TSTP Solution File: RNG025-7 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG025-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 20:39:13 EDT 2022
% Result : Unsatisfiable 18.73s 19.01s
% Output : Refutation 18.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG025-7 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon May 30 06:16:06 EDT 2022
% 0.12/0.34 % CPUTime :
% 4.13/4.46 ============================== Prover9 ===============================
% 4.13/4.46 Prover9 (32) version 2009-11A, November 2009.
% 4.13/4.46 Process 5331 was started by sandbox on n024.cluster.edu,
% 4.13/4.46 Mon May 30 06:16:07 2022
% 4.13/4.46 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5178_n024.cluster.edu".
% 4.13/4.46 ============================== end of head ===========================
% 4.13/4.46
% 4.13/4.46 ============================== INPUT =================================
% 4.13/4.46
% 4.13/4.46 % Reading from file /tmp/Prover9_5178_n024.cluster.edu
% 4.13/4.46
% 4.13/4.46 set(prolog_style_variables).
% 4.13/4.46 set(auto2).
% 4.13/4.46 % set(auto2) -> set(auto).
% 4.13/4.46 % set(auto) -> set(auto_inference).
% 4.13/4.46 % set(auto) -> set(auto_setup).
% 4.13/4.46 % set(auto_setup) -> set(predicate_elim).
% 4.13/4.46 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.13/4.46 % set(auto) -> set(auto_limits).
% 4.13/4.46 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.13/4.46 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.13/4.46 % set(auto) -> set(auto_denials).
% 4.13/4.46 % set(auto) -> set(auto_process).
% 4.13/4.46 % set(auto2) -> assign(new_constants, 1).
% 4.13/4.46 % set(auto2) -> assign(fold_denial_max, 3).
% 4.13/4.46 % set(auto2) -> assign(max_weight, "200.000").
% 4.13/4.46 % set(auto2) -> assign(max_hours, 1).
% 4.13/4.46 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.13/4.46 % set(auto2) -> assign(max_seconds, 0).
% 4.13/4.46 % set(auto2) -> assign(max_minutes, 5).
% 4.13/4.46 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.13/4.46 % set(auto2) -> set(sort_initial_sos).
% 4.13/4.46 % set(auto2) -> assign(sos_limit, -1).
% 4.13/4.46 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.13/4.46 % set(auto2) -> assign(max_megs, 400).
% 4.13/4.46 % set(auto2) -> assign(stats, some).
% 4.13/4.46 % set(auto2) -> clear(echo_input).
% 4.13/4.46 % set(auto2) -> set(quiet).
% 4.13/4.46 % set(auto2) -> clear(print_initial_clauses).
% 4.13/4.46 % set(auto2) -> clear(print_given).
% 4.13/4.46 assign(lrs_ticks,-1).
% 4.13/4.46 assign(sos_limit,10000).
% 4.13/4.46 assign(order,kbo).
% 4.13/4.46 set(lex_order_vars).
% 4.13/4.46 clear(print_given).
% 4.13/4.46
% 4.13/4.46 % formulas(sos). % not echoed (23 formulas)
% 4.13/4.46
% 4.13/4.46 ============================== end of input ==========================
% 4.13/4.46
% 4.13/4.46 % From the command line: assign(max_seconds, 300).
% 4.13/4.46
% 4.13/4.46 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.13/4.46
% 4.13/4.46 % Formulas that are not ordinary clauses:
% 4.13/4.46
% 4.13/4.46 ============================== end of process non-clausal formulas ===
% 4.13/4.46
% 4.13/4.46 ============================== PROCESS INITIAL CLAUSES ===============
% 4.13/4.46
% 4.13/4.46 ============================== PREDICATE ELIMINATION =================
% 4.13/4.46
% 4.13/4.46 ============================== end predicate elimination =============
% 4.13/4.46
% 4.13/4.46 Auto_denials:
% 4.13/4.46 % copying label prove_flexible_law to answer in negative clause
% 4.13/4.46
% 4.13/4.46 Term ordering decisions:
% 4.13/4.46
% 4.13/4.46 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (9).
