TSTP Solution File: GRP682+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP682+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 11:20:34 EDT 2022
% Result : Theorem 0.72s 1.06s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP682+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n009.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 : Tue Jun 14 04:22:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.72/1.06 ============================== Prover9 ===============================
% 0.72/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.72/1.06 Process 10390 was started by sandbox2 on n009.cluster.edu,
% 0.72/1.06 Tue Jun 14 04:22:38 2022
% 0.72/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_10235_n009.cluster.edu".
% 0.72/1.06 ============================== end of head ===========================
% 0.72/1.06
% 0.72/1.06 ============================== INPUT =================================
% 0.72/1.06
% 0.72/1.06 % Reading from file /tmp/Prover9_10235_n009.cluster.edu
% 0.72/1.06
% 0.72/1.06 set(prolog_style_variables).
% 0.72/1.06 set(auto2).
% 0.72/1.06 % set(auto2) -> set(auto).
% 0.72/1.06 % set(auto) -> set(auto_inference).
% 0.72/1.06 % set(auto) -> set(auto_setup).
% 0.72/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.72/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/1.06 % set(auto) -> set(auto_limits).
% 0.72/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/1.06 % set(auto) -> set(auto_denials).
% 0.72/1.06 % set(auto) -> set(auto_process).
% 0.72/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.72/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.72/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.72/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.72/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.72/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.72/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.72/1.06 % set(auto2) -> assign(stats, some).
% 0.72/1.06 % set(auto2) -> clear(echo_input).
% 0.72/1.06 % set(auto2) -> set(quiet).
% 0.72/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.72/1.06 % set(auto2) -> clear(print_given).
% 0.72/1.06 assign(lrs_ticks,-1).
% 0.72/1.06 assign(sos_limit,10000).
% 0.72/1.06 assign(order,kbo).
% 0.72/1.06 set(lex_order_vars).
% 0.72/1.06 clear(print_given).
% 0.72/1.06
% 0.72/1.06 % formulas(sos). % not echoed (8 formulas)
% 0.72/1.06
% 0.72/1.06 ============================== end of input ==========================
% 0.72/1.06
% 0.72/1.06 % From the command line: assign(max_seconds, 300).
% 0.72/1.06
% 0.72/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/1.06
% 0.72/1.06 % Formulas that are not ordinary clauses:
% 0.72/1.06 1 (all A ld(A,mult(A,A)) = A) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 2 (all A rd(mult(A,A),A) = A) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 3 (all B all A mult(A,ld(A,B)) = ld(A,mult(A,B))) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 4 (all B all A mult(rd(A,B),B) = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 5 (all D all C all B all A ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D)) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 6 (all D all C all B all A rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D))) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 7 (all B all A ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B)) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 8 -(all X0 all X1 all X2 (ld(ld(X0,X1),mult(ld(X0,X1),X2)) = ld(X0,mult(X0,X2)) & ld(rd(X0,X1),mult(rd(X0,X1),X2)) = ld(X0,mult(X0,X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.72/1.06
% 0.72/1.06 ============================== end of process non-clausal formulas ===
% 0.72/1.06
% 0.72/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/1.06
% 0.72/1.06 ============================== PREDICATE ELIMINATION =================
% 0.72/1.06
% 0.72/1.06 ============================== end predicate elimination =============
% 0.72/1.06
% 0.72/1.06 Auto_denials:
% 0.72/1.06 % copying label goals to answer in negative clause
% 0.72/1.06
% 0.72/1.06 Term ordering decisions:
% 0.72/1.06 Function symbol KB weights: c1=1. c2=1. c3=1. mult=1. ld=1. rd=1.
% 0.72/1.06
% 0.72/1.06 ============================== end of process initial clauses ========
% 0.72/1.06
% 0.72/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.72/1.06
% 0.72/1.06 ============================== end of clauses for search =============
% 0.72/1.06
% 0.72/1.06 ============================== SEARCH ================================
% 0.72/1.06
% 0.72/1.06 % Starting search at 0.01 seconds.
% 0.72/1.06
% 0.72/1.06 ============================== PROOF =================================
% 0.72/1.06 % SZS status Theorem
% 0.72/1.06 % SZS output start Refutation
% 0.72/1.06
% 0.72/1.06 % Proof 1 at 0.09 (+ 0.01) seconds: goals.
% 0.72/1.06 % Length of proof is 47.
% 0.72/1.06 % Level of proof is 12.
% 0.72/1.06 % Maximum clause weight is 30.000.
