TSTP Solution File: RNG004-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG004-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 20:39:08 EDT 2022
% Result : Unsatisfiable 1.25s 1.57s
% Output : Refutation 1.25s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n020.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon May 30 13:49:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.25/1.57 ============================== Prover9 ===============================
% 1.25/1.57 Prover9 (32) version 2009-11A, November 2009.
% 1.25/1.57 Process 27538 was started by sandbox on n020.cluster.edu,
% 1.25/1.57 Mon May 30 13:49:24 2022
% 1.25/1.57 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_27385_n020.cluster.edu".
% 1.25/1.57 ============================== end of head ===========================
% 1.25/1.57
% 1.25/1.57 ============================== INPUT =================================
% 1.25/1.57
% 1.25/1.57 % Reading from file /tmp/Prover9_27385_n020.cluster.edu
% 1.25/1.57
% 1.25/1.57 set(prolog_style_variables).
% 1.25/1.57 set(auto2).
% 1.25/1.57 % set(auto2) -> set(auto).
% 1.25/1.57 % set(auto) -> set(auto_inference).
% 1.25/1.57 % set(auto) -> set(auto_setup).
% 1.25/1.57 % set(auto_setup) -> set(predicate_elim).
% 1.25/1.57 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.25/1.57 % set(auto) -> set(auto_limits).
% 1.25/1.57 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.25/1.57 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.25/1.57 % set(auto) -> set(auto_denials).
% 1.25/1.57 % set(auto) -> set(auto_process).
% 1.25/1.57 % set(auto2) -> assign(new_constants, 1).
% 1.25/1.57 % set(auto2) -> assign(fold_denial_max, 3).
% 1.25/1.57 % set(auto2) -> assign(max_weight, "200.000").
% 1.25/1.57 % set(auto2) -> assign(max_hours, 1).
% 1.25/1.57 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.25/1.57 % set(auto2) -> assign(max_seconds, 0).
% 1.25/1.57 % set(auto2) -> assign(max_minutes, 5).
% 1.25/1.57 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.25/1.57 % set(auto2) -> set(sort_initial_sos).
% 1.25/1.57 % set(auto2) -> assign(sos_limit, -1).
% 1.25/1.57 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.25/1.57 % set(auto2) -> assign(max_megs, 400).
% 1.25/1.57 % set(auto2) -> assign(stats, some).
% 1.25/1.57 % set(auto2) -> clear(echo_input).
% 1.25/1.57 % set(auto2) -> set(quiet).
% 1.25/1.57 % set(auto2) -> clear(print_initial_clauses).
% 1.25/1.57 % set(auto2) -> clear(print_given).
% 1.25/1.57 assign(lrs_ticks,-1).
% 1.25/1.57 assign(sos_limit,10000).
% 1.25/1.57 assign(order,kbo).
% 1.25/1.57 set(lex_order_vars).
% 1.25/1.57 clear(print_given).
% 1.25/1.57
% 1.25/1.57 % formulas(sos). % not echoed (20 formulas)
% 1.25/1.57
% 1.25/1.57 ============================== end of input ==========================
% 1.25/1.57
% 1.25/1.57 % From the command line: assign(max_seconds, 300).
% 1.25/1.57
% 1.25/1.57 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.25/1.57
% 1.25/1.57 % Formulas that are not ordinary clauses:
% 1.25/1.57
% 1.25/1.57 ============================== end of process non-clausal formulas ===
% 1.25/1.57
% 1.25/1.57 ============================== PROCESS INITIAL CLAUSES ===============
% 1.25/1.57
% 1.25/1.57 ============================== PREDICATE ELIMINATION =================
% 1.25/1.57
% 1.25/1.57 ============================== end predicate elimination =============
% 1.25/1.57
% 1.25/1.57 Auto_denials:
% 1.25/1.57 % copying label prove_c_equals_d to answer in negative clause
% 1.25/1.57
% 1.25/1.57 Term ordering decisions:
% 1.25/1.57
% 1.25/1.57 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (11).
% 1.25/1.57 Function symbol KB weights: additive_identity=1. a=1. b=1. c=1. d=1. add=1. multiply=1. additive_inverse=0.
% 1.25/1.57
% 1.25/1.57 ============================== end of process initial clauses ========
% 1.25/1.57
% 1.25/1.57 ============================== CLAUSES FOR SEARCH ====================
% 1.25/1.57
% 1.25/1.57 ============================== end of clauses for search =============
% 1.25/1.57
% 1.25/1.57 ============================== SEARCH ================================
% 1.25/1.57
% 1.25/1.57 % Starting search at 0.01 seconds.
