TSTP Solution File: GRP702+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP702+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 11:20:41 EDT 2022
% Result : Theorem 0.43s 1.01s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP702+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n007.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 Jun 13 12:11:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.01 ============================== Prover9 ===============================
% 0.43/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.01 Process 10968 was started by sandbox2 on n007.cluster.edu,
% 0.43/1.01 Mon Jun 13 12:11:54 2022
% 0.43/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_10586_n007.cluster.edu".
% 0.43/1.01 ============================== end of head ===========================
% 0.43/1.01
% 0.43/1.01 ============================== INPUT =================================
% 0.43/1.01
% 0.43/1.01 % Reading from file /tmp/Prover9_10586_n007.cluster.edu
% 0.43/1.01
% 0.43/1.01 set(prolog_style_variables).
% 0.43/1.01 set(auto2).
% 0.43/1.01 % set(auto2) -> set(auto).
% 0.43/1.01 % set(auto) -> set(auto_inference).
% 0.43/1.01 % set(auto) -> set(auto_setup).
% 0.43/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.01 % set(auto) -> set(auto_limits).
% 0.43/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.01 % set(auto) -> set(auto_denials).
% 0.43/1.01 % set(auto) -> set(auto_process).
% 0.43/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.01 % set(auto2) -> assign(stats, some).
% 0.43/1.01 % set(auto2) -> clear(echo_input).
% 0.43/1.01 % set(auto2) -> set(quiet).
% 0.43/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.01 % set(auto2) -> clear(print_given).
% 0.43/1.01 assign(lrs_ticks,-1).
% 0.43/1.01 assign(sos_limit,10000).
% 0.43/1.01 assign(order,kbo).
% 0.43/1.01 set(lex_order_vars).
% 0.43/1.01 clear(print_given).
% 0.43/1.01
% 0.43/1.01 % formulas(sos). % not echoed (14 formulas)
% 0.43/1.01
% 0.43/1.01 ============================== end of input ==========================
% 0.43/1.01
% 0.43/1.01 % From the command line: assign(max_seconds, 300).
% 0.43/1.01
% 0.43/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.01
% 0.43/1.01 % Formulas that are not ordinary clauses:
% 0.43/1.01 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 5 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 6 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 7 (all C all B all A mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C)) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 8 (all B all A mult(op_c,mult(A,B)) = mult(mult(op_c,A),B)) # label(f08) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 9 (all B all A mult(A,mult(B,op_c)) = mult(mult(A,B),op_c)) # label(f09) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 10 (all B all A mult(A,mult(op_c,B)) = mult(mult(A,op_c),B)) # label(f10) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 11 (all A op_d = ld(A,mult(op_c,A))) # label(f11) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 12 (all B all A op_e = mult(mult(rd(op_c,mult(A,B)),B),A)) # label(f12) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 13 (all B all A op_f = mult(A,mult(B,ld(mult(A,B),op_c)))) # label(f13) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 14 -(all X0 all X1 (mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1) & mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d) & mult(X0,mult(op_d,X1)) = mult(mult(X0,op_d),X1))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.01
% 0.43/1.01 ============================== end of process non-clausal formulas ===
% 0.43/1.01
% 0.43/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.01
% 0.43/1.01 ============================== PREDICATE ELIMINATION =================
% 0.43/1.01
% 0.43/1.01 ============================== end predicate elimination =============
% 0.43/1.01
% 0.43/1.01 Auto_denials:
% 0.43/1.01 % copying label goals to answer in negative clause
% 0.43/1.01
% 0.43/1.01 Term ordering decisions:
% 0.43/1.01 Function symbol KB weights: op_c=1. unit=1. op_d=1. op_e=1. op_f=1. c1=1. c2=1. mult=1. ld=1. rd=1.
% 0.43/1.01
% 0.43/1.01 ============================== end of process initial clauses ========
% 0.43/1.01
% 0.43/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.43/1.01
% 0.43/1.01 ============================== end of clauses for search =============
% 0.43/1.01
% 0.43/1.01 ============================== SEARCH ================================
% 0.43/1.01
% 0.43/1.01 % Starting search at 0.01 seconds.
