TSTP Solution File: GRP748+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP748+1 : TPTP v8.1.0. Released v4.0.0.
% 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 11:20:53 EDT 2022
% Result : Theorem 5.86s 6.17s
% Output : Refutation 5.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP748+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 21:47:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.70/1.00 ============================== Prover9 ===============================
% 0.70/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.70/1.00 Process 19683 was started by sandbox2 on n028.cluster.edu,
% 0.70/1.00 Mon Jun 13 21:47:09 2022
% 0.70/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19530_n028.cluster.edu".
% 0.70/1.00 ============================== end of head ===========================
% 0.70/1.00
% 0.70/1.00 ============================== INPUT =================================
% 0.70/1.00
% 0.70/1.00 % Reading from file /tmp/Prover9_19530_n028.cluster.edu
% 0.70/1.00
% 0.70/1.00 set(prolog_style_variables).
% 0.70/1.00 set(auto2).
% 0.70/1.00 % set(auto2) -> set(auto).
% 0.70/1.00 % set(auto) -> set(auto_inference).
% 0.70/1.00 % set(auto) -> set(auto_setup).
% 0.70/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.70/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.70/1.00 % set(auto) -> set(auto_limits).
% 0.70/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.70/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.70/1.00 % set(auto) -> set(auto_denials).
% 0.70/1.00 % set(auto) -> set(auto_process).
% 0.70/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.70/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.70/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.70/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.70/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.70/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.70/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.70/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.70/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.70/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.70/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.70/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.70/1.00 % set(auto2) -> assign(stats, some).
% 0.70/1.00 % set(auto2) -> clear(echo_input).
% 0.70/1.00 % set(auto2) -> set(quiet).
% 0.70/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.70/1.00 % set(auto2) -> clear(print_given).
% 0.70/1.00 assign(lrs_ticks,-1).
% 0.70/1.00 assign(sos_limit,10000).
% 0.70/1.00 assign(order,kbo).
% 0.70/1.00 set(lex_order_vars).
% 0.70/1.00 clear(print_given).
% 0.70/1.00
% 0.70/1.00 % formulas(sos). % not echoed (12 formulas)
% 0.70/1.00
% 0.70/1.00 ============================== end of input ==========================
% 0.70/1.00
% 0.70/1.00 % From the command line: assign(max_seconds, 300).
% 0.70/1.00
% 0.70/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.70/1.00
% 0.70/1.00 % Formulas that are not ordinary clauses:
% 0.70/1.00 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.00 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.00 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.00 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.00 5 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.00 6 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.00 7 (all C all B all A mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B))) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.00 8 (all B all A mult(mult(A,B),i(B)) = A) # label(f08) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.00 9 (all A mult(A,i(A)) = unit) # label(f09) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.00 10 (all A mult(i(A),A) = unit) # label(f10) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.00 11 (all B all A (mult(A,B) = mult(B,A) | mult(i(A),mult(A,B)) = B)) # label(f11) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.00 12 -((all X0 all X1 all X2 mult(X2,mult(X0,mult(X2,X1))) = mult(mult(mult(X2,X0),X2),X1)) | (all X3 all X4 all X5 mult(X3,mult(X5,mult(X4,X5))) = mult(mult(mult(X3,X5),X4),X5)) | (all X6 all X7 all X8 mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)) | (all X9 all X10 all X11 mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.70/1.00
% 0.70/1.00 ============================== end of process non-clausal formulas ===
% 0.70/1.00
% 0.70/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.70/1.00
% 0.70/1.00 ============================== PREDICATE ELIMINATION =================
% 0.70/1.00
% 0.70/1.00 ============================== end predicate elimination =============
% 0.70/1.00
% 0.70/1.00 Auto_denials: (non-Horn, no changes).
% 0.70/1.00
% 0.70/1.00 Term ordering decisions:
% 0.70/1.00
% 0.70/1.00 % Assigning unary symbol i kb_weight 0 and highest precedence (18).
% 5.86/6.17 Function symbol KB weights: unit=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. mult=1. ld=1. rd=1. i=0.
% 5.86/6.17
% 5.86/6.17 ============================== end of process initial clauses ========
% 5.86/6.17
% 5.86/6.17 ============================== CLAUSES FOR SEARCH ====================
% 5.86/6.17
% 5.86/6.17 ============================== end of clauses for search =============
% 5.86/6.17
% 5.86/6.17 ============================== SEARCH ================================
% 5.86/6.17
% 5.86/6.17 % Starting search at 0.01 seconds.
