TSTP Solution File: BOO007-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO007-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 : Thu Jul 14 23:47:58 EDT 2022
% Result : Unsatisfiable 3.58s 3.87s
% Output : Refutation 3.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO007-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 : Wed Jun 1 21:26:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.58/3.87 ============================== Prover9 ===============================
% 3.58/3.87 Prover9 (32) version 2009-11A, November 2009.
% 3.58/3.87 Process 18749 was started by sandbox2 on n025.cluster.edu,
% 3.58/3.87 Wed Jun 1 21:26:15 2022
% 3.58/3.87 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_18596_n025.cluster.edu".
% 3.58/3.87 ============================== end of head ===========================
% 3.58/3.87
% 3.58/3.87 ============================== INPUT =================================
% 3.58/3.87
% 3.58/3.87 % Reading from file /tmp/Prover9_18596_n025.cluster.edu
% 3.58/3.87
% 3.58/3.87 set(prolog_style_variables).
% 3.58/3.87 set(auto2).
% 3.58/3.87 % set(auto2) -> set(auto).
% 3.58/3.87 % set(auto) -> set(auto_inference).
% 3.58/3.87 % set(auto) -> set(auto_setup).
% 3.58/3.87 % set(auto_setup) -> set(predicate_elim).
% 3.58/3.87 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.58/3.87 % set(auto) -> set(auto_limits).
% 3.58/3.87 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.58/3.87 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.58/3.87 % set(auto) -> set(auto_denials).
% 3.58/3.87 % set(auto) -> set(auto_process).
% 3.58/3.87 % set(auto2) -> assign(new_constants, 1).
% 3.58/3.87 % set(auto2) -> assign(fold_denial_max, 3).
% 3.58/3.87 % set(auto2) -> assign(max_weight, "200.000").
% 3.58/3.87 % set(auto2) -> assign(max_hours, 1).
% 3.58/3.87 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.58/3.87 % set(auto2) -> assign(max_seconds, 0).
% 3.58/3.87 % set(auto2) -> assign(max_minutes, 5).
% 3.58/3.87 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.58/3.87 % set(auto2) -> set(sort_initial_sos).
% 3.58/3.87 % set(auto2) -> assign(sos_limit, -1).
% 3.58/3.87 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.58/3.87 % set(auto2) -> assign(max_megs, 400).
% 3.58/3.87 % set(auto2) -> assign(stats, some).
% 3.58/3.87 % set(auto2) -> clear(echo_input).
% 3.58/3.87 % set(auto2) -> set(quiet).
% 3.58/3.87 % set(auto2) -> clear(print_initial_clauses).
% 3.58/3.87 % set(auto2) -> clear(print_given).
% 3.58/3.87 assign(lrs_ticks,-1).
% 3.58/3.87 assign(sos_limit,10000).
% 3.58/3.87 assign(order,kbo).
% 3.58/3.87 set(lex_order_vars).
% 3.58/3.87 clear(print_given).
% 3.58/3.87
% 3.58/3.87 % formulas(sos). % not echoed (27 formulas)
% 3.58/3.87
% 3.58/3.87 ============================== end of input ==========================
% 3.58/3.87
% 3.58/3.87 % From the command line: assign(max_seconds, 300).
% 3.58/3.87
% 3.58/3.87 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.58/3.87
% 3.58/3.87 % Formulas that are not ordinary clauses:
% 3.58/3.87
% 3.58/3.87 ============================== end of process non-clausal formulas ===
% 3.58/3.87
% 3.58/3.87 ============================== PROCESS INITIAL CLAUSES ===============
% 3.58/3.87
% 3.58/3.87 ============================== PREDICATE ELIMINATION =================
% 3.58/3.87
% 3.58/3.87 ============================== end predicate elimination =============
% 3.58/3.87
% 3.58/3.87 Auto_denials:
% 3.58/3.87 % copying label prove_equality to answer in negative clause
% 3.58/3.87
% 3.58/3.87 Term ordering decisions:
% 3.58/3.87
% 3.58/3.87 % Assigning unary symbol inverse kb_weight 0 and highest precedence (15).
% 3.58/3.87 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. x=1. x_times_y=1. y=1. y_times_z=1. z=1. x_times__y_times_z=1. x_times_y__times_z=1. add=1. multiply=1. inverse=0.
% 3.58/3.87
% 3.58/3.87 ============================== end of process initial clauses ========
% 3.58/3.87
% 3.58/3.87 ============================== CLAUSES FOR SEARCH ====================
% 3.58/3.87
% 3.58/3.87 ============================== end of clauses for search =============
% 3.58/3.87
% 3.58/3.87 ============================== SEARCH ================================
% 3.58/3.87
% 3.58/3.87 % Starting search at 0.01 seconds.
