TSTP Solution File: RNG008-3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG008-3 : 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 20:39:10 EDT 2022
% Result : Unsatisfiable 0.66s 0.98s
% Output : Refutation 0.66s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG008-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.32 % Computer : n024.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Mon May 30 18:45:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.66/0.98 ============================== Prover9 ===============================
% 0.66/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.66/0.98 Process 24127 was started by sandbox2 on n024.cluster.edu,
% 0.66/0.98 Mon May 30 18:45:22 2022
% 0.66/0.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_23974_n024.cluster.edu".
% 0.66/0.98 ============================== end of head ===========================
% 0.66/0.98
% 0.66/0.98 ============================== INPUT =================================
% 0.66/0.98
% 0.66/0.98 % Reading from file /tmp/Prover9_23974_n024.cluster.edu
% 0.66/0.98
% 0.66/0.98 set(prolog_style_variables).
% 0.66/0.98 set(auto2).
% 0.66/0.98 % set(auto2) -> set(auto).
% 0.66/0.98 % set(auto) -> set(auto_inference).
% 0.66/0.98 % set(auto) -> set(auto_setup).
% 0.66/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.66/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.66/0.98 % set(auto) -> set(auto_limits).
% 0.66/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.66/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.66/0.98 % set(auto) -> set(auto_denials).
% 0.66/0.98 % set(auto) -> set(auto_process).
% 0.66/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.66/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.66/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.66/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.66/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.66/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.66/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.66/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.66/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.66/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.66/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.66/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.66/0.98 % set(auto2) -> assign(stats, some).
% 0.66/0.98 % set(auto2) -> clear(echo_input).
% 0.66/0.98 % set(auto2) -> set(quiet).
% 0.66/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.66/0.98 % set(auto2) -> clear(print_given).
% 0.66/0.98 assign(lrs_ticks,-1).
% 0.66/0.98 assign(sos_limit,10000).
% 0.66/0.98 assign(order,kbo).
% 0.66/0.98 set(lex_order_vars).
% 0.66/0.98 clear(print_given).
% 0.66/0.98
% 0.66/0.98 % formulas(sos). % not echoed (19 formulas)
% 0.66/0.98
% 0.66/0.98 ============================== end of input ==========================
% 0.66/0.98
% 0.66/0.98 % From the command line: assign(max_seconds, 300).
% 0.66/0.98
% 0.66/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.66/0.98
% 0.66/0.98 % Formulas that are not ordinary clauses:
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% 0.66/0.98 ============================== end of process non-clausal formulas ===
% 0.66/0.98
% 0.66/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.66/0.98
% 0.66/0.98 ============================== PREDICATE ELIMINATION =================
% 0.66/0.98
% 0.66/0.98 ============================== end predicate elimination =============
% 0.66/0.98
% 0.66/0.98 Auto_denials:
% 0.66/0.98 % copying label prove_commutativity to answer in negative clause
% 0.66/0.98
% 0.66/0.98 Term ordering decisions:
% 0.66/0.98
% 0.66/0.98 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (8).
% 0.66/0.98 Function symbol KB weights: additive_identity=1. a=1. b=1. c=1. multiply=1. add=1. additive_inverse=0.
% 0.66/0.98
% 0.66/0.98 ============================== end of process initial clauses ========
% 0.66/0.98
% 0.66/0.98 ============================== CLAUSES FOR SEARCH ====================
% 0.66/0.98
% 0.66/0.98 ============================== end of clauses for search =============
% 0.66/0.98
% 0.66/0.98 ============================== SEARCH ================================
% 0.66/0.98
% 0.66/0.98 % Starting search at 0.01 seconds.
% 0.66/0.98
% 0.66/0.98 ============================== PROOF =================================
% 0.66/0.98 % SZS status Unsatisfiable
% 0.66/0.98 % SZS output start Refutation
% 0.66/0.98
% 0.66/0.98 % Proof 1 at 0.03 (+ 0.00) seconds: prove_commutativity.
% 0.66/0.98 % Length of proof is 35.
% 0.66/0.98 % Level of proof is 9.
% 0.66/0.98 % Maximum clause weight is 13.000.
% 0.66/0.98 % Given clauses 40.
% 0.66/0.98
% 0.66/0.98 3 additive_inverse(additive_inverse(A)) = A # label(additive_inverse_additive_inverse) # label(axiom). [assumption].
% 0.66/0.98 4 multiply(A,additive_identity) = additive_identity # label(multiply_additive_id1) # label(axiom). [assumption].
% 0.66/0.98 5 multiply(additive_identity,A) = additive_identity # label(multiply_additive_id2) # label(axiom). [assumption].
% 0.66/0.98 6 add(A,additive_identity) = A # label(right_identity) # label(axiom). [assumption].
% 0.66/0.98 7 multiply(A,A) = A # label(boolean_ring) # label(hypothesis). [assumption].
% 0.66/0.98 8 multiply(a,b) = c # label(a_times_b_is_c) # label(negated_conjecture). [assumption].
% 0.66/0.98 9 c = multiply(a,b). [copy(8),flip(a)].