% 1.25/1.57
% 1.25/1.57 ============================== PROOF =================================
% 1.25/1.57 % SZS status Unsatisfiable
% 1.25/1.57 % SZS output start Refutation
% 1.25/1.57
% 1.25/1.57 % Proof 1 at 0.58 (+ 0.02) seconds: prove_c_equals_d.
% 1.25/1.57 % Length of proof is 51.
% 1.25/1.57 % Level of proof is 10.
% 1.25/1.57 % Maximum clause weight is 20.000.
% 1.25/1.57 % Given clauses 121.
% 1.25/1.57
% 1.25/1.57 1 sum(additive_identity,A,A) # label(additive_identity1) # label(axiom). [assumption].
% 1.25/1.57 2 sum(A,additive_identity,A) # label(additive_identity2) # label(axiom). [assumption].
% 1.25/1.57 3 product(a,b,c) # label(a_times_b) # label(hypothesis). [assumption].
% 1.25/1.57 4 sum(additive_inverse(A),A,additive_identity) # label(left_inverse) # label(axiom). [assumption].
% 1.25/1.57 5 sum(A,additive_inverse(A),additive_identity) # label(right_inverse) # label(axiom). [assumption].
% 1.25/1.57 6 product(A,B,multiply(A,B)) # label(closure_of_multiplication) # label(axiom). [assumption].
% 1.25/1.57 7 sum(A,B,add(A,B)) # label(closure_of_addition) # label(axiom). [assumption].
% 1.25/1.57 8 product(additive_inverse(a),additive_inverse(b),d) # label(a_inverse_times_b_inverse) # label(hypothesis). [assumption].
% 1.25/1.57 9 c != d # label(prove_c_equals_d) # label(negated_conjecture) # answer(prove_c_equals_d). [assumption].
% 1.25/1.57 10 d != c # answer(prove_c_equals_d). [copy(9),flip(a)].
% 1.25/1.57 11 -sum(A,B,C) | sum(B,A,C) # label(commutativity_of_addition) # label(axiom). [assumption].
% 1.25/1.57 12 -sum(A,B,C) | -sum(A,B,D) | C = D # label(addition_is_well_defined) # label(axiom). [assumption].
% 1.25/1.57 13 -product(A,B,C) | -product(A,B,D) | C = D # label(multiplication_is_well_defined) # label(axiom). [assumption].
% 1.25/1.57 14 -sum(A,B,C) | -sum(B,D,E) | -sum(C,D,F) | sum(A,E,F) # label(associativity_of_addition1) # label(axiom). [assumption].
% 1.25/1.57 15 -sum(A,B,C) | -sum(B,D,E) | -sum(A,E,F) | sum(C,D,F) # label(associativity_of_addition2) # label(axiom). [assumption].
% 1.25/1.57 18 -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].
% 1.25/1.57 19 -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].
% 1.25/1.57 20 -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].
% 1.25/1.57 21 -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].
% 1.25/1.57 22 sum(A,B,add(B,A)). [hyper(11,a,7,a)].
% 1.25/1.57 23 add(A,additive_inverse(A)) = additive_identity. [hyper(12,a,7,a,b,5,a)].
% 1.25/1.57 25 add(A,additive_identity) = A. [hyper(12,a,7,a,b,2,a)].
% 1.25/1.57 26 add(additive_identity,A) = A. [hyper(12,a,7,a,b,1,a)].
% 1.25/1.57 27 additive_inverse(additive_identity) = additive_identity. [hyper(12,a,5,a,b,1,a),flip(a)].
% 1.25/1.57 31 -sum(additive_identity,d,c) # answer(prove_c_equals_d). [ur(12,b,1,a,c,10,a(flip))].
% 1.25/1.57 33 multiply(a,b) = c. [hyper(13,a,6,a,b,3,a)].
% 1.25/1.57 42 sum(additive_inverse(A),add(A,B),B). [hyper(14,a,4,a,b,7,a,c,7,a),rewrite([26(4)])].
% 1.25/1.57 75 sum(c,multiply(a,additive_identity),c). [hyper(18,a,6,a,b,6,a,c,2,a,d,3,a),rewrite([33(3)])].
% 1.25/1.57 81 sum(c,multiply(a,additive_inverse(b)),multiply(a,additive_identity)). [hyper(18,a,3,a,b,6,a,c,5,a,d,6,a)].
% 1.25/1.57 117 sum(c,multiply(additive_identity,b),c). [hyper(20,a,6,a,b,6,a,c,2,a,d,3,a),rewrite([33(3)])].
% 1.25/1.57 193 sum(A,add(B,additive_inverse(A)),B). [hyper(14,a,5,a,b,22,a,c,22,a),rewrite([25(4)])].