% 0.72/1.06 % Given clauses 66.
% 0.72/1.06
% 0.72/1.06 1 (all A ld(A,mult(A,A)) = A) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 2 (all A rd(mult(A,A),A) = A) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 3 (all B all A mult(A,ld(A,B)) = ld(A,mult(A,B))) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 4 (all B all A mult(rd(A,B),B) = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 5 (all D all C all B all A ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D)) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 6 (all D all C all B all A rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D))) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 7 (all B all A ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B)) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 8 -(all X0 all X1 all X2 (ld(ld(X0,X1),mult(ld(X0,X1),X2)) = ld(X0,mult(X0,X2)) & ld(rd(X0,X1),mult(rd(X0,X1),X2)) = ld(X0,mult(X0,X2)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.72/1.06 9 ld(A,mult(A,A)) = A # label(f01) # label(axiom). [clausify(1)].
% 0.72/1.06 10 rd(mult(A,A),A) = A # label(f02) # label(axiom). [clausify(2)].
% 0.72/1.06 11 ld(A,mult(A,B)) = mult(A,ld(A,B)) # label(f03) # label(axiom). [clausify(3)].
% 0.72/1.06 12 rd(mult(A,B),B) = mult(rd(A,B),B) # label(f04) # label(axiom). [clausify(4)].
% 0.72/1.06 13 rd(mult(rd(A,A),B),B) = ld(A,mult(A,ld(B,B))) # label(f07) # label(axiom). [clausify(7)].
% 0.72/1.06 14 mult(rd(rd(A,A),B),B) = mult(A,ld(A,ld(B,B))). [copy(13),rewrite([12(3),11(6)])].
% 0.72/1.06 15 ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D) # label(f05) # label(axiom). [clausify(5)].
% 0.72/1.06 16 mult(ld(A,B),ld(ld(A,B),mult(C,D))) = mult(mult(A,ld(A,C)),D). [copy(15),rewrite([11(5),11(7)])].
% 0.72/1.06 17 rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)) # label(f06) # label(axiom). [clausify(6)].
% 0.72/1.06 18 mult(rd(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,mult(rd(B,D),D)). [copy(17),rewrite([12(5),12(7)])].
% 0.72/1.06 19 ld(ld(c1,c2),mult(ld(c1,c2),c3)) != ld(c1,mult(c1,c3)) | ld(rd(c1,c2),mult(rd(c1,c2),c3)) != ld(c1,mult(c1,c3)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(8)].
% 0.72/1.06 20 mult(ld(c1,c2),ld(ld(c1,c2),c3)) != mult(c1,ld(c1,c3)) | mult(rd(c1,c2),ld(rd(c1,c2),c3)) != mult(c1,ld(c1,c3)) # answer(goals). [copy(19),rewrite([11(9),11(14),11(24),11(29)])].
% 0.72/1.06 21 mult(A,ld(A,A)) = A. [back_rewrite(9),rewrite([11(2)])].
% 0.72/1.06 22 mult(rd(A,A),A) = A. [back_rewrite(10),rewrite([12(2)])].
% 0.72/1.06 26 mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),mult(C,D))) = mult(mult(A,ld(A,C)),D). [para(11(a,1),16(a,1,1)),rewrite([11(4)])].
% 0.72/1.06 39 mult(A,ld(A,ld(A,A))) = ld(A,A). [para(21(a,1),11(a,1,2)),flip(a)].
% 0.72/1.06 40 mult(rd(A,ld(A,A)),ld(A,A)) = rd(A,ld(A,A)). [para(21(a,1),12(a,1,1)),flip(a)].
% 0.72/1.06 42 mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,mult(rd(ld(A,A),C),C)). [para(21(a,1),18(a,1,1,1))].
% 0.72/1.06 44 rd(A,A) = ld(A,A). [para(22(a,1),12(a,1,1)),rewrite([14(4),39(4)])].
% 0.72/1.06 45 mult(ld(A,A),A) = A. [para(22(a,1),12(a,2)),rewrite([12(2),44(1)])].
% 0.72/1.06 46 mult(A,ld(A,ld(ld(A,A),ld(A,A)))) = ld(A,A). [para(22(a,1),14(a,1)),rewrite([44(1),44(2),44(3)]),flip(a)].
% 0.72/1.06 47 mult(ld(A,B),ld(ld(A,B),C)) = mult(mult(A,ld(A,ld(C,C))),C). [para(22(a,1),16(a,1,2,2)),rewrite([44(5)])].