% 4.13/4.46 Function symbol KB weights: additive_identity=1. x=1. y=1. multiply=1. add=1. commutator=1. associator=1. additive_inverse=0.
% 4.13/4.46
% 4.13/4.46 ============================== end of process initial clauses ========
% 4.13/4.46
% 4.13/4.46 ============================== CLAUSES FOR SEARCH ====================
% 4.13/4.46
% 4.13/4.46 ============================== end of clauses for search =============
% 4.13/4.46
% 4.13/4.46 ============================== SEARCH ================================
% 4.13/4.46
% 4.13/4.46 % Starting search at 0.01 seconds.
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=67.000, iters=3352
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=63.000, iters=3366
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=53.000, iters=3333
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=51.000, iters=3401
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=49.000, iters=3360
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=47.000, iters=3337
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=46.000, iters=3349
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=44.000, iters=3376
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=43.000, iters=3340
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=42.000, iters=3447
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=41.000, iters=3388
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=39.000, iters=3340
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=38.000, iters=3355
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=37.000, iters=3384
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=36.000, iters=3352
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=35.000, iters=3340
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=34.000, iters=3370
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=33.000, iters=3430
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=32.000, iters=3364
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=31.000, iters=3399
% 4.13/4.46
% 4.13/4.46 Low Water (keep): wt=30.000, iters=3374
% 4.13/4.46
% 4.13/4.46 Low Water (displace): id=6327, wt=103.000
% 4.13/4.46
% 4.13/4.46 Low Water (displace): id=6333, wt=101.000
% 4.13/4.46
% 4.13/4.46 Low Water (displace): id=6340, wt=85.000
% 4.13/4.46
% 4.13/4.46 Low Water (displace): id=6338, wt=83.000
% 4.13/4.46
% 4.13/4.46 Low Water (displace): id=4573, wt=80.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=6310, wt=79.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=4570, wt=77.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=4572, wt=73.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=6346, wt=71.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=4569, wt=70.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=6313, wt=67.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=12365, wt=29.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=12375, wt=23.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=12871, wt=22.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=14779, wt=21.000
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=29.000, iters=3333
% 18.73/19.01
% 18.73/19.01 ============================== PROOF =================================
% 18.73/19.01 % SZS status Unsatisfiable
% 18.73/19.01 % SZS output start Refutation
% 18.73/19.01
% 18.73/19.01 % Proof 1 at 17.82 (+ 0.21) seconds: prove_flexible_law.
% 18.73/19.01 % Length of proof is 42.
% 18.73/19.01 % Level of proof is 9.
% 18.73/19.01 % Maximum clause weight is 21.000.
% 18.73/19.01 % Given clauses 386.
% 18.73/19.01
% 18.73/19.01 2 add(A,additive_identity) = A # label(right_additive_identity) # label(axiom). [assumption].
% 18.73/19.01 4 multiply(A,additive_identity) = additive_identity # label(right_multiplicative_zero) # label(axiom). [assumption].
% 18.73/19.01 5 additive_inverse(additive_inverse(A)) = A # label(additive_inverse_additive_inverse) # label(axiom). [assumption].
% 18.73/19.01 7 add(A,additive_inverse(A)) = additive_identity # label(right_additive_inverse) # label(axiom). [assumption].
% 18.73/19.01 8 add(A,B) = add(B,A) # label(commutativity_for_addition) # label(axiom). [assumption].
% 18.73/19.01 10 multiply(additive_inverse(A),B) = additive_inverse(multiply(A,B)) # label(inverse_product1) # label(axiom). [assumption].
% 18.73/19.01 11 additive_inverse(multiply(A,B)) = multiply(additive_inverse(A),B). [copy(10),flip(a)].
% 18.73/19.01 12 multiply(A,additive_inverse(B)) = additive_inverse(multiply(A,B)) # label(inverse_product2) # label(axiom). [assumption].
