TSTP Solution File: RNG008-5 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG008-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 1.55s 1.87s
% Output : Refutation 1.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG008-5 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon May 30 18:00:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.55/1.87 ============================== Prover9 ===============================
% 1.55/1.87 Prover9 (32) version 2009-11A, November 2009.
% 1.55/1.87 Process 29783 was started by sandbox on n026.cluster.edu,
% 1.55/1.87 Mon May 30 18:00:56 2022
% 1.55/1.87 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29630_n026.cluster.edu".
% 1.55/1.87 ============================== end of head ===========================
% 1.55/1.87
% 1.55/1.87 ============================== INPUT =================================
% 1.55/1.87
% 1.55/1.87 % Reading from file /tmp/Prover9_29630_n026.cluster.edu
% 1.55/1.87
% 1.55/1.87 set(prolog_style_variables).
% 1.55/1.87 set(auto2).
% 1.55/1.87 % set(auto2) -> set(auto).
% 1.55/1.87 % set(auto) -> set(auto_inference).
% 1.55/1.87 % set(auto) -> set(auto_setup).
% 1.55/1.87 % set(auto_setup) -> set(predicate_elim).
% 1.55/1.87 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.55/1.87 % set(auto) -> set(auto_limits).
% 1.55/1.87 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.55/1.87 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.55/1.87 % set(auto) -> set(auto_denials).
% 1.55/1.87 % set(auto) -> set(auto_process).
% 1.55/1.87 % set(auto2) -> assign(new_constants, 1).
% 1.55/1.87 % set(auto2) -> assign(fold_denial_max, 3).
% 1.55/1.87 % set(auto2) -> assign(max_weight, "200.000").
% 1.55/1.87 % set(auto2) -> assign(max_hours, 1).
% 1.55/1.87 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.55/1.87 % set(auto2) -> assign(max_seconds, 0).
% 1.55/1.87 % set(auto2) -> assign(max_minutes, 5).
% 1.55/1.87 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.55/1.87 % set(auto2) -> set(sort_initial_sos).
% 1.55/1.87 % set(auto2) -> assign(sos_limit, -1).
% 1.55/1.87 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.55/1.87 % set(auto2) -> assign(max_megs, 400).
% 1.55/1.87 % set(auto2) -> assign(stats, some).
% 1.55/1.87 % set(auto2) -> clear(echo_input).
% 1.55/1.87 % set(auto2) -> set(quiet).
% 1.55/1.87 % set(auto2) -> clear(print_initial_clauses).
% 1.55/1.87 % set(auto2) -> clear(print_given).
% 1.55/1.87 assign(lrs_ticks,-1).
% 1.55/1.87 assign(sos_limit,10000).
% 1.55/1.87 assign(order,kbo).
% 1.55/1.87 set(lex_order_vars).
% 1.55/1.87 clear(print_given).
% 1.55/1.87
% 1.55/1.87 % formulas(sos). % not echoed (26 formulas)
% 1.55/1.87
% 1.55/1.87 ============================== end of input ==========================
% 1.55/1.87
% 1.55/1.87 % From the command line: assign(max_seconds, 300).
% 1.55/1.87
% 1.55/1.87 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.55/1.87
% 1.55/1.87 % Formulas that are not ordinary clauses:
% 1.55/1.87
% 1.55/1.87 ============================== end of process non-clausal formulas ===
% 1.55/1.87
% 1.55/1.87 ============================== PROCESS INITIAL CLAUSES ===============
% 1.55/1.87
% 1.55/1.87 ============================== PREDICATE ELIMINATION =================
% 1.55/1.87
% 1.55/1.87 ============================== end predicate elimination =============
% 1.55/1.87
% 1.55/1.87 Auto_denials:
% 1.55/1.87 % copying label prove_b_times_a_is_c to answer in negative clause
% 1.55/1.87
% 1.55/1.87 Term ordering decisions:
% 1.55/1.87
% 1.55/1.87 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (10).
% 1.55/1.87 Function symbol KB weights: additive_identity=1. a=1. b=1. c=1. add=1. multiply=1. additive_inverse=0.
% 1.55/1.87
% 1.55/1.87 ============================== end of process initial clauses ========
% 1.55/1.87
% 1.55/1.87 ============================== CLAUSES FOR SEARCH ====================
% 1.55/1.87
% 1.55/1.87 ============================== end of clauses for search =============
% 1.55/1.87
% 1.55/1.87 ============================== SEARCH ================================
% 1.55/1.87
% 1.55/1.87 % Starting search at 0.01 seconds.
% 1.55/1.87
% 1.55/1.87 ============================== PROOF =================================
% 1.55/1.87 % SZS status Unsatisfiable
% 1.55/1.87 % SZS output start Refutation
% 1.55/1.87
% 1.55/1.87 % Proof 1 at 0.84 (+ 0.03) seconds: prove_b_times_a_is_c.
% 1.55/1.87 % Length of proof is 55.
