% 4.60/4.88
% 4.60/4.88 Low Water (displace): id=2065, wt=147.000
% 4.60/4.88
% 4.60/4.88 Low Water (displace): id=2033, wt=139.000
% 4.60/4.88
% 4.60/4.88 Low Water (displace): id=2426, wt=135.000
% 4.60/4.88
% 4.60/4.88 Low Water (displace): id=2063, wt=131.000
% 4.60/4.88
% 4.60/4.88 Low Water (displace): id=5028, wt=123.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=5039, wt=115.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=2454, wt=111.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=5029, wt=107.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=5040, wt=99.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=4349, wt=95.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=3159, wt=94.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=4838, wt=92.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=5327, wt=91.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=7558, wt=89.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=8439, wt=87.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=6457, wt=85.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=7994, wt=81.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=7993, wt=77.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=7557, wt=73.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=7561, wt=71.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=7496, wt=69.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=7560, wt=65.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=8617, wt=61.000
% 7.01/7.28
% 7.01/7.28 Low Water (keep): wt=30.000, iters=3344
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=11477, wt=39.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=11480, wt=35.000
% 7.01/7.28
% 7.01/7.28 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 75 (0.00 of 4.61 sec).
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=11706, wt=31.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=11943, wt=29.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=12310, wt=26.000
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=12689, wt=22.000
% 7.01/7.28
% 7.01/7.28 Low Water (keep): wt=29.000, iters=3355
% 7.01/7.28
% 7.01/7.28 Low Water (keep): wt=28.000, iters=3368
% 7.01/7.28
% 7.01/7.28 Low Water (displace): id=14983, wt=20.000
% 7.01/7.28
% 7.01/7.28 ============================== PROOF =================================
% 7.01/7.28 % SZS status Unsatisfiable
% 7.01/7.28 % SZS output start Refutation
% 7.01/7.28
% 7.01/7.28 % Proof 1 at 6.21 (+ 0.04) seconds: prove_quotient4.
% 7.01/7.28 % Length of proof is 22.
% 7.01/7.28 % Level of proof is 6.
% 7.01/7.28 % Maximum clause weight is 23.000.
% 7.01/7.28 % Given clauses 852.
% 7.01/7.28
% 7.01/7.28 1 multiply(b,b0) = multiply(a,a0) # label(prove_quotient1) # label(negated_conjecture). [assumption].
% 7.01/7.28 2 multiply(d,b0) = multiply(c,a0) # label(prove_quotient2) # label(negated_conjecture). [assumption].
% 7.01/7.28 3 multiply(b,d0) = multiply(a,c0) # label(prove_quotient3) # label(negated_conjecture). [assumption].
% 7.01/7.28 4 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity_of_multiply) # label(axiom). [assumption].
% 7.01/7.28 5 multiply(A,multiply(B,multiply(C,multiply(B,A)))) = multiply(B,multiply(A,multiply(C,multiply(A,B)))) # label(nilpotency) # label(hypothesis). [assumption].
% 7.01/7.28 6 multiply(d,d0) != multiply(c,c0) # label(prove_quotient4) # label(negated_conjecture) # answer(prove_quotient4). [assumption].
% 7.01/7.28 7 multiply(A,B) != multiply(C,B) | A = C # label(right_cancellation) # label(axiom). [assumption].
% 7.01/7.28 8 multiply(A,B) != multiply(A,C) | B = C # label(left_cancellation) # label(axiom). [assumption].
% 7.01/7.28 9 multiply(d,d0) = c_0. [new_symbol(6)].
% 7.01/7.28 10 multiply(c,c0) != c_0 # answer(prove_quotient4). [back_rewrite(6),rewrite([9(3)]),flip(a)].
% 7.01/7.28 11 multiply(b,multiply(b0,A)) = multiply(a,multiply(a0,A)). [para(1(a,1),4(a,1,1)),rewrite([4(4)]),flip(a)].
% 7.01/7.28 12 multiply(d,multiply(b0,A)) = multiply(c,multiply(a0,A)). [para(2(a,1),4(a,1,1)),rewrite([4(4)]),flip(a)].
% 7.01/7.28 13 multiply(b,multiply(d0,A)) = multiply(a,multiply(c0,A)). [para(3(a,1),4(a,1,1)),rewrite([4(4)]),flip(a)].
% 7.01/7.28 19 multiply(A,multiply(B,multiply(C,multiply(D,multiply(C,B))))) = multiply(A,multiply(C,multiply(B,multiply(D,multiply(B,C))))). [para(5(a,1),4(a,2,2)),rewrite([4(5)])].
% 7.01/7.28 35 multiply(d,multiply(d0,A)) = multiply(c_0,A). [para(9(a,1),4(a,1,1)),flip(a)].
% 7.01/7.28 40 multiply(c,multiply(c0,A)) != multiply(c_0,A) # answer(prove_quotient4). [ur(7,b,10,a),rewrite([4(4)])].
% 7.01/7.28 46 multiply(a,multiply(a0,A)) != multiply(b,B) | multiply(b0,A) = B. [para(11(a,1),8(a,1))].
% 7.01/7.28 49 multiply(c,multiply(A,multiply(c0,multiply(B,multiply(c0,A))))) != multiply(c_0,multiply(A,multiply(B,multiply(A,c0)))) # answer(prove_quotient4). [para(5(a,1),40(a,1,2))].
% 7.01/7.28 868 multiply(a,multiply(c0,A)) != multiply(a,multiply(a0,B)) | multiply(d0,A) = multiply(b0,B). [para(13(a,1),46(a,2)),flip(a),flip(b)].
% 7.01/7.28 8632 multiply(d0,multiply(a0,multiply(A,multiply(a0,c0)))) = multiply(b0,multiply(c0,multiply(A,multiply(c0,a0)))). [hyper(868,a,19,a)].
% 7.01/7.28 15128 multiply(c,multiply(a0,multiply(c0,multiply(A,multiply(c0,a0))))) = multiply(c_0,multiply(a0,multiply(A,multiply(a0,c0)))). [para(8632(a,1),35(a,1,2)),rewrite([12(10)])].
% 7.01/7.28 15129 $F # answer(prove_quotient4). [resolve(15128,a,49,a)].
% 7.01/7.28
% 7.01/7.28 % SZS output end Refutation
% 7.01/7.28 ============================== end of proof ==========================
% 7.01/7.28
% 7.01/7.28 ============================== STATISTICS ============================
% 7.01/7.28
% 7.01/7.28 Given=852. Generated=50045. Kept=15128. proofs=1.
% 7.01/7.28 Usable=801. Sos=9999. Demods=541. Limbo=5, Disabled=4330. Hints=0.
% 7.01/7.28 Megabytes=23.41.
% 7.01/7.28 User_CPU=6.21, System_CPU=0.04, Wall_clock=6.
% 7.01/7.28
% 7.01/7.28 ============================== end of statistics =====================
% 7.01/7.28
% 7.01/7.28 ============================== end of search =========================
% 7.01/7.28
% 7.01/7.28 THEOREM PROVED
% 7.01/7.28 % SZS status Unsatisfiable
% 7.01/7.28
% 7.01/7.28 Exiting with 1 proof.
% 7.01/7.28
% 7.01/7.28 Process 3140 exit (max_proofs) Mon Jun 13 09:31:25 2022
% 7.01/7.28 Prover9 interrupted
%------------------------------------------------------------------------------