TSTP Solution File: RNG008-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG008-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 0.44s 1.00s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG008-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n018.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 12:25:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.44/1.00 ============================== Prover9 ===============================
% 0.44/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.00 Process 4013 was started by sandbox2 on n018.cluster.edu,
% 0.44/1.00 Mon May 30 12:25:27 2022
% 0.44/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3860_n018.cluster.edu".
% 0.44/1.00 ============================== end of head ===========================
% 0.44/1.00
% 0.44/1.00 ============================== INPUT =================================
% 0.44/1.00
% 0.44/1.00 % Reading from file /tmp/Prover9_3860_n018.cluster.edu
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% 0.44/1.00 set(prolog_style_variables).
% 0.44/1.00 set(auto2).
% 0.44/1.00 % set(auto2) -> set(auto).
% 0.44/1.00 % set(auto) -> set(auto_inference).
% 0.44/1.00 % set(auto) -> set(auto_setup).
% 0.44/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.00 % set(auto) -> set(auto_limits).
% 0.44/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.00 % set(auto) -> set(auto_denials).
% 0.44/1.00 % set(auto) -> set(auto_process).
% 0.44/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.00 % set(auto2) -> assign(stats, some).
% 0.44/1.00 % set(auto2) -> clear(echo_input).
% 0.44/1.00 % set(auto2) -> set(quiet).
% 0.44/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.00 % set(auto2) -> clear(print_given).
% 0.44/1.00 assign(lrs_ticks,-1).
% 0.44/1.00 assign(sos_limit,10000).
% 0.44/1.00 assign(order,kbo).
% 0.44/1.00 set(lex_order_vars).
% 0.44/1.00 clear(print_given).
% 0.44/1.00
% 0.44/1.00 % formulas(sos). % not echoed (17 formulas)
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% 0.44/1.00 ============================== end of input ==========================
% 0.44/1.00
% 0.44/1.00 % From the command line: assign(max_seconds, 300).
% 0.44/1.00
% 0.44/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.00
% 0.44/1.00 % Formulas that are not ordinary clauses:
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% 0.44/1.00 ============================== end of process non-clausal formulas ===
% 0.44/1.00
% 0.44/1.00 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.44/1.00 ============================== PREDICATE ELIMINATION =================
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% 0.44/1.00 ============================== end predicate elimination =============
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% 0.44/1.00 Auto_denials:
% 0.44/1.00 % copying label prove_commutativity to answer in negative clause
% 0.44/1.00
% 0.44/1.00 Term ordering decisions:
% 0.44/1.00
% 0.44/1.00 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (8).
% 0.44/1.00 Function symbol KB weights: additive_identity=1. a=1. b=1. c=1. multiply=1. add=1. additive_inverse=0.
% 0.44/1.00
% 0.44/1.00 ============================== end of process initial clauses ========
% 0.44/1.00
% 0.44/1.00 ============================== CLAUSES FOR SEARCH ====================
% 0.44/1.00
% 0.44/1.00 ============================== end of clauses for search =============
% 0.44/1.00
% 0.44/1.00 ============================== SEARCH ================================
% 0.44/1.00
% 0.44/1.00 % Starting search at 0.01 seconds.
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% 0.44/1.00 ============================== PROOF =================================
% 0.44/1.00 % SZS status Unsatisfiable
% 0.44/1.00 % SZS output start Refutation
% 0.44/1.00
% 0.44/1.00 % Proof 1 at 0.03 (+ 0.00) seconds: prove_commutativity.
% 0.44/1.00 % Length of proof is 37.
% 0.44/1.00 % Level of proof is 9.
% 0.44/1.00 % Maximum clause weight is 13.000.
% 0.44/1.00 % Given clauses 39.
% 0.44/1.00
% 0.44/1.00 2 add(additive_identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 0.44/1.00 3 additive_inverse(additive_inverse(A)) = A # label(additive_inverse_additive_inverse) # label(axiom). [assumption].
% 0.44/1.00 4 multiply(A,additive_identity) = additive_identity # label(multiply_additive_id1) # label(axiom). [assumption].
% 0.44/1.00 5 multiply(additive_identity,A) = additive_identity # label(multiply_additive_id2) # label(axiom). [assumption].
% 0.44/1.00 6 multiply(A,A) = A # label(boolean_ring) # label(hypothesis). [assumption].
% 0.44/1.00 7 multiply(a,b) = c # label(a_times_b_is_c) # label(negated_conjecture). [assumption].
% 0.44/1.00 8 c = multiply(a,b). [copy(7),flip(a)].
% 0.44/1.00 9 add(additive_inverse(A),A) = additive_identity # label(left_additive_inverse) # label(axiom). [assumption].
% 0.44/1.00 10 add(A,B) = add(B,A) # label(commutative_addition) # label(axiom). [assumption].
% 0.44/1.00 11 multiply(A,additive_inverse(B)) = additive_inverse(multiply(A,B)) # label(multiply_additive_inverse1) # label(axiom). [assumption].