% 0.66/0.98 11 add(A,additive_inverse(A)) = additive_identity # label(right_inverse) # label(axiom). [assumption].
% 0.66/0.98 12 add(A,B) = add(B,A) # label(commutative_addition) # label(axiom). [assumption].
% 0.66/0.98 13 multiply(A,additive_inverse(B)) = additive_inverse(multiply(A,B)) # label(multiply_additive_inverse1) # label(axiom). [assumption].
% 0.66/0.98 14 additive_inverse(multiply(A,B)) = multiply(A,additive_inverse(B)). [copy(13),flip(a)].
% 0.66/0.98 15 multiply(additive_inverse(A),B) = additive_inverse(multiply(A,B)) # label(multiply_additive_inverse2) # label(axiom). [assumption].
% 0.66/0.98 16 multiply(additive_inverse(A),B) = multiply(A,additive_inverse(B)). [copy(15),rewrite([14(4)])].
% 0.66/0.98 18 add(add(A,B),C) = add(A,add(B,C)) # label(associative_addition) # label(axiom). [assumption].
% 0.66/0.98 19 add(A,add(B,C)) = add(C,add(A,B)). [copy(18),rewrite([12(2)]),flip(a)].
% 0.66/0.98 21 multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)) # label(distribute1) # label(axiom). [assumption].
% 0.66/0.98 22 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [copy(21),flip(a)].
% 0.66/0.98 23 multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)) # label(distribute2) # label(axiom). [assumption].
% 0.66/0.98 24 add(multiply(A,B),multiply(C,B)) = multiply(add(A,C),B). [copy(23),flip(a)].
% 0.66/0.98 25 multiply(b,a) != c # label(prove_commutativity) # label(negated_conjecture) # answer(prove_commutativity). [assumption].
% 0.66/0.98 26 multiply(b,a) != multiply(a,b) # answer(prove_commutativity). [copy(25),rewrite([9(4)])].
% 0.66/0.98 27 multiply(b,a) = c_0. [new_symbol(26)].
% 0.66/0.98 28 multiply(a,b) != c_0 # answer(prove_commutativity). [back_rewrite(26),rewrite([27(3)]),flip(a)].
% 0.66/0.98 29 multiply(A,additive_inverse(A)) = additive_inverse(A). [para(7(a,1),14(a,1,1)),flip(a)].
% 0.66/0.98 30 additive_inverse(A) = A. [para(7(a,1),14(a,2)),rewrite([16(2),29(2),3(2)]),flip(a)].
% 0.66/0.98 32 add(A,A) = additive_identity. [back_rewrite(11),rewrite([30(1)])].
% 0.66/0.98 35 add(additive_identity,multiply(A,B)) = multiply(A,B). [para(4(a,1),22(a,1,1)),rewrite([12(5),6(5)])].
% 0.66/0.98 36 add(A,multiply(A,B)) = multiply(A,add(A,B)). [para(7(a,1),22(a,1,1))].
% 0.66/0.98 37 add(A,multiply(B,A)) = multiply(add(A,B),A). [para(7(a,1),24(a,1,1))].
% 0.66/0.98 43 add(A,add(A,B)) = B. [para(32(a,1),19(a,2,2)),rewrite([6(4)])].
% 0.66/0.98 86 multiply(add(a,b),a) = add(a,c_0). [para(27(a,1),37(a,1,2)),flip(a)].
% 0.66/0.98 102 multiply(add(a,b),b) = add(b,c_0). [para(86(a,1),36(a,1,2)),rewrite([19(7),12(6),43(6),12(3),12(11),43(11)]),flip(a)].
% 0.66/0.98 159 multiply(add(additive_identity,a),b) = c_0. [para(102(a,1),37(a,1,2)),rewrite([43(5),19(6,R),32(5),12(4)]),flip(a)].
% 0.66/0.98 166 multiply(a,b) = c_0. [para(159(a,1),24(a,2)),rewrite([5(3),35(5)])].
% 0.66/0.98 167 $F # answer(prove_commutativity). [resolve(166,a,28,a)].
% 0.66/0.98
% 0.66/0.98 % SZS output end Refutation
% 0.66/0.98 ============================== end of proof ==========================
% 0.66/0.98
% 0.66/0.98 ============================== STATISTICS ============================
% 0.66/0.98
% 0.66/0.98 Given=40. Generated=718. Kept=159. proofs=1.
% 0.66/0.98 Usable=36. Sos=104. Demods=135. Limbo=3, Disabled=34. Hints=0.
% 0.66/0.98 Megabytes=0.18.
% 0.66/0.98 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.66/0.98
% 0.66/0.98 ============================== end of statistics =====================
% 0.66/0.98
% 0.66/0.98 ============================== end of search =========================
% 0.66/0.98
% 0.66/0.98 THEOREM PROVED
% 0.66/0.98 % SZS status Unsatisfiable
% 0.66/0.98
% 0.66/0.98 Exiting with 1 proof.
% 0.66/0.98
% 0.66/0.98 Process 24127 exit (max_proofs) Mon May 30 18:45:22 2022
% 0.66/0.98 Prover9 interrupted
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