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=59.000, iters=3405
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=55.000, iters=3366
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=53.000, iters=3338
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=50.000, iters=3388
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=48.000, iters=3421
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=45.000, iters=3356
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=44.000, iters=3366
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=43.000, iters=3378
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=42.000, iters=3404
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=40.000, iters=3385
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=39.000, iters=3375
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=38.000, iters=3360
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=37.000, iters=3408
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=36.000, iters=3336
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=35.000, iters=3430
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=34.000, iters=3381
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=33.000, iters=3341
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=32.000, iters=3358
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=31.000, iters=3352
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=30.000, iters=3398
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=29.000, iters=3342
% 5.86/6.17
% 5.86/6.17 Low Water (displace): id=2386, wt=109.000
% 5.86/6.17
% 5.86/6.17 Low Water (displace): id=2384, wt=101.000
% 5.86/6.17
% 5.86/6.17 Low Water (displace): id=2385, wt=97.000
% 5.86/6.17
% 5.86/6.17 Low Water (displace): id=2318, wt=95.000
% 5.86/6.17
% 5.86/6.17 Low Water (displace): id=5618, wt=93.000
% 5.86/6.17
% 5.86/6.17 Low Water (displace): id=6142, wt=89.000
% 5.86/6.17
% 5.86/6.17 Low Water (displace): id=5094, wt=87.000
% 5.86/6.17
% 5.86/6.17 Low Water (displace): id=6138, wt=85.000
% 5.86/6.17
% 5.86/6.17 Low Water (displace): id=5147, wt=83.000
% 5.86/6.17
% 5.86/6.17 Low Water (displace): id=4429, wt=81.000
% 5.86/6.17
% 5.86/6.17 Low Water (displace): id=11640, wt=28.000
% 5.86/6.17
% 5.86/6.17 Low Water (displace): id=11694, wt=25.000
% 5.86/6.17
% 5.86/6.17 Low Water (displace): id=11903, wt=24.000
% 5.86/6.17
% 5.86/6.17 Low Water (displace): id=11911, wt=23.000
% 5.86/6.17
% 5.86/6.17 Low Water (displace): id=12076, wt=22.000
% 5.86/6.17
% 5.86/6.17 Low Water (displace): id=12078, wt=21.000
% 5.86/6.17
% 5.86/6.17 Low Water (keep): wt=28.000, iters=3341
% 5.86/6.17
% 5.86/6.17 ============================== PROOF =================================
% 5.86/6.17 % SZS status Theorem
% 5.86/6.17 % SZS output start Refutation
% 5.86/6.17
% 5.86/6.17 % Proof 1 at 5.14 (+ 0.04) seconds.
% 5.86/6.17 % Length of proof is 35.
% 5.86/6.17 % Level of proof is 10.
% 5.86/6.17 % Maximum clause weight is 16.000.
% 5.86/6.17 % Given clauses 227.
% 5.86/6.17
% 5.86/6.17 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 5.86/6.17 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 5.86/6.17 6 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 5.86/6.17 7 (all C all B all A mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B))) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 5.86/6.17 8 (all B all A mult(mult(A,B),i(B)) = A) # label(f08) # label(axiom) # label(non_clause). [assumption].
% 5.86/6.17 9 (all A mult(A,i(A)) = unit) # label(f09) # label(axiom) # label(non_clause). [assumption].
% 5.86/6.17 10 (all A mult(i(A),A) = unit) # label(f10) # label(axiom) # label(non_clause). [assumption].
% 5.86/6.17 11 (all B all A (mult(A,B) = mult(B,A) | mult(i(A),mult(A,B)) = B)) # label(f11) # label(axiom) # label(non_clause). [assumption].
% 5.86/6.17 12 -((all X0 all X1 all X2 mult(X2,mult(X0,mult(X2,X1))) = mult(mult(mult(X2,X0),X2),X1)) | (all X3 all X4 all X5 mult(X3,mult(X5,mult(X4,X5))) = mult(mult(mult(X3,X5),X4),X5)) | (all X6 all X7 all X8 mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)) | (all X9 all X10 all X11 mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 5.86/6.17 14 mult(unit,A) = A # label(f06) # label(axiom). [clausify(6)].
% 5.86/6.17 15 mult(A,i(A)) = unit # label(f09) # label(axiom). [clausify(9)].
% 5.86/6.17 16 mult(i(A),A) = unit # label(f10) # label(axiom). [clausify(10)].
% 5.86/6.17 17 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)].
% 5.86/6.17 18 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(2)].
% 5.86/6.17 21 mult(mult(A,B),i(B)) = A # label(f08) # label(axiom). [clausify(8)].
% 5.86/6.17 22 mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) # label(f07) # label(axiom). [clausify(7)].