% 3.58/3.87
% 3.58/3.87 Low Water (keep): wt=17.000, iters=3363
% 3.58/3.87
% 3.58/3.87 Low Water (keep): wt=14.000, iters=3340
% 3.58/3.87
% 3.58/3.87 Low Water (keep): wt=13.000, iters=3411
% 3.58/3.87
% 3.58/3.87 Low Water (keep): wt=12.000, iters=3350
% 3.58/3.87
% 3.58/3.87 Low Water (keep): wt=11.000, iters=3341
% 3.58/3.87
% 3.58/3.87 Low Water (keep): wt=10.000, iters=3362
% 3.58/3.87
% 3.58/3.87 ============================== PROOF =================================
% 3.58/3.87 % SZS status Unsatisfiable
% 3.58/3.87 % SZS output start Refutation
% 3.58/3.87
% 3.58/3.87 % Proof 1 at 2.80 (+ 0.07) seconds: prove_equality.
% 3.58/3.87 % Length of proof is 72.
% 3.58/3.87 % Level of proof is 11.
% 3.58/3.87 % Maximum clause weight is 20.000.
% 3.58/3.87 % Given clauses 324.
% 3.58/3.87
% 3.58/3.87 1 sum(additive_identity,A,A) # label(additive_identity1) # label(axiom). [assumption].
% 3.58/3.87 2 sum(A,additive_identity,A) # label(additive_identity2) # label(axiom). [assumption].
% 3.58/3.87 3 product(multiplicative_identity,A,A) # label(multiplicative_identity1) # label(axiom). [assumption].
% 3.58/3.87 4 product(A,multiplicative_identity,A) # label(multiplicative_identity2) # label(axiom). [assumption].
% 3.58/3.87 5 product(y,z,y_times_z) # label(y_times_z) # label(hypothesis). [assumption].
% 3.58/3.87 6 product(x,y_times_z,x_times__y_times_z) # label(x_times__y_times_z) # label(hypothesis). [assumption].
% 3.58/3.87 7 product(x,y,x_times_y) # label(x_times_y) # label(hypothesis). [assumption].
% 3.58/3.87 8 product(x_times_y,z,x_times_y__times_z) # label(x_times_y__times_z) # label(hypothesis). [assumption].
% 3.58/3.87 10 sum(A,inverse(A),multiplicative_identity) # label(additive_inverse2) # label(axiom). [assumption].
% 3.58/3.87 12 product(A,inverse(A),additive_identity) # label(multiplicative_inverse2) # label(axiom). [assumption].
% 3.58/3.87 13 sum(A,B,add(A,B)) # label(closure_of_addition) # label(axiom). [assumption].
% 3.58/3.87 14 product(A,B,multiply(A,B)) # label(closure_of_multiplication) # label(axiom). [assumption].
% 3.58/3.87 15 x_times__y_times_z != x_times_y__times_z # label(prove_equality) # label(negated_conjecture) # answer(prove_equality). [assumption].
% 3.58/3.87 16 x_times_y__times_z != x_times__y_times_z # answer(prove_equality). [copy(15),flip(a)].
% 3.58/3.87 17 -sum(A,B,C) | sum(B,A,C) # label(commutativity_of_addition) # label(axiom). [assumption].
% 3.58/3.87 18 -product(A,B,C) | product(B,A,C) # label(commutativity_of_multiplication) # label(axiom). [assumption].
% 3.58/3.87 19 -sum(A,B,C) | -sum(A,B,D) | C = D # label(addition_is_well_defined) # label(axiom). [assumption].
% 3.58/3.87 20 -product(A,B,C) | -product(A,B,D) | C = D # label(multiplication_is_well_defined) # label(axiom). [assumption].
% 3.58/3.87 21 -product(A,B,C) | -product(A,D,E) | -sum(B,D,F) | -product(A,F,V6) | sum(C,E,V6) # label(distributivity1) # label(axiom). [assumption].
% 3.58/3.87 23 -product(A,B,C) | -product(D,B,E) | -sum(A,D,F) | -product(F,B,V6) | sum(C,E,V6) # label(distributivity3) # label(axiom). [assumption].
% 3.58/3.87 25 -sum(A,B,C) | -sum(A,D,E) | -product(B,D,F) | -sum(A,F,V6) | product(C,E,V6) # label(distributivity5) # label(axiom). [assumption].
% 3.58/3.87 26 -sum(A,B,C) | -sum(A,D,E) | -product(B,D,F) | -product(C,E,V6) | sum(A,F,V6) # label(distributivity6) # label(axiom). [assumption].