% 18.73/19.01 13 multiply(additive_inverse(A),B) = multiply(A,additive_inverse(B)). [copy(12),rewrite([11(4)]),flip(a)].
% 18.73/19.01 14 add(A,add(B,C)) = add(add(A,B),C) # label(associativity_for_addition) # label(axiom). [assumption].
% 18.73/19.01 15 add(A,add(B,C)) = add(C,add(A,B)). [copy(14),rewrite([8(4)])].
% 18.73/19.01 16 multiply(multiply(A,B),B) = multiply(A,multiply(B,B)) # label(right_alternative) # label(axiom). [assumption].
% 18.73/19.01 17 multiply(multiply(A,A),B) = multiply(A,multiply(A,B)) # label(left_alternative) # label(axiom). [assumption].
% 18.73/19.01 20 multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)) # label(distribute1) # label(axiom). [assumption].
% 18.73/19.01 21 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [copy(20),flip(a)].
% 18.73/19.01 22 multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)) # label(distribute2) # label(axiom). [assumption].
% 18.73/19.01 23 add(multiply(A,B),multiply(C,B)) = multiply(add(A,C),B). [copy(22),flip(a)].
% 18.73/19.01 25 multiply(add(A,additive_inverse(B)),C) = add(multiply(A,C),additive_inverse(multiply(B,C))) # label(distributivity_of_difference2) # label(axiom). [assumption].
% 18.73/19.01 26 add(multiply(A,B),multiply(C,additive_inverse(B))) = multiply(add(A,additive_inverse(C)),B). [copy(25),rewrite([11(6),13(6)]),flip(a)].
% 18.73/19.01 27 multiply(additive_inverse(A),add(B,C)) = add(additive_inverse(multiply(A,B)),additive_inverse(multiply(A,C))) # label(distributivity_of_difference3) # label(axiom). [assumption].
% 18.73/19.01 28 multiply(A,additive_inverse(add(B,C))) = multiply(A,add(additive_inverse(B),additive_inverse(C))). [copy(27),rewrite([13(3),11(5),13(5),11(7),13(7),21(8)])].
% 18.73/19.01 30 associator(A,B,C) = add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C)))) # label(associator) # label(axiom). [assumption].
% 18.73/19.01 31 associator(A,B,C) = add(multiply(A,multiply(B,additive_inverse(C))),multiply(multiply(A,B),C)). [copy(30),rewrite([11(6),13(6),11(5),13(5),8(7)])].
% 18.73/19.01 32 associator(x,y,x) != additive_identity # label(prove_flexible_law) # label(negated_conjecture) # answer(prove_flexible_law). [assumption].
% 18.73/19.01 33 add(multiply(x,multiply(y,additive_inverse(x))),multiply(multiply(x,y),x)) != additive_identity # answer(prove_flexible_law). [copy(32),rewrite([31(4)])].
% 18.73/19.01 34 additive_inverse(multiply(A,B)) = multiply(A,additive_inverse(B)). [back_rewrite(11),rewrite([13(4)])].
% 18.73/19.01 36 add(A,add(B,additive_inverse(A))) = B. [para(7(a,1),15(a,2,2)),rewrite([8(2),2(5)])].
% 18.73/19.01 45 add(multiply(A,additive_inverse(B)),multiply(C,B)) = multiply(add(C,additive_inverse(A)),B). [para(13(a,1),23(a,1,1)),rewrite([8(6)])].
% 18.73/19.01 46 add(multiply(A,multiply(B,B)),multiply(C,B)) = multiply(add(C,multiply(A,B)),B). [para(16(a,1),23(a,1,1)),rewrite([8(6)])].
% 18.73/19.01 54 multiply(add(additive_inverse(A),additive_inverse(B)),C) = multiply(add(A,B),additive_inverse(C)). [para(13(a,1),26(a,1,1)),rewrite([23(5)]),flip(a)].
% 18.73/19.01 61 multiply(A,add(B,additive_inverse(add(C,D)))) = multiply(A,add(B,add(additive_inverse(C),additive_inverse(D)))). [para(28(a,1),21(a,1,1)),rewrite([21(6),8(4),8(8)]),flip(a)].