% 5.86/6.17 23 mult(A,B) = mult(B,A) | mult(i(A),mult(A,B)) = B # label(f11) # label(axiom). [clausify(11)].
% 5.86/6.17 25 mult(mult(mult(c4,c6),c5),c6) != mult(c4,mult(c6,mult(c5,c6))) # label(goals) # label(negated_conjecture). [clausify(12)].
% 5.86/6.17 26 mult(c4,mult(mult(c6,c5),c6)) != mult(c4,mult(c6,mult(c5,c6))). [copy(25),rewrite([22(7)])].
% 5.86/6.17 32 ld(A,unit) = i(A). [para(15(a,1),18(a,1,2))].
% 5.86/6.17 33 i(i(A)) = A. [para(16(a,1),18(a,1,2)),rewrite([32(3)])].
% 5.86/6.17 45 mult(A,mult(mult(i(A),B),i(A))) = mult(B,i(A)). [para(15(a,1),22(a,1,1,1)),rewrite([14(2)]),flip(a)].
% 5.86/6.17 47 mult(i(A),mult(mult(A,B),A)) = mult(B,A). [para(16(a,1),22(a,1,1,1)),rewrite([14(2)]),flip(a)].
% 5.86/6.17 56 mult(ld(A,B),A) = B | ld(A,B) = mult(i(A),B). [para(17(a,1),23(b,1,2)),rewrite([17(2)]),flip(a),flip(b)].
% 5.86/6.17 136 mult(ld(A,B),A) = mult(i(A),mult(B,A)). [para(17(a,1),47(a,1,2,1)),flip(a)].
% 5.86/6.17 138 ld(i(A),mult(B,A)) = mult(mult(A,B),A). [para(47(a,1),18(a,1,2))].
% 5.86/6.17 152 mult(i(A),mult(B,A)) = B | ld(A,B) = mult(i(A),B). [back_rewrite(56),rewrite([136(2)])].
% 5.86/6.17 3550 ld(A,B) = mult(i(A),B) | mult(A,mult(B,i(A))) = B. [para(152(a,1),45(a,1,2,1)),rewrite([21(10)])].
% 5.86/6.17 3562 ld(A,B) = mult(i(A),B) | ld(A,B) = mult(B,i(A)). [para(152(a,1),138(a,2,1)),rewrite([33(6),21(7)])].
% 5.86/6.17 9506 mult(mult(A,B),i(A)) = B | mult(i(A),mult(A,B)) = B. [para(3562(a,1),18(a,1)),rewrite([18(2)]),flip(a)].
% 5.86/6.17 9712 ld(i(A),B) = mult(A,B) | ld(A,mult(B,A)) = B. [para(3550(b,1),3562(a,2)),rewrite([33(4),33(6),33(9),33(11),21(12)]),merge(c)].
% 5.86/6.17 11566 mult(i(A),mult(A,B)) = B | ld(i(A),B) = mult(A,B). [para(9506(a,1),9712(b,1,2)),rewrite([33(6),18(6)]),flip(b),merge(b)].
% 5.86/6.17 12427 ld(i(A),B) = mult(A,B). [para(11566(a,1),18(a,1,2)),merge(b)].
% 5.86/6.17 13352 mult(mult(A,B),A) = mult(A,mult(B,A)). [back_rewrite(138),rewrite([12427(3)]),flip(a)].
% 5.86/6.17 14551 $F. [back_rewrite(26),rewrite([13352(6)]),xx(a)].
% 5.86/6.17
% 5.86/6.17 % SZS output end Refutation
% 5.86/6.17 ============================== end of proof ==========================
% 5.86/6.17
% 5.86/6.17 ============================== STATISTICS ============================
% 5.86/6.17
% 5.86/6.17 Given=227. Generated=47353. Kept=14537. proofs=1.
% 5.86/6.17 Usable=143. Sos=5912. Demods=2669. Limbo=1199, Disabled=7298. Hints=0.
% 5.86/6.17 Megabytes=17.06.
% 5.86/6.17 User_CPU=5.14, System_CPU=0.04, Wall_clock=5.
% 5.86/6.17
% 5.86/6.17 ============================== end of statistics =====================
% 5.86/6.17
% 5.86/6.17 ============================== end of search =========================
% 5.86/6.17
% 5.86/6.17 THEOREM PROVED
% 5.86/6.17 % SZS status Theorem
% 5.86/6.17
% 5.86/6.17 Exiting with 1 proof.
% 5.86/6.17
% 5.86/6.17 Process 19683 exit (max_proofs) Mon Jun 13 21:47:14 2022
% 5.86/6.17 Prover9 interrupted
%------------------------------------------------------------------------------