TSTP Solution File: BOO008-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : BOO008-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 2.72s 3.00s
% Output : Refutation 2.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : BOO008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 2 00:09:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.72/3.00 ============================== Prover9 ===============================
% 2.72/3.00 Prover9 (32) version 2009-11A, November 2009.
% 2.72/3.00 Process 32484 was started by sandbox2 on n029.cluster.edu,
% 2.72/3.00 Thu Jun 2 00:09:46 2022
% 2.72/3.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_32331_n029.cluster.edu".
% 2.72/3.00 ============================== end of head ===========================
% 2.72/3.00
% 2.72/3.00 ============================== INPUT =================================
% 2.72/3.00
% 2.72/3.00 % Reading from file /tmp/Prover9_32331_n029.cluster.edu
% 2.72/3.00
% 2.72/3.00 set(prolog_style_variables).
% 2.72/3.00 set(auto2).
% 2.72/3.00 % set(auto2) -> set(auto).
% 2.72/3.00 % set(auto) -> set(auto_inference).
% 2.72/3.00 % set(auto) -> set(auto_setup).
% 2.72/3.00 % set(auto_setup) -> set(predicate_elim).
% 2.72/3.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.72/3.00 % set(auto) -> set(auto_limits).
% 2.72/3.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.72/3.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.72/3.00 % set(auto) -> set(auto_denials).
% 2.72/3.00 % set(auto) -> set(auto_process).
% 2.72/3.00 % set(auto2) -> assign(new_constants, 1).
% 2.72/3.00 % set(auto2) -> assign(fold_denial_max, 3).
% 2.72/3.00 % set(auto2) -> assign(max_weight, "200.000").
% 2.72/3.00 % set(auto2) -> assign(max_hours, 1).
% 2.72/3.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.72/3.00 % set(auto2) -> assign(max_seconds, 0).
% 2.72/3.00 % set(auto2) -> assign(max_minutes, 5).
% 2.72/3.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.72/3.00 % set(auto2) -> set(sort_initial_sos).
% 2.72/3.00 % set(auto2) -> assign(sos_limit, -1).
% 2.72/3.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.72/3.00 % set(auto2) -> assign(max_megs, 400).
% 2.72/3.00 % set(auto2) -> assign(stats, some).
% 2.72/3.00 % set(auto2) -> clear(echo_input).
% 2.72/3.00 % set(auto2) -> set(quiet).
% 2.72/3.00 % set(auto2) -> clear(print_initial_clauses).
% 2.72/3.00 % set(auto2) -> clear(print_given).
% 2.72/3.00 assign(lrs_ticks,-1).
% 2.72/3.00 assign(sos_limit,10000).
% 2.72/3.00 assign(order,kbo).
% 2.72/3.00 set(lex_order_vars).
% 2.72/3.00 clear(print_given).
% 2.72/3.00
% 2.72/3.00 % formulas(sos). % not echoed (27 formulas)
% 2.72/3.00
% 2.72/3.00 ============================== end of input ==========================
% 2.72/3.00
% 2.72/3.00 % From the command line: assign(max_seconds, 300).
% 2.72/3.00
% 2.72/3.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.72/3.00
% 2.72/3.00 % Formulas that are not ordinary clauses:
% 2.72/3.00
% 2.72/3.00 ============================== end of process non-clausal formulas ===
% 2.72/3.00
% 2.72/3.00 ============================== PROCESS INITIAL CLAUSES ===============
% 2.72/3.00
% 2.72/3.00 ============================== PREDICATE ELIMINATION =================
% 2.72/3.00
% 2.72/3.00 ============================== end predicate elimination =============
% 2.72/3.00
% 2.72/3.00 Auto_denials:
% 2.72/3.00 % copying label prove_equality to answer in negative clause
% 2.72/3.00
% 2.72/3.00 Term ordering decisions:
% 2.72/3.00
% 2.72/3.00 % Assigning unary symbol inverse kb_weight 0 and highest precedence (15).
% 2.72/3.00 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. x=1. x_plus_y=1. y=1. y_plus_z=1. z=1. x__plus_y_plus_z=1. x_plus_y__plus_z=1. add=1. multiply=1. inverse=0.
% 2.72/3.00
% 2.72/3.00 ============================== end of process initial clauses ========
% 2.72/3.00
% 2.72/3.00 ============================== CLAUSES FOR SEARCH ====================
% 2.72/3.00
% 2.72/3.00 ============================== end of clauses for search =============
% 2.72/3.00
% 2.72/3.00 ============================== SEARCH ================================
% 2.72/3.00
% 2.72/3.00 % Starting search at 0.01 seconds.