% 1.55/1.87 % Level of proof is 8.
% 1.55/1.87 % Maximum clause weight is 20.000.
% 1.55/1.87 % Given clauses 149.
% 1.55/1.87
% 1.55/1.87 1 sum(additive_identity,A,A) # label(additive_identity1) # label(axiom). [assumption].
% 1.55/1.87 2 sum(A,additive_identity,A) # label(additive_identity2) # label(axiom). [assumption].
% 1.55/1.87 3 product(A,additive_identity,additive_identity) # label(multiply_additive_id1) # label(axiom). [assumption].
% 1.55/1.87 4 product(additive_identity,A,additive_identity) # label(multiply_additive_id2) # label(axiom). [assumption].
% 1.55/1.87 5 product(A,A,A) # label(x_squared_is_x) # label(hypothesis). [assumption].
% 1.55/1.87 6 product(a,b,c) # label(a_times_b_is_c) # label(hypothesis). [assumption].
% 1.55/1.87 7 sum(additive_inverse(A),A,additive_identity) # label(left_inverse) # label(axiom). [assumption].
% 1.55/1.87 8 sum(A,additive_inverse(A),additive_identity) # label(right_inverse) # label(axiom). [assumption].
% 1.55/1.87 9 product(A,B,multiply(A,B)) # label(closure_of_multiplication) # label(axiom). [assumption].
% 1.55/1.87 10 sum(A,B,add(A,B)) # label(closure_of_addition) # label(axiom). [assumption].
% 1.55/1.87 11 sum(additive_inverse(additive_inverse(A)),additive_identity,A) # label(additive_inverse_additive_inverse) # label(axiom). [assumption].
% 1.55/1.87 12 product(A,additive_inverse(B),additive_inverse(multiply(A,B))) # label(multiply_additive_inverse) # label(axiom). [assumption].
% 1.55/1.87 13 sum(additive_inverse(A),additive_inverse(B),additive_inverse(add(A,B))) # label(distribute_additive_inverse) # label(axiom). [assumption].
% 1.55/1.87 14 -product(b,a,c) # label(prove_b_times_a_is_c) # label(negated_conjecture) # answer(prove_b_times_a_is_c). [assumption].
% 1.55/1.87 15 -sum(A,B,C) | sum(B,A,C) # label(commutativity_of_addition) # label(axiom). [assumption].
% 1.55/1.87 16 -sum(A,B,C) | -sum(A,B,D) | C = D # label(addition_is_well_defined) # label(axiom). [assumption].
% 1.55/1.87 17 -product(A,B,C) | -product(A,B,D) | C = D # label(multiplication_is_well_defined) # label(axiom). [assumption].
% 1.55/1.87 18 -sum(A,B,C) | -sum(B,D,E) | -sum(C,D,F) | sum(A,E,F) # label(associativity_of_addition1) # label(axiom). [assumption].
% 1.55/1.87 19 -sum(A,B,C) | -sum(B,D,E) | -sum(A,E,F) | sum(C,D,F) # label(associativity_of_addition2) # label(axiom). [assumption].
% 1.55/1.87 23 -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].
% 1.55/1.87 24 -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].
% 1.55/1.87 25 -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].
% 1.55/1.87 28 sum(A,B,add(B,A)). [hyper(15,a,10,a)].
% 1.55/1.87 29 additive_inverse(add(A,B)) = add(additive_inverse(A),additive_inverse(B)). [hyper(16,a,13,a,b,10,a)].
% 1.55/1.87 33 additive_inverse(additive_inverse(A)) = A. [hyper(16,a,11,a,b,2,a),flip(a)].
% 1.55/1.87 34 add(A,additive_identity) = A. [hyper(16,a,10,a,b,11,a),rewrite([33(2)])].
% 1.55/1.87 35 add(A,additive_inverse(A)) = additive_identity. [hyper(16,a,10,a,b,8,a)].
% 1.55/1.87 37 add(additive_identity,A) = A. [hyper(16,a,10,a,b,1,a)].
% 1.55/1.87 38 additive_inverse(additive_identity) = additive_identity. [hyper(16,a,8,a,b,13,a),rewrite([35(3)]),flip(a)].
% 1.55/1.87 39 additive_inverse(multiply(A,B)) = multiply(A,additive_inverse(B)). [hyper(17,a,12,a,b,9,a)].
% 1.55/1.87 43 multiply(A,A) = A. [hyper(17,a,9,a,b,5,a)].
% 1.55/1.87 44 multiply(additive_identity,A) = additive_identity. [hyper(17,a,9,a,b,4,a)].
% 1.55/1.87 45 multiply(A,additive_identity) = additive_identity. [hyper(17,a,9,a,b,3,a)].
% 1.55/1.87 51 sum(additive_inverse(A),add(A,B),B). [hyper(18,a,7,a,b,10,a,c,10,a),rewrite([37(4)])].