% 1.25/1.57 204 add(A,B) = add(B,A). [hyper(12,a,7,a,b,22,a)].
% 1.25/1.57 291 sum(additive_identity,multiply(a,additive_identity),additive_identity). [hyper(15,a,7,a,b,75,a,c,4,a),rewrite([204(4),23(4)])].
% 1.25/1.57 304 sum(c,add(A,multiply(a,additive_identity)),add(A,c)). [hyper(14,a,75,a,b,7,a,c,7,a),rewrite([204(5),204(7)])].
% 1.25/1.57 382 sum(additive_identity,multiply(additive_identity,b),additive_identity). [hyper(15,a,7,a,b,117,a,c,4,a),rewrite([204(4),23(4)])].
% 1.25/1.57 498 multiply(a,additive_identity) = additive_identity. [hyper(12,a,1,a,b,291,a)].
% 1.25/1.57 504 sum(c,A,add(A,c)). [back_rewrite(304),rewrite([498(4),25(3)])].
% 1.25/1.57 505 sum(c,multiply(a,additive_inverse(b)),additive_identity). [back_rewrite(81),rewrite([498(8)])].
% 1.25/1.57 608 product(a,additive_identity,additive_identity). [para(498(a,1),6(a,3))].
% 1.25/1.57 615 product(a,additive_identity,multiply(additive_identity,additive_identity)). [hyper(21,a,6,a,b,608,a,c,1,a,d,2,a)].
% 1.25/1.57 742 -sum(A,d,add(A,c)) # answer(prove_c_equals_d). [ur(15,a,42,a,c,42,a,d,31,a),rewrite([25(2)])].
% 1.25/1.57 849 multiply(additive_identity,b) = additive_identity. [hyper(12,a,1,a,b,382,a)].
% 1.25/1.57 860 product(additive_identity,b,additive_identity). [para(849(a,1),6(a,3))].
% 1.25/1.57 1217 multiply(additive_identity,additive_identity) = additive_identity. [hyper(13,a,608,a,b,615,a),flip(a)].
% 1.25/1.57 1226 product(additive_identity,additive_identity,additive_identity). [para(1217(a,1),6(a,3))].
% 1.25/1.57 1356 -product(additive_identity,additive_inverse(b),add(c,multiply(a,additive_inverse(b)))) # answer(prove_c_equals_d). [ur(20,a,6,a,b,8,a,c,5,a,e,742,a),rewrite([204(9)])].
% 1.25/1.57 3925 sum(additive_identity,multiply(additive_identity,add(additive_identity,additive_inverse(b))),additive_identity). [hyper(18,a,860,a,b,6,a,c,193,a,d,1226,a)].
% 1.25/1.57 5486 add(c,multiply(a,additive_inverse(b))) = additive_identity. [hyper(12,a,504,a,b,505,a),rewrite([204(6)])].
% 1.25/1.57 5530 -product(additive_identity,additive_inverse(b),additive_identity) # answer(prove_c_equals_d). [back_rewrite(1356),rewrite([5486(9)])].
% 1.25/1.57 6050 -sum(additive_identity,multiply(additive_identity,add(additive_identity,additive_inverse(b))),additive_identity) # answer(prove_c_equals_d). [ur(19,a,1226,a,b,6,a,c,193,a,e,5530,a),rewrite([27(6),204(6)])].
% 1.25/1.57 6051 $F # answer(prove_c_equals_d). [resolve(6050,a,3925,a)].
% 1.25/1.57
% 1.25/1.57 % SZS output end Refutation
% 1.25/1.57 ============================== end of proof ==========================
% 1.25/1.57
% 1.25/1.57 ============================== STATISTICS ============================
% 1.25/1.57
% 1.25/1.57 Given=121. Generated=22448. Kept=6049. proofs=1.
% 1.25/1.57 Usable=95. Sos=3260. Demods=31. Limbo=102, Disabled=2611. Hints=0.
% 1.25/1.57 Megabytes=3.98.
% 1.25/1.57 User_CPU=0.58, System_CPU=0.02, Wall_clock=1.
% 1.25/1.57
% 1.25/1.57 ============================== end of statistics =====================
% 1.25/1.57
% 1.25/1.57 ============================== end of search =========================
% 1.25/1.57
% 1.25/1.57 THEOREM PROVED
% 1.25/1.57 % SZS status Unsatisfiable
% 1.25/1.57
% 1.25/1.57 Exiting with 1 proof.
% 1.25/1.57
% 1.25/1.57 Process 27538 exit (max_proofs) Mon May 30 13:49:25 2022
% 1.25/1.57 Prover9 interrupted
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