% 0.44/1.00 12 additive_inverse(multiply(A,B)) = multiply(A,additive_inverse(B)). [copy(11),flip(a)].
% 0.44/1.00 13 multiply(additive_inverse(A),B) = additive_inverse(multiply(A,B)) # label(multiply_additive_inverse2) # label(axiom). [assumption].
% 0.44/1.00 14 multiply(additive_inverse(A),B) = multiply(A,additive_inverse(B)). [copy(13),rewrite([12(4)])].
% 0.44/1.00 16 add(add(A,B),C) = add(A,add(B,C)) # label(associative_addition) # label(axiom). [assumption].
% 0.44/1.00 17 add(A,add(B,C)) = add(C,add(A,B)). [copy(16),rewrite([10(2)]),flip(a)].
% 0.44/1.00 19 multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)) # label(distribute1) # label(axiom). [assumption].
% 0.44/1.00 20 add(multiply(A,B),multiply(A,C)) = multiply(A,add(B,C)). [copy(19),flip(a)].
% 0.44/1.00 21 multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)) # label(distribute2) # label(axiom). [assumption].
% 0.44/1.00 22 add(multiply(A,B),multiply(C,B)) = multiply(add(A,C),B). [copy(21),flip(a)].
% 0.44/1.00 23 multiply(b,a) != c # label(prove_commutativity) # label(negated_conjecture) # answer(prove_commutativity). [assumption].
% 0.44/1.00 24 multiply(b,a) != multiply(a,b) # answer(prove_commutativity). [copy(23),rewrite([8(4)])].
% 0.44/1.00 25 add(A,additive_inverse(A)) = additive_identity. [back_rewrite(9),rewrite([10(2)])].
% 0.44/1.00 26 add(A,additive_identity) = A. [back_rewrite(2),rewrite([10(2)])].
% 0.44/1.00 27 multiply(b,a) = c_0. [new_symbol(24)].
% 0.44/1.00 28 multiply(a,b) != c_0 # answer(prove_commutativity). [back_rewrite(24),rewrite([27(3)]),flip(a)].
% 0.44/1.00 29 multiply(A,additive_inverse(A)) = additive_inverse(A). [para(6(a,1),12(a,1,1)),flip(a)].
% 0.44/1.00 30 additive_inverse(A) = A. [para(6(a,1),12(a,2)),rewrite([14(2),29(2),3(2)]),flip(a)].
% 0.44/1.00 31 add(A,A) = additive_identity. [back_rewrite(25),rewrite([30(1)])].
% 0.44/1.00 34 add(additive_identity,multiply(A,B)) = multiply(A,B). [para(4(a,1),20(a,1,1)),rewrite([10(5),26(5)])].
% 0.44/1.00 35 add(A,multiply(A,B)) = multiply(A,add(A,B)). [para(6(a,1),20(a,1,1))].
% 0.44/1.00 36 add(A,multiply(B,A)) = multiply(add(A,B),A). [para(6(a,1),22(a,1,1))].
% 0.44/1.00 42 add(A,add(A,B)) = B. [para(31(a,1),17(a,2,2)),rewrite([26(4)])].
% 0.44/1.00 85 multiply(add(a,b),a) = add(a,c_0). [para(27(a,1),36(a,1,2)),flip(a)].
% 0.44/1.00 101 multiply(add(a,b),b) = add(b,c_0). [para(85(a,1),35(a,1,2)),rewrite([17(7),10(6),42(6),10(3),10(11),42(11)]),flip(a)].
% 0.44/1.00 158 multiply(add(additive_identity,a),b) = c_0. [para(101(a,1),36(a,1,2)),rewrite([42(5),17(6,R),31(5),10(4)]),flip(a)].
% 0.44/1.00 165 multiply(a,b) = c_0. [para(158(a,1),22(a,2)),rewrite([5(3),34(5)])].
% 0.44/1.00 166 $F # answer(prove_commutativity). [resolve(165,a,28,a)].
% 0.44/1.00
% 0.44/1.00 % SZS output end Refutation
% 0.44/1.00 ============================== end of proof ==========================
% 0.44/1.00
% 0.44/1.00 ============================== STATISTICS ============================
% 0.44/1.00
% 0.44/1.00 Given=39. Generated=709. Kept=158. proofs=1.
% 0.44/1.00 Usable=36. Sos=104. Demods=135. Limbo=3, Disabled=31. Hints=0.
% 0.44/1.00 Megabytes=0.18.
% 0.44/1.00 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.44/1.00
% 0.44/1.00 ============================== end of statistics =====================
% 0.44/1.00
% 0.44/1.00 ============================== end of search =========================
% 0.44/1.00
% 0.44/1.00 THEOREM PROVED
% 0.44/1.00 % SZS status Unsatisfiable
% 0.44/1.00
% 0.44/1.00 Exiting with 1 proof.
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% 0.44/1.00 Process 4013 exit (max_proofs) Mon May 30 12:25:27 2022
% 0.44/1.00 Prover9 interrupted
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