TSTP Solution File: BOO014-3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO014-3 : TPTP v8.1.0. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 23:48:01 EDT 2022
% Result : Unsatisfiable 11.25s 11.57s
% Output : Refutation 11.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : BOO014-3 : TPTP v8.1.0. Bugfixed v2.2.0.
% 0.09/0.10 % Command : tptp2X_and_run_prover9 %d %s
% 0.09/0.31 % Computer : n017.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 600
% 0.09/0.31 % DateTime : Wed Jun 1 22:03:27 EDT 2022
% 0.09/0.31 % CPUTime :
% 11.25/11.57 ============================== Prover9 ===============================
% 11.25/11.57 Prover9 (32) version 2009-11A, November 2009.
% 11.25/11.57 Process 1409 was started by sandbox on n017.cluster.edu,
% 11.25/11.57 Wed Jun 1 22:03:28 2022
% 11.25/11.57 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_1255_n017.cluster.edu".
% 11.25/11.57 ============================== end of head ===========================
% 11.25/11.57
% 11.25/11.57 ============================== INPUT =================================
% 11.25/11.57
% 11.25/11.57 % Reading from file /tmp/Prover9_1255_n017.cluster.edu
% 11.25/11.57
% 11.25/11.57 set(prolog_style_variables).
% 11.25/11.57 set(auto2).
% 11.25/11.57 % set(auto2) -> set(auto).
% 11.25/11.57 % set(auto) -> set(auto_inference).
% 11.25/11.57 % set(auto) -> set(auto_setup).
% 11.25/11.57 % set(auto_setup) -> set(predicate_elim).
% 11.25/11.57 % set(auto_setup) -> assign(eq_defs, unfold).
% 11.25/11.57 % set(auto) -> set(auto_limits).
% 11.25/11.57 % set(auto_limits) -> assign(max_weight, "100.000").
% 11.25/11.57 % set(auto_limits) -> assign(sos_limit, 20000).
% 11.25/11.57 % set(auto) -> set(auto_denials).
% 11.25/11.57 % set(auto) -> set(auto_process).
% 11.25/11.57 % set(auto2) -> assign(new_constants, 1).
% 11.25/11.57 % set(auto2) -> assign(fold_denial_max, 3).
% 11.25/11.57 % set(auto2) -> assign(max_weight, "200.000").
% 11.25/11.57 % set(auto2) -> assign(max_hours, 1).
% 11.25/11.57 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 11.25/11.57 % set(auto2) -> assign(max_seconds, 0).
% 11.25/11.57 % set(auto2) -> assign(max_minutes, 5).
% 11.25/11.57 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 11.25/11.57 % set(auto2) -> set(sort_initial_sos).
% 11.25/11.57 % set(auto2) -> assign(sos_limit, -1).
% 11.25/11.57 % set(auto2) -> assign(lrs_ticks, 3000).
% 11.25/11.57 % set(auto2) -> assign(max_megs, 400).
% 11.25/11.57 % set(auto2) -> assign(stats, some).
% 11.25/11.57 % set(auto2) -> clear(echo_input).
% 11.25/11.57 % set(auto2) -> set(quiet).
% 11.25/11.57 % set(auto2) -> clear(print_initial_clauses).
% 11.25/11.57 % set(auto2) -> clear(print_given).
% 11.25/11.57 assign(lrs_ticks,-1).
% 11.25/11.57 assign(sos_limit,10000).
% 11.25/11.57 assign(order,kbo).
% 11.25/11.57 set(lex_order_vars).
% 11.25/11.57 clear(print_given).
% 11.25/11.57
% 11.25/11.57 % formulas(sos). % not echoed (27 formulas)
% 11.25/11.57
% 11.25/11.57 ============================== end of input ==========================
% 11.25/11.57
% 11.25/11.57 % From the command line: assign(max_seconds, 300).