% 2.72/3.00
% 2.72/3.00 Low Water (keep): wt=23.000, iters=3343
% 2.72/3.00
% 2.72/3.00 Low Water (keep): wt=21.000, iters=3739
% 2.72/3.00
% 2.72/3.00 Low Water (keep): wt=20.000, iters=3709
% 2.72/3.00
% 2.72/3.00 Low Water (keep): wt=18.000, iters=3586
% 2.72/3.00
% 2.72/3.00 Low Water (keep): wt=17.000, iters=3462
% 2.72/3.00
% 2.72/3.00 Low Water (keep): wt=16.000, iters=3333
% 2.72/3.00
% 2.72/3.00 Low Water (keep): wt=15.000, iters=3333
% 2.72/3.00
% 2.72/3.00 Low Water (keep): wt=14.000, iters=3344
% 2.72/3.00
% 2.72/3.00 Low Water (keep): wt=13.000, iters=3375
% 2.72/3.00
% 2.72/3.00 Low Water (keep): wt=12.000, iters=3359
% 2.72/3.00
% 2.72/3.00 Low Water (keep): wt=11.000, iters=3388
% 2.72/3.00
% 2.72/3.00 ============================== PROOF =================================
% 2.72/3.00 % SZS status Unsatisfiable
% 2.72/3.00 % SZS output start Refutation
% 2.72/3.00
% 2.72/3.00 % Proof 1 at 1.93 (+ 0.06) seconds: prove_equality.
% 2.72/3.00 % Length of proof is 72.
% 2.72/3.00 % Level of proof is 10.
% 2.72/3.00 % Maximum clause weight is 20.000.
% 2.72/3.00 % Given clauses 268.
% 2.72/3.00
% 2.72/3.00 1 sum(additive_identity,A,A) # label(additive_identity1) # label(axiom). [assumption].
% 2.72/3.00 2 sum(A,additive_identity,A) # label(additive_identity2) # label(axiom). [assumption].
% 2.72/3.00 3 product(multiplicative_identity,A,A) # label(multiplicative_identity1) # label(axiom). [assumption].
% 2.72/3.00 4 product(A,multiplicative_identity,A) # label(multiplicative_identity2) # label(axiom). [assumption].
% 2.72/3.00 5 sum(y,z,y_plus_z) # label(y_plus_z) # label(hypothesis). [assumption].
% 2.72/3.00 6 sum(x,y_plus_z,x__plus_y_plus_z) # label(x_plus__y_plus_z) # label(hypothesis). [assumption].
% 2.72/3.00 7 sum(x,y,x_plus_y) # label(x_plus_y) # label(hypothesis). [assumption].
% 2.72/3.00 8 sum(x_plus_y,z,x_plus_y__plus_z) # label(x_plus_y__plus_z) # label(hypothesis). [assumption].
% 2.72/3.00 10 sum(A,inverse(A),multiplicative_identity) # label(additive_inverse2) # label(axiom). [assumption].
% 2.72/3.00 12 product(A,inverse(A),additive_identity) # label(multiplicative_inverse2) # label(axiom). [assumption].
% 2.72/3.00 13 sum(A,B,add(A,B)) # label(closure_of_addition) # label(axiom). [assumption].
% 2.72/3.00 14 product(A,B,multiply(A,B)) # label(closure_of_multiplication) # label(axiom). [assumption].
% 2.72/3.00 15 x__plus_y_plus_z != x_plus_y__plus_z # label(prove_equality) # label(negated_conjecture) # answer(prove_equality). [assumption].
% 2.72/3.00 16 x_plus_y__plus_z != x__plus_y_plus_z # answer(prove_equality). [copy(15),flip(a)].
% 2.72/3.00 17 -sum(A,B,C) | sum(B,A,C) # label(commutativity_of_addition) # label(axiom). [assumption].
% 2.72/3.00 18 -product(A,B,C) | product(B,A,C) # label(commutativity_of_multiplication) # label(axiom). [assumption].
% 2.72/3.00 19 -sum(A,B,C) | -sum(A,B,D) | C = D # label(addition_is_well_defined) # label(axiom). [assumption].
% 2.72/3.00 20 -product(A,B,C) | -product(A,B,D) | C = D # label(multiplication_is_well_defined) # label(axiom). [assumption].
% 2.72/3.00 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].