% 3.58/3.87 27 -sum(A,B,C) | -sum(D,B,E) | -product(A,D,F) | -sum(F,B,V6) | product(C,E,V6) # label(distributivity7) # label(axiom). [assumption].
% 3.58/3.87 28 -sum(A,B,C) | -sum(D,B,E) | -product(A,D,F) | -product(C,E,V6) | sum(F,B,V6) # label(distributivity8) # label(axiom). [assumption].
% 3.58/3.87 29 sum(A,B,add(B,A)). [hyper(17,a,13,a)].
% 3.58/3.87 30 product(A,B,multiply(B,A)). [hyper(18,a,14,a)].
% 3.58/3.87 31 product(z,x_times_y,x_times_y__times_z). [hyper(18,a,8,a)].
% 3.58/3.87 32 product(y,x,x_times_y). [hyper(18,a,7,a)].
% 3.58/3.87 33 product(y_times_z,x,x_times__y_times_z). [hyper(18,a,6,a)].
% 3.58/3.87 34 product(z,y,y_times_z). [hyper(18,a,5,a)].
% 3.58/3.87 35 add(A,inverse(A)) = multiplicative_identity. [hyper(19,a,13,a,b,10,a)].
% 3.58/3.87 37 add(A,additive_identity) = A. [hyper(19,a,13,a,b,2,a)].
% 3.58/3.87 41 -sum(x_times_y__times_z,additive_identity,x_times__y_times_z) # answer(prove_equality). [ur(19,b,2,a,c,16,a(flip))].
% 3.58/3.87 44 multiply(A,inverse(A)) = additive_identity. [hyper(20,a,14,a,b,12,a)].
% 3.58/3.87 46 multiply(x_times_y,z) = x_times_y__times_z. [hyper(20,a,14,a,b,8,a)].
% 3.58/3.87 49 multiply(y,z) = y_times_z. [hyper(20,a,14,a,b,5,a)].
% 3.58/3.87 50 multiply(A,multiplicative_identity) = A. [hyper(20,a,14,a,b,4,a)].
% 3.58/3.87 64 sum(additive_identity,multiply(A,additive_identity),additive_identity). [hyper(21,a,14,a,b,14,a,c,2,a,d,12,a),rewrite([44(2)])].
% 3.58/3.87 384 product(multiplicative_identity,add(A,multiplicative_identity),multiplicative_identity). [hyper(25,a,13,a,b,13,a,c,4,a,d,10,a),rewrite([35(2)])].
% 3.58/3.87 419 product(A,A,add(A,multiply(additive_identity,additive_identity))). [hyper(25,a,2,a,b,2,a,c,14,a,d,13,a)].
% 3.58/3.87 861 add(A,B) = add(B,A). [hyper(19,a,13,a,b,29,a)].
% 3.58/3.87 1132 -product(y_times_z,x,x_times_y__times_z) # answer(prove_equality). [ur(28,a,2,a,b,2,a,d,33,a,e,41,a)].
% 3.58/3.87 1202 sum(y_times_z,x_times_y__times_z,multiply(z,add(x_times_y,y))). [hyper(21,a,34,a,b,31,a,c,13,a,d,14,a),rewrite([861(6)])].
% 3.58/3.87 1234 product(A,add(A,B),add(A,multiply(B,additive_identity))). [hyper(27,a,1,a,b,13,a,c,30,a,d,13,a),rewrite([861(1),861(4)])].
% 3.58/3.87 1434 multiply(A,B) = multiply(B,A). [hyper(20,a,14,a,b,30,a)].
% 3.58/3.87 1551 product(A,additive_identity,additive_identity). [hyper(25,a,13,a,b,13,a,c,14,a,d,64,a),rewrite([861(2),37(2),37(3)])].
% 3.58/3.87 1576 multiply(A,additive_identity) = additive_identity. [hyper(19,a,1,a,b,64,a)].
% 3.58/3.87 1579 product(A,add(A,B),A). [back_rewrite(1234),rewrite([1576(3),37(3)])].
% 3.58/3.87 1586 product(A,A,A). [back_rewrite(419),rewrite([1576(3),37(2)])].
% 3.58/3.87 1862 sum(multiplicative_identity,A,multiply(multiplicative_identity,add(A,multiplicative_identity))). [hyper(23,a,1586,a,b,4,a,c,13,a,d,14,a),rewrite([861(3),1434(5)])].
% 3.58/3.87 1882 multiply(A,A) = A. [hyper(20,a,14,a,b,1586,a)].
% 3.58/3.87 2977 sum(A,multiplicative_identity,multiplicative_identity). [hyper(21,a,14,a,b,1586,a,c,13,a,d,384,a),rewrite([1434(2),50(2)])].