% 11.25/11.57
% 11.25/11.57 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 11.25/11.57
% 11.25/11.57 % Formulas that are not ordinary clauses:
% 11.25/11.57
% 11.25/11.57 ============================== end of process non-clausal formulas ===
% 11.25/11.57
% 11.25/11.57 ============================== PROCESS INITIAL CLAUSES ===============
% 11.25/11.57
% 11.25/11.57 ============================== PREDICATE ELIMINATION =================
% 11.25/11.57
% 11.25/11.57 ============================== end predicate elimination =============
% 11.25/11.57
% 11.25/11.57 Auto_denials:
% 11.25/11.57 % copying label prove_equation to answer in negative clause
% 11.25/11.57
% 11.25/11.57 Term ordering decisions:
% 11.25/11.57
% 11.25/11.57 % Assigning unary symbol inverse kb_weight 0 and highest precedence (12).
% 11.25/11.57 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. x=1. y=1. x_inverse_times_y_inverse=1. x_plus_y=1. add=1. multiply=1. inverse=0.
% 11.25/11.57
% 11.25/11.57 ============================== end of process initial clauses ========
% 11.25/11.57
% 11.25/11.57 ============================== CLAUSES FOR SEARCH ====================
% 11.25/11.57
% 11.25/11.57 ============================== end of clauses for search =============
% 11.25/11.57
% 11.25/11.57 ============================== SEARCH ================================
% 11.25/11.57
% 11.25/11.57 % Starting search at 0.01 seconds.
% 11.25/11.57
% 11.25/11.57 Low Water (keep): wt=28.000, iters=3348
% 11.25/11.57
% 11.25/11.57 Low Water (keep): wt=24.000, iters=3406
% 11.25/11.57
% 11.25/11.57 Low Water (keep): wt=23.000, iters=3351
% 11.25/11.57
% 11.25/11.57 Low Water (keep): wt=22.000, iters=3448
% 11.25/11.57
% 11.25/11.57 Low Water (keep): wt=21.000, iters=3368
% 11.25/11.57
% 11.25/11.57 Low Water (keep): wt=20.000, iters=3808
% 11.25/11.57
% 11.25/11.57 Low Water (keep): wt=19.000, iters=3541
% 11.25/11.57
% 11.25/11.57 Low Water (keep): wt=18.000, iters=3403
% 11.25/11.57
% 11.25/11.57 Low Water (keep): wt=17.000, iters=3406
% 11.25/11.57
% 11.25/11.57 Low Water (keep): wt=16.000, iters=3444
% 11.25/11.57
% 11.25/11.57 Low Water (keep): wt=15.000, iters=3361
% 11.25/11.57
% 11.25/11.57 Low Water (keep): wt=14.000, iters=3361
% 11.25/11.57
% 11.25/11.57 Low Water (keep): wt=13.000, iters=3390
% 11.25/11.57
% 11.25/11.57 ============================== PROOF =================================
% 11.25/11.57 % SZS status Unsatisfiable
% 11.25/11.57 % SZS output start Refutation
% 11.25/11.57
% 11.25/11.57 % Proof 1 at 10.29 (+ 0.27) seconds: prove_equation.
% 11.25/11.57 % Length of proof is 69.
% 11.25/11.57 % Level of proof is 13.
% 11.25/11.57 % Maximum clause weight is 20.000.
% 11.25/11.57 % Given clauses 349.
% 11.25/11.57
% 11.25/11.57 1 sum(additive_identity,A,A) # label(additive_identity1) # label(axiom). [assumption].
% 11.25/11.57 2 sum(A,additive_identity,A) # label(additive_identity2) # label(axiom). [assumption].
% 11.25/11.57 3 product(multiplicative_identity,A,A) # label(multiplicative_identity1) # label(axiom). [assumption].
% 11.25/11.57 4 product(A,multiplicative_identity,A) # label(multiplicative_identity2) # label(axiom). [assumption].
% 11.25/11.57 5 sum(x,y,x_plus_y) # label(x_plus_y) # label(hypothesis). [assumption].
% 11.25/11.57 7 sum(A,inverse(A),multiplicative_identity) # label(additive_inverse2) # label(axiom). [assumption].