% 18.73/19.01 66 multiply(multiply(A,additive_inverse(B)),C) = multiply(multiply(A,B),additive_inverse(C)). [para(34(a,1),13(a,1,1))].
% 18.73/19.01 67 multiply(multiply(A,B),additive_inverse(B)) = multiply(A,multiply(B,additive_inverse(B))). [para(16(a,1),34(a,1,1)),rewrite([34(3),34(2)]),flip(a)].
% 18.73/19.01 144 add(multiply(A,multiply(B,additive_inverse(B))),multiply(multiply(A,B),C)) = multiply(multiply(A,B),add(C,additive_inverse(B))). [para(67(a,1),21(a,1,1)),rewrite([8(9)])].
% 18.73/19.01 205 multiply(add(A,additive_inverse(add(B,C))),D) = multiply(add(A,add(additive_inverse(B),additive_inverse(C))),D). [para(54(a,1),23(a,1,1)),rewrite([45(5),8(8)])].
% 18.73/19.01 207 multiply(add(A,add(additive_inverse(A),additive_inverse(B))),C) = multiply(B,additive_inverse(C)). [para(36(a,1),54(a,2,1)),rewrite([205(6),5(4),8(3),15(4,R),8(3)])].
% 18.73/19.01 1034 add(multiply(A,multiply(B,B)),multiply(C,multiply(C,B))) = multiply(add(multiply(C,C),multiply(A,B)),B). [para(17(a,1),46(a,1,2))].
% 18.73/19.01 3363 multiply(A,add(B,add(additive_inverse(B),additive_inverse(C)))) = multiply(A,additive_inverse(C)). [para(36(a,1),61(a,2,2)),rewrite([8(1),61(4)])].
% 18.73/19.01 18595 multiply(multiply(A,add(A,B)),B) = multiply(A,multiply(add(A,B),B)). [para(1034(a,1),21(a,1)),rewrite([21(3),23(6),8(4)])].
% 18.73/19.01 18700 multiply(multiply(A,B),add(A,B)) = multiply(A,multiply(B,add(A,B))). [para(207(a,1),18595(a,2,2)),rewrite([3363(5),66(6),28(6),5(3),5(3),28(8),5(5),5(5)])].
% 18.73/19.01 18864 multiply(multiply(A,B),A) = multiply(A,multiply(B,A)). [para(18700(a,1),144(a,1,2)),rewrite([21(7),21(5),15(3),8(2),36(3),8(6),15(6),8(5),36(6)]),flip(a)].
% 18.73/19.01 18880 $F # answer(prove_flexible_law). [back_rewrite(33),rewrite([18864(11),8(12),21(12),21(9),7(6),4(4),4(3)]),xx(a)].
% 18.73/19.01
% 18.73/19.01 % SZS output end Refutation
% 18.73/19.01 ============================== end of proof ==========================
% 18.73/19.01
% 18.73/19.01 ============================== STATISTICS ============================
% 18.73/19.01
% 18.73/19.01 Given=386. Generated=318405. Kept=18867. proofs=1.
% 18.73/19.01 Usable=339. Sos=9997. Demods=3032. Limbo=16, Disabled=8538. Hints=0.
% 18.73/19.01 Megabytes=21.18.
% 18.73/19.01 User_CPU=17.82, System_CPU=0.21, Wall_clock=18.
% 18.73/19.01
% 18.73/19.01 ============================== end of statistics =====================
% 18.73/19.01
% 18.73/19.01 ============================== end of search =========================
% 18.73/19.01
% 18.73/19.01 THEOREM PROVED
% 18.73/19.01 % SZS status Unsatisfiable
% 18.73/19.01
% 18.73/19.01 Exiting with 1 proof.
% 18.73/19.01
% 18.73/19.01 Process 5331 exit (max_proofs) Mon May 30 06:16:25 2022
% 18.73/19.01 Prover9 interrupted
%------------------------------------------------------------------------------