% 0.72/1.06 54 mult(rd(ld(A,A),B),B) = mult(A,ld(A,ld(B,B))). [back_rewrite(14),rewrite([44(1)])].
% 0.72/1.06 55 mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,mult(A,ld(A,ld(C,C)))). [back_rewrite(42),rewrite([54(7)])].
% 0.72/1.06 82 mult(mult(A,ld(A,B)),C) = mult(A,ld(A,mult(B,C))). [para(21(a,1),26(a,1,1)),rewrite([21(2)]),flip(a)].
% 0.72/1.06 83 mult(A,ld(A,mult(B,ld(mult(A,ld(A,B)),C)))) = mult(A,ld(A,C)). [para(21(a,1),26(a,1,2,2)),rewrite([82(6),82(10),21(8)])].
% 0.72/1.06 84 mult(A,mult(A,ld(A,B))) = mult(A,B). [para(21(a,1),26(a,2,1)),rewrite([82(7),83(7),11(2)])].
% 0.72/1.06 86 mult(A,ld(A,mult(ld(A,A),B))) = mult(ld(A,A),B). [para(39(a,1),26(a,2,1)),rewrite([82(8),83(8)])].
% 0.72/1.06 103 mult(ld(A,B),ld(ld(A,B),C)) = mult(A,ld(A,C)). [back_rewrite(47),rewrite([82(8),45(6)])].
% 0.72/1.06 108 mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,ld(C,C)). [back_rewrite(55),rewrite([84(8)])].
% 0.72/1.06 111 mult(rd(c1,c2),ld(rd(c1,c2),c3)) != mult(c1,ld(c1,c3)) # answer(goals). [back_rewrite(20),rewrite([103(9)]),xx(a)].
% 0.72/1.06 140 mult(A,ld(A,mult(mult(A,B),C))) = mult(mult(A,B),C). [para(11(a,1),82(a,1,1,2)),rewrite([84(3)]),flip(a)].
% 0.72/1.06 152 ld(ld(A,A),ld(A,A)) = ld(A,A). [para(39(a,1),86(a,1,2,2)),rewrite([46(5),39(8)]),flip(a)].
% 0.72/1.06 208 mult(rd(A,ld(B,B)),ld(B,B)) = mult(A,ld(B,B)). [para(44(a,1),108(a,1,1,2)),rewrite([44(3)])].
% 0.72/1.06 217 rd(A,ld(A,A)) = A. [back_rewrite(40),rewrite([208(4),21(2)]),flip(a)].
% 0.72/1.06 260 mult(rd(A,B),B) = mult(A,ld(B,B)). [para(217(a,1),108(a,1,1,2)),rewrite([217(3),152(5)])].
% 0.72/1.06 304 mult(mult(A,B),ld(mult(A,B),C)) = mult(A,ld(A,C)). [para(11(a,1),83(a,1,2,2,2,1,2)),rewrite([84(4),140(6)])].
% 0.72/1.06 492 mult(rd(A,B),ld(rd(A,B),C)) = mult(A,ld(A,C)). [para(260(a,1),304(a,1,1)),rewrite([260(4),304(6)]),flip(a)].
% 0.72/1.06 493 $F # answer(goals). [resolve(492,a,111,a)].
% 0.72/1.06
% 0.72/1.06 % SZS output end Refutation
% 0.72/1.06 ============================== end of proof ==========================
% 0.72/1.06
% 0.72/1.06 ============================== STATISTICS ============================
% 0.72/1.06
% 0.72/1.06 Given=66. Generated=2212. Kept=480. proofs=1.
% 0.72/1.06 Usable=27. Sos=106. Demods=131. Limbo=0, Disabled=354. Hints=0.
% 0.72/1.06 Megabytes=0.60.
% 0.72/1.06 User_CPU=0.09, System_CPU=0.01, Wall_clock=0.
% 0.72/1.06
% 0.72/1.06 ============================== end of statistics =====================
% 0.72/1.06
% 0.72/1.06 ============================== end of search =========================
% 0.72/1.06
% 0.72/1.06 THEOREM PROVED
% 0.72/1.06 % SZS status Theorem
% 0.72/1.06
% 0.72/1.06 Exiting with 1 proof.
% 0.72/1.06
% 0.72/1.06 Process 10390 exit (max_proofs) Tue Jun 14 04:22:38 2022
% 0.72/1.06 Prover9 interrupted
%------------------------------------------------------------------------------