% 11.25/11.57 9 product(A,inverse(A),additive_identity) # label(multiplicative_inverse2) # label(axiom). [assumption].
% 11.25/11.57 10 inverse(inverse(A)) = A # label(inverse_is_self_cancelling) # label(axiom). [assumption].
% 11.25/11.57 11 sum(A,B,add(A,B)) # label(closure_of_addition) # label(axiom). [assumption].
% 11.25/11.57 12 product(A,B,multiply(A,B)) # label(closure_of_multiplication) # label(axiom). [assumption].
% 11.25/11.57 13 product(inverse(x),inverse(y),x_inverse_times_y_inverse) # label(x_inverse_times_y_inverse) # label(hypothesis). [assumption].
% 11.25/11.57 14 inverse(x_plus_y) != x_inverse_times_y_inverse # label(prove_equation) # label(negated_conjecture) # answer(prove_equation). [assumption].
% 11.25/11.57 15 -sum(A,B,C) | sum(B,A,C) # label(commutativity_of_addition) # label(axiom). [assumption].
% 11.25/11.57 16 -product(A,B,C) | product(B,A,C) # label(commutativity_of_multiplication) # label(axiom). [assumption].
% 11.25/11.57 17 -sum(A,B,C) | -sum(A,B,D) | C = D # label(addition_is_well_defined) # label(axiom). [assumption].
% 11.25/11.57 18 -product(A,B,C) | -product(A,B,D) | C = D # label(multiplication_is_well_defined) # label(axiom). [assumption].
% 11.25/11.57 19 -sum(A,B,multiplicative_identity) | -sum(A,C,multiplicative_identity) | -product(A,B,additive_identity) | -product(A,C,additive_identity) | B = C # label(inverse_is_unique) # label(axiom). [assumption].
% 11.25/11.57 20 -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].
% 11.25/11.57 21 -product(A,B,C) | -product(A,D,E) | -sum(B,D,F) | -sum(C,E,V6) | product(A,F,V6) # label(distributivity2) # label(axiom). [assumption].
% 11.25/11.57 22 -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].
% 11.25/11.57 23 -product(A,B,C) | -product(D,B,E) | -sum(A,D,F) | -sum(C,E,V6) | product(F,B,V6) # label(distributivity4) # label(axiom). [assumption].
% 11.25/11.57 24 -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].
% 11.25/11.57 25 -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].
% 11.25/11.57 26 -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].
% 11.25/11.57 28 sum(A,B,add(B,A)). [hyper(15,a,11,a)].
% 11.25/11.57 29 sum(y,x,x_plus_y). [hyper(15,a,5,a)].
% 11.25/11.57 30 product(inverse(y),inverse(x),x_inverse_times_y_inverse). [hyper(16,a,13,a)].
% 11.25/11.57 31 product(A,B,multiply(B,A)). [hyper(16,a,12,a)].
% 11.25/11.57 32 add(A,inverse(A)) = multiplicative_identity. [hyper(17,a,11,a,b,7,a)].
% 11.25/11.57 35 add(A,additive_identity) = A. [hyper(17,a,11,a,b,2,a)].
% 11.25/11.57 43 multiply(A,inverse(A)) = additive_identity. [hyper(18,a,12,a,b,9,a)].
% 11.25/11.57 45 multiply(A,multiplicative_identity) = A. [hyper(18,a,12,a,b,4,a)].
% 11.25/11.57 69 sum(additive_identity,multiply(A,additive_identity),additive_identity). [hyper(20,a,12,a,b,12,a,c,2,a,d,9,a),rewrite([43(2)])].
% 11.25/11.57 74 sum(multiply(A,B),additive_identity,multiply(A,add(B,inverse(A)))). [hyper(20,a,12,a,b,9,a,c,11,a,d,12,a)].
% 11.25/11.57 80 sum(additive_identity,x_inverse_times_y_inverse,multiply(inverse(x),add(x,inverse(y)))). [hyper(20,a,9,a,b,13,a,c,11,a,d,12,a),rewrite([10(7)])].