% 1.55/1.87 52 sum(add(A,B),C,add(A,add(B,C))). [hyper(19,a,10,a,b,10,a,c,10,a)].
% 1.55/1.87 111 product(a,add(a,b),add(a,c)). [hyper(23,a,5,a,b,6,a,c,10,a,d,10,a)].
% 1.55/1.87 113 -sum(multiply(b,a),additive_identity,c) # answer(prove_b_times_a_is_c). [ur(23,a,9,a,b,9,a,c,2,a,e,14,a),rewrite([45(6)])].
% 1.55/1.87 130 sum(additive_inverse(A),multiply(A,additive_inverse(A)),additive_identity). [hyper(24,a,5,a,b,9,a,c,7,a,d,9,a),rewrite([44(6)])].
% 1.55/1.87 182 sum(add(A,B),additive_inverse(A),B). [hyper(19,a,28,a,b,8,a,c,28,a),rewrite([37(4)])].
% 1.55/1.87 218 add(A,B) = add(B,A). [hyper(16,a,10,a,b,28,a)].
% 1.55/1.87 237 -sum(multiply(b,a),additive_inverse(c),additive_identity) # answer(prove_b_times_a_is_c). [ur(18,b,7,a,c,1,a,d,113,a)].
% 1.55/1.87 342 add(additive_identity,additive_inverse(A)) = additive_inverse(A). [para(38(a,1),29(a,2,1)),rewrite([218(2),34(2)]),flip(a)].
% 1.55/1.87 428 multiply(A,additive_inverse(A)) = additive_inverse(A). [para(43(a,1),39(a,1,1)),flip(a)].
% 1.55/1.87 433 sum(additive_inverse(A),additive_inverse(A),additive_identity). [back_rewrite(130),rewrite([428(3)])].
% 1.55/1.87 435 -product(additive_inverse(b),a,additive_inverse(c)) # answer(prove_b_times_a_is_c). [ur(24,a,9,a,c,8,a,d,4,a,e,237,a)].
% 1.55/1.87 951 sum(additive_identity,additive_inverse(A),A). [hyper(19,a,8,a,b,433,a,c,10,a),rewrite([34(4)])].
% 1.55/1.87 1024 add(additive_inverse(A),add(B,A)) = B. [hyper(16,a,51,a,b,10,a),rewrite([218(2)]),flip(a)].
% 1.55/1.87 1045 -product(additive_inverse(b),add(a,b),add(b,additive_inverse(c))) # answer(prove_b_times_a_is_c). [ur(23,a,5,a,c,51,a,d,51,a,e,435,a),rewrite([218(5)])].
% 1.55/1.87 1290 additive_inverse(A) = A. [hyper(16,a,10,a,b,951,a),rewrite([342(3)])].
% 1.55/1.87 1339 -product(b,add(a,b),add(b,c)) # answer(prove_b_times_a_is_c). [back_rewrite(1045),rewrite([1290(2),1290(7)])].
% 1.55/1.87 1347 add(A,add(A,B)) = B. [back_rewrite(1024),rewrite([1290(1),218(1)])].
% 1.55/1.87 1405 sum(add(A,B),A,B). [back_rewrite(182),rewrite([1290(2)])].
% 1.55/1.87 1516 add(A,add(B,C)) = add(C,add(A,B)). [hyper(16,a,10,a,b,52,a),rewrite([218(2)]),flip(a)].
% 1.55/1.87 6557 product(b,add(a,b),add(b,c)). [hyper(25,a,5,a,b,111,a,c,1405,a,d,52,a),rewrite([1516(10,R),218(9),1347(11)])].
% 1.55/1.87 6558 $F # answer(prove_b_times_a_is_c). [resolve(6557,a,1339,a)].
% 1.55/1.87
% 1.55/1.87 % SZS output end Refutation
% 1.55/1.87 ============================== end of proof ==========================
% 1.55/1.87
% 1.55/1.87 ============================== STATISTICS ============================
% 1.55/1.87
% 1.55/1.87 Given=149. Generated=40721. Kept=6557. proofs=1.
% 1.55/1.87 Usable=102. Sos=3832. Demods=29. Limbo=7, Disabled=2641. Hints=0.
% 1.55/1.87 Megabytes=4.83.
% 1.55/1.87 User_CPU=0.84, System_CPU=0.03, Wall_clock=1.
% 1.55/1.87
% 1.55/1.87 ============================== end of statistics =====================
% 1.55/1.87
% 1.55/1.87 ============================== end of search =========================
% 1.55/1.87
% 1.55/1.87 THEOREM PROVED
% 1.55/1.87 % SZS status Unsatisfiable
% 1.55/1.87
% 1.55/1.87 Exiting with 1 proof.
% 1.55/1.87
% 1.55/1.87 Process 29783 exit (max_proofs) Mon May 30 18:00:57 2022
% 1.55/1.87 Prover9 interrupted
%------------------------------------------------------------------------------