% 3.58/3.87 2997 add(A,multiplicative_identity) = multiplicative_identity. [hyper(20,a,3,a,b,384,a)].
% 3.58/3.87 2998 sum(multiplicative_identity,A,multiplicative_identity). [back_rewrite(1862),rewrite([2997(4),1882(4)])].
% 3.58/3.87 3371 sum(y_times_z,y,y). [hyper(23,a,34,a,b,3,a,c,2977,a,d,3,a)].
% 3.58/3.87 3383 sum(x_times_y__times_z,x_times_y,x_times_y). [hyper(23,a,31,a,b,3,a,c,2977,a,d,3,a)].
% 3.58/3.87 3392 sum(x_times_y,y,y). [hyper(23,a,7,a,b,3,a,c,2977,a,d,3,a)].
% 3.58/3.87 3396 sum(x_times__y_times_z,y_times_z,y_times_z). [hyper(23,a,6,a,b,3,a,c,2977,a,d,3,a)].
% 3.58/3.87 3482 sum(x,x_times_y,x). [hyper(23,a,3,a,b,32,a,c,2998,a,d,3,a)].
% 3.58/3.87 3492 sum(z,y_times_z,z). [hyper(23,a,3,a,b,5,a,c,2998,a,d,3,a)].
% 3.58/3.87 3646 sum(x_times__y_times_z,x_times_y,x_times_y). [hyper(23,a,33,a,b,32,a,c,3371,a,d,32,a)].
% 3.58/3.87 4057 product(x_times_y,x_times_y__times_z,x_times_y__times_z). [hyper(25,a,3383,a,b,2,a,c,1551,a,d,2,a)].
% 3.58/3.87 4411 add(x_times_y,y) = y. [hyper(19,a,13,a,b,3392,a)].
% 3.58/3.87 4414 sum(y_times_z,x_times_y__times_z,y_times_z). [back_rewrite(1202),rewrite([4411(6),1434(5),49(5)])].
% 3.58/3.87 4482 product(y_times_z,x_times__y_times_z,x_times__y_times_z). [hyper(25,a,3396,a,b,2,a,c,1551,a,d,2,a)].
% 3.58/3.87 5352 sum(x_times__y_times_z,x_times_y__times_z,multiply(x_times_y,add(z,x_times__y_times_z))). [hyper(26,a,13,a,b,3646,a,c,31,a,d,14,a),rewrite([861(5),1434(7)])].
% 3.58/3.87 11618 sum(z,x_times__y_times_z,z). [hyper(26,a,3492,a,b,13,a,c,4482,a,d,1579,a)].
% 3.58/3.87 11624 sum(x,x_times_y__times_z,x). [hyper(26,a,3482,a,b,13,a,c,4057,a,d,1579,a)].
% 3.58/3.87 11982 add(z,x_times__y_times_z) = z. [hyper(19,a,13,a,b,11618,a)].
% 3.58/3.87 12148 sum(x_times__y_times_z,x_times_y__times_z,x_times_y__times_z). [back_rewrite(5352),rewrite([11982(6),46(5)])].
% 3.58/3.87 12360 -sum(x_times__y_times_z,x_times_y__times_z,x_times_y__times_z) # answer(prove_equality). [ur(27,a,4414,a,b,11624,a,c,33,a,e,1132,a)].
% 3.58/3.87 12361 $F # answer(prove_equality). [resolve(12360,a,12148,a)].
% 3.58/3.87
% 3.58/3.87 % SZS output end Refutation
% 3.58/3.87 ============================== end of proof ==========================
% 3.58/3.87
% 3.58/3.87 ============================== STATISTICS ============================
% 3.58/3.87
% 3.58/3.87 Given=324. Generated=113567. Kept=12359. proofs=1.
% 3.58/3.87 Usable=283. Sos=6244. Demods=74. Limbo=211, Disabled=5647. Hints=0.
% 3.58/3.87 Megabytes=7.12.
% 3.58/3.87 User_CPU=2.80, System_CPU=0.07, Wall_clock=2.
% 3.58/3.87
% 3.58/3.87 ============================== end of statistics =====================
% 3.58/3.87
% 3.58/3.87 ============================== end of search =========================
% 3.58/3.87
% 3.58/3.87 THEOREM PROVED
% 3.58/3.87 % SZS status Unsatisfiable
% 3.58/3.87
% 3.58/3.87 Exiting with 1 proof.
% 3.58/3.87
% 3.58/3.87 Process 18749 exit (max_proofs) Wed Jun 1 21:26:17 2022
% 3.58/3.87 Prover9 interrupted
%------------------------------------------------------------------------------