% 11.25/11.57 133 product(A,add(multiplicative_identity,inverse(A)),A). [hyper(21,a,4,a,b,9,a,c,11,a,d,11,a),rewrite([35(5)])].
% 11.25/11.57 187 product(add(A,B),C,add(multiply(A,C),multiply(B,C))). [hyper(23,a,12,a,b,12,a,c,11,a,d,11,a)].
% 11.25/11.57 225 product(multiplicative_identity,add(A,multiplicative_identity),multiplicative_identity). [hyper(24,a,11,a,b,11,a,c,4,a,d,7,a),rewrite([32(2)])].
% 11.25/11.57 259 product(A,A,add(A,multiply(additive_identity,additive_identity))). [hyper(24,a,2,a,b,2,a,c,12,a,d,11,a)].
% 11.25/11.57 615 add(A,B) = add(B,A). [hyper(17,a,11,a,b,28,a)].
% 11.25/11.57 1008 multiply(A,B) = multiply(B,A). [hyper(18,a,12,a,b,31,a)].
% 11.25/11.57 1077 product(A,additive_identity,additive_identity). [hyper(24,a,11,a,b,11,a,c,12,a,d,69,a),rewrite([615(2),35(2),35(3)])].
% 11.25/11.57 1095 product(additive_identity,A,add(multiply(A,additive_identity),multiply(A,multiply(B,additive_identity)))). [hyper(23,a,12,a,b,12,a,c,69,a,d,11,a),rewrite([1008(3),1008(6)])].
% 11.25/11.57 1102 multiply(A,additive_identity) = additive_identity. [hyper(17,a,1,a,b,69,a)].
% 11.25/11.57 1103 product(additive_identity,A,additive_identity). [back_rewrite(1095),rewrite([1102(3),1102(4),1102(4),35(4)])].
% 11.25/11.57 1112 product(A,A,A). [back_rewrite(259),rewrite([1102(3),35(2)])].
% 11.25/11.57 1123 product(x_plus_y,x,add(additive_identity,x)). [hyper(26,a,29,a,b,1,a,c,1077,a,d,11,a)].
% 11.25/11.57 1124 product(x_plus_y,x,x). [hyper(26,a,29,a,b,1,a,c,1077,a,d,1,a)].
% 11.25/11.57 1220 product(y,x_plus_y,y). [hyper(26,a,1,a,b,5,a,c,1103,a,d,1,a)].
% 11.25/11.57 1294 product(add(x_plus_y,inverse(x)),multiplicative_identity,multiplicative_identity). [hyper(26,a,11,a,b,11,a,c,1124,a,d,7,a),rewrite([32(8)])].
% 11.25/11.57 1621 product(multiplicative_identity,add(x_plus_y,inverse(y)),multiplicative_identity). [hyper(26,a,11,a,b,11,a,c,1220,a,d,7,a),rewrite([32(4)])].
% 11.25/11.57 1868 sum(A,multiplicative_identity,multiplicative_identity). [hyper(20,a,12,a,b,1112,a,c,11,a,d,225,a),rewrite([1008(2),45(2)])].
% 11.25/11.57 1963 sum(x_inverse_times_y_inverse,inverse(x),inverse(x)). [hyper(22,a,30,a,b,3,a,c,1868,a,d,3,a)].
% 11.25/11.57 1967 sum(x_inverse_times_y_inverse,inverse(y),inverse(y)). [hyper(22,a,13,a,b,3,a,c,1868,a,d,3,a)].
% 11.25/11.57 3099 multiply(A,add(B,inverse(A))) = multiply(A,B). [hyper(17,a,2,a,b,74,a),flip(a)].
% 11.25/11.57 3877 multiply(inverse(x),add(x,inverse(y))) = add(additive_identity,x_inverse_times_y_inverse). [hyper(17,a,11,a,b,80,a),flip(a)].