% 0.43/1.01
% 0.43/1.01 ============================== PROOF =================================
% 0.43/1.01 % SZS status Theorem
% 0.43/1.01 % SZS output start Refutation
% 0.43/1.01
% 0.43/1.01 % Proof 1 at 0.02 (+ 0.00) seconds: goals.
% 0.43/1.01 % Length of proof is 20.
% 0.43/1.01 % Level of proof is 6.
% 0.43/1.01 % Maximum clause weight is 33.000.
% 0.43/1.01 % Given clauses 31.
% 0.43/1.01
% 0.43/1.01 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 5 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 6 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 8 (all B all A mult(op_c,mult(A,B)) = mult(mult(op_c,A),B)) # label(f08) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 9 (all B all A mult(A,mult(B,op_c)) = mult(mult(A,B),op_c)) # label(f09) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 11 (all A op_d = ld(A,mult(op_c,A))) # label(f11) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 14 -(all X0 all X1 (mult(op_d,mult(X0,X1)) = mult(mult(op_d,X0),X1) & mult(X0,mult(X1,op_d)) = mult(mult(X0,X1),op_d) & mult(X0,mult(op_d,X1)) = mult(mult(X0,op_d),X1))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.01 15 mult(A,unit) = A # label(f05) # label(axiom). [clausify(5)].
% 0.43/1.01 16 mult(unit,A) = A # label(f06) # label(axiom). [clausify(6)].
% 0.43/1.01 17 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)].
% 0.43/1.01 21 ld(A,mult(op_c,A)) = op_d # label(f11) # label(axiom). [clausify(11)].
% 0.43/1.01 22 mult(mult(op_c,A),B) = mult(op_c,mult(A,B)) # label(f08) # label(axiom). [clausify(8)].
% 0.43/1.01 23 mult(mult(A,B),op_c) = mult(A,mult(B,op_c)) # label(f09) # label(axiom). [clausify(9)].
% 0.43/1.01 28 mult(mult(op_d,c1),c2) != mult(op_d,mult(c1,c2)) | mult(mult(c1,c2),op_d) != mult(c1,mult(c2,op_d)) | mult(mult(c1,op_d),c2) != mult(c1,mult(op_d,c2)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(14)].
% 0.43/1.01 29 ld(unit,A) = A. [para(17(a,1),16(a,1)),flip(a)].
% 0.43/1.01 35 op_d = op_c. [para(15(a,1),21(a,1,2)),rewrite([29(3)]),flip(a)].
% 0.43/1.01 36 mult(op_c,A) = mult(A,op_c). [para(21(a,1),17(a,1,2)),rewrite([35(1)]),flip(a)].
% 0.43/1.01 38 mult(c1,mult(op_c,c2)) != mult(op_c,mult(c1,c2)) # answer(goals). [back_rewrite(28),rewrite([35(1),22(5),35(6),35(15),36(16,R),35(19),36(20,R),35(24),36(25,R),22(27),35(29)]),flip(b),flip(c),xx(a),merge(b)].
% 0.43/1.01 40 mult(op_c,mult(A,B)) = mult(A,mult(B,op_c)). [back_rewrite(23),rewrite([36(3,R)])].
% 0.43/1.01 91 $F # answer(goals). [para(40(a,1),38(a,2)),rewrite([36(9,R)]),xx(a)].
% 0.43/1.01
% 0.43/1.01 % SZS output end Refutation
% 0.43/1.01 ============================== end of proof ==========================
% 0.43/1.01
% 0.43/1.01 ============================== STATISTICS ============================
% 0.43/1.01
% 0.43/1.01 Given=31. Generated=264. Kept=76. proofs=1.
% 0.43/1.01 Usable=26. Sos=25. Demods=54. Limbo=4, Disabled=35. Hints=0.
% 0.43/1.01 Megabytes=0.12.
% 0.43/1.01 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.43/1.01
% 0.43/1.01 ============================== end of statistics =====================
% 0.43/1.01
% 0.43/1.01 ============================== end of search =========================
% 0.43/1.01
% 0.43/1.01 THEOREM PROVED
% 0.43/1.01 % SZS status Theorem
% 0.43/1.01
% 0.43/1.01 Exiting with 1 proof.
% 0.43/1.01
% 0.43/1.01 Process 10968 exit (max_proofs) Mon Jun 13 12:11:54 2022
% 0.43/1.01 Prover9 interrupted
%------------------------------------------------------------------------------