% 2.72/3.00 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].
% 2.72/3.00 24 -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].
% 2.72/3.00 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].
% 2.72/3.00 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].
% 2.72/3.00 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].
% 2.72/3.00 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].
% 2.72/3.00 29 sum(A,B,add(B,A)). [hyper(17,a,13,a)].
% 2.72/3.00 30 sum(z,x_plus_y,x_plus_y__plus_z). [hyper(17,a,8,a)].
% 2.72/3.00 31 sum(y,x,x_plus_y). [hyper(17,a,7,a)].
% 2.72/3.00 32 sum(y_plus_z,x,x__plus_y_plus_z). [hyper(17,a,6,a)].
% 2.72/3.00 33 sum(z,y,y_plus_z). [hyper(17,a,5,a)].
% 2.72/3.00 34 product(A,B,multiply(B,A)). [hyper(18,a,14,a)].
% 2.72/3.00 35 add(A,inverse(A)) = multiplicative_identity. [hyper(19,a,13,a,b,10,a)].
% 2.72/3.00 37 add(x_plus_y,z) = x_plus_y__plus_z. [hyper(19,a,13,a,b,8,a)].
% 2.72/3.00 38 add(x,y) = x_plus_y. [hyper(19,a,13,a,b,7,a)].
% 2.72/3.00 40 add(y,z) = y_plus_z. [hyper(19,a,13,a,b,5,a)].
% 2.72/3.00 41 add(A,additive_identity) = A. [hyper(19,a,13,a,b,2,a)].
% 2.72/3.00 45 -sum(x,y_plus_z,x_plus_y__plus_z) # answer(prove_equality). [ur(19,b,6,a,c,16,a)].
% 2.72/3.00 50 multiply(A,inverse(A)) = additive_identity. [hyper(20,a,14,a,b,12,a)].
% 2.72/3.00 72 sum(additive_identity,multiply(A,additive_identity),additive_identity). [hyper(21,a,14,a,b,14,a,c,2,a,d,12,a),rewrite([50(2)])].
% 2.72/3.00 248 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)])].
% 2.72/3.00 300 product(x_plus_y,x__plus_y_plus_z,add(x,multiply(y,y_plus_z))). [hyper(25,a,7,a,b,6,a,c,14,a,d,13,a)].
% 2.72/3.00 321 product(A,A,add(A,multiply(additive_identity,additive_identity))). [hyper(25,a,2,a,b,2,a,c,14,a,d,13,a)].
% 2.72/3.00 945 add(A,B) = add(B,A). [hyper(19,a,13,a,b,29,a)].
% 2.72/3.00 956 -sum(y_plus_z,x,x_plus_y__plus_z) # answer(prove_equality). [ur(17,b,45,a)].
% 2.72/3.00 1270 product(A,add(A,B),add(A,multiply(B,additive_identity))). [hyper(27,a,1,a,b,13,a,c,34,a,d,13,a),rewrite([945(1),945(4)])].
% 2.72/3.00 1576 multiply(A,B) = multiply(B,A). [hyper(20,a,14,a,b,34,a)].
% 2.72/3.00 1711 product(A,additive_identity,additive_identity). [hyper(25,a,13,a,b,13,a,c,14,a,d,72,a),rewrite([945(2),41(2),41(3)])].
% 2.72/3.00 1729 product(additive_identity,A,add(multiply(A,additive_identity),multiply(A,multiply(B,additive_identity)))). [hyper(24,a,14,a,b,14,a,c,72,a,d,13,a),rewrite([1576(3),1576(6)])].
% 2.72/3.00 1736 multiply(A,additive_identity) = additive_identity. [hyper(19,a,1,a,b,72,a)].
% 2.72/3.00 1737 product(additive_identity,A,additive_identity). [back_rewrite(1729),rewrite([1736(3),1736(4),1736(4),41(4)])].
% 2.72/3.00 1739 product(A,add(A,B),A). [back_rewrite(1270),rewrite([1736(3),41(3)])].
% 2.72/3.00 1746 product(A,A,A). [back_rewrite(321),rewrite([1736(3),41(2)])].
% 2.72/3.00 1770 product(y_plus_z,y,y). [hyper(27,a,33,a,b,1,a,c,1711,a,d,1,a)].
% 2.72/3.00 1778 product(x_plus_y,x,x). [hyper(27,a,31,a,b,1,a,c,1711,a,d,1,a)].