% 11.25/11.57 3878 add(additive_identity,x_inverse_times_y_inverse) = x_inverse_times_y_inverse. [hyper(17,a,1,a,b,80,a),rewrite([3877(8)]),flip(a)].
% 11.25/11.57 4185 add(additive_identity,x) = x. [hyper(18,a,1124,a,b,1123,a),flip(a)].
% 11.25/11.57 9286 sum(multiply(x,x_inverse_times_y_inverse),additive_identity,additive_identity). [hyper(22,a,12,a,b,12,a,c,1963,a,d,9,a),rewrite([10(4),1008(3),10(8),1008(7),43(7)])].
% 11.25/11.57 9723 sum(multiply(y,x_inverse_times_y_inverse),additive_identity,additive_identity). [hyper(22,a,12,a,b,12,a,c,1967,a,d,9,a),rewrite([10(4),1008(3),10(8),1008(7),43(7)])].
% 11.25/11.57 11802 add(multiply(A,B),multiply(C,B)) = multiply(B,add(A,C)). [hyper(18,a,12,a,b,187,a),rewrite([1008(2)]),flip(a)].
% 11.25/11.57 11803 multiply(multiplicative_identity,add(A,B)) = add(A,B). [hyper(18,a,187,a,b,133,a),rewrite([11802(11),1008(6),3099(6),1008(3)])].
% 11.25/11.57 13956 product(x,x_inverse_times_y_inverse,additive_identity). [hyper(26,a,11,a,b,11,a,c,12,a,d,9286,a),rewrite([615(3),4185(3),615(4),3878(4)])].
% 11.25/11.57 14393 product(x_plus_y,x_inverse_times_y_inverse,additive_identity). [hyper(23,a,12,a,b,13956,a,c,29,a,d,9723,a)].
% 11.25/11.57 14812 -sum(x_plus_y,x_inverse_times_y_inverse,multiplicative_identity) # answer(prove_equation). [ur(19,a,7,a,c,9,a,d,14393,a,e,14,a)].
% 11.25/11.57 15082 -product(add(x_plus_y,inverse(x)),add(x_plus_y,inverse(y)),multiplicative_identity) # answer(prove_equation). [ur(25,a,11,a,b,11,a,c,13,a,e,14812,a)].
% 11.25/11.57 19182 add(x_plus_y,inverse(x)) = multiplicative_identity. [hyper(18,a,12,a,b,1294,a),rewrite([1008(6),11803(6)])].
% 11.25/11.57 19199 -product(multiplicative_identity,add(x_plus_y,inverse(y)),multiplicative_identity) # answer(prove_equation). [back_rewrite(15082),rewrite([19182(4)])].
% 11.25/11.57 19200 $F # answer(prove_equation). [resolve(19199,a,1621,a)].
% 11.25/11.57
% 11.25/11.57 % SZS output end Refutation
% 11.25/11.57 ============================== end of proof ==========================
% 11.25/11.57
% 11.25/11.57 ============================== STATISTICS ============================
% 11.25/11.57
% 11.25/11.57 Given=349. Generated=375797. Kept=19199. proofs=1.
% 11.25/11.57 Usable=268. Sos=8832. Demods=73. Limbo=17, Disabled=10108. Hints=0.
% 11.25/11.57 Megabytes=12.24.
% 11.25/11.57 User_CPU=10.29, System_CPU=0.27, Wall_clock=10.
% 11.25/11.57
% 11.25/11.57 ============================== end of statistics =====================
% 11.25/11.57
% 11.25/11.57 ============================== end of search =========================
% 11.25/11.57
% 11.25/11.57 THEOREM PROVED
% 11.25/11.57 % SZS status Unsatisfiable
% 11.25/11.57
% 11.25/11.57 Exiting with 1 proof.
% 11.25/11.57
% 11.25/11.57 Process 1409 exit (max_proofs) Wed Jun 1 22:03:38 2022
% 11.25/11.57 Prover9 interrupted
%------------------------------------------------------------------------------