% 2.72/3.00 1792 product(x_plus_y,y,y). [hyper(27,a,7,a,b,1,a,c,1711,a,d,1,a)].
% 2.72/3.00 1800 product(y_plus_z,z,z). [hyper(27,a,5,a,b,1,a,c,1711,a,d,1,a)].
% 2.72/3.00 1905 product(x_plus_y,x_plus_y__plus_z,x_plus_y). [hyper(27,a,1,a,b,30,a,c,1737,a,d,1,a)].
% 2.72/3.00 1912 product(y_plus_z,x__plus_y_plus_z,y_plus_z). [hyper(27,a,1,a,b,6,a,c,1737,a,d,1,a)].
% 2.72/3.00 2187 sum(multiplicative_identity,A,multiply(multiplicative_identity,add(A,multiplicative_identity))). [hyper(23,a,1746,a,b,4,a,c,13,a,d,14,a),rewrite([945(3),1576(5)])].
% 2.72/3.00 2207 multiply(A,A) = A. [hyper(20,a,14,a,b,1746,a)].
% 2.72/3.00 2298 multiply(y,y_plus_z) = y. [hyper(20,a,14,a,b,1770,a),rewrite([1576(3)])].
% 2.72/3.00 2299 product(x_plus_y,x__plus_y_plus_z,x_plus_y). [back_rewrite(300),rewrite([2298(6),38(5)])].
% 2.72/3.00 2866 product(x_plus_y__plus_z,y_plus_z,y_plus_z). [hyper(27,a,13,a,b,13,a,c,1792,a,d,5,a),rewrite([37(3),40(4)])].
% 2.72/3.00 5032 add(A,multiplicative_identity) = multiplicative_identity. [hyper(20,a,3,a,b,248,a)].
% 2.72/3.00 5033 sum(multiplicative_identity,A,multiplicative_identity). [back_rewrite(2187),rewrite([5032(4),2207(4)])].
% 2.72/3.00 5376 sum(x__plus_y_plus_z,y_plus_z,x__plus_y_plus_z). [hyper(23,a,3,a,b,1912,a,c,5033,a,d,3,a)].
% 2.72/3.00 5382 sum(x_plus_y__plus_z,x_plus_y,x_plus_y__plus_z). [hyper(23,a,3,a,b,1905,a,c,5033,a,d,3,a)].
% 2.72/3.00 9634 sum(x_plus_y__plus_z,x,x_plus_y__plus_z). [hyper(26,a,5382,a,b,13,a,c,1778,a,d,1739,a)].
% 2.72/3.00 9638 sum(x__plus_y_plus_z,z,x__plus_y_plus_z). [hyper(26,a,5376,a,b,13,a,c,1800,a,d,1739,a)].
% 2.72/3.00 10477 -product(x_plus_y__plus_z,x__plus_y_plus_z,x_plus_y__plus_z) # answer(prove_equality). [ur(28,a,9634,a,b,32,a,c,2866,a,e,956,a)].
% 2.72/3.00 10597 product(x_plus_y__plus_z,x__plus_y_plus_z,x_plus_y__plus_z). [hyper(27,a,13,a,b,9638,a,c,2299,a,d,13,a),rewrite([37(3),37(5)])].
% 2.72/3.00 10598 $F # answer(prove_equality). [resolve(10597,a,10477,a)].
% 2.72/3.00
% 2.72/3.00 % SZS output end Refutation
% 2.72/3.00 ============================== end of proof ==========================
% 2.72/3.00
% 2.72/3.00 ============================== STATISTICS ============================
% 2.72/3.00
% 2.72/3.00 Given=268. Generated=84939. Kept=10596. proofs=1.
% 2.72/3.00 Usable=244. Sos=6122. Demods=62. Limbo=39, Disabled=4217. Hints=0.
% 2.72/3.00 Megabytes=6.30.
% 2.72/3.00 User_CPU=1.94, System_CPU=0.06, Wall_clock=2.
% 2.72/3.00
% 2.72/3.00 ============================== end of statistics =====================
% 2.72/3.00
% 2.72/3.00 ============================== end of search =========================
% 2.72/3.00
% 2.72/3.00 THEOREM PROVED
% 2.72/3.00 % SZS status Unsatisfiable
% 2.72/3.00
% 2.72/3.00 Exiting with 1 proof.
% 2.72/3.00
% 2.72/3.00 Process 32484 exit (max_proofs) Thu Jun 2 00:09:48 2022
% 2.72/3.00 Prover9 interrupted
%------------------------------------------------------------------------------