TSTP Solution File: RNG004-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : RNG004-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 1.27s 1.52s
% Output : Refutation 1.27s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : RNG004-2 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n019.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 22:19:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.27/1.52 ============================== Prover9 ===============================
% 1.27/1.52 Prover9 (32) version 2009-11A, November 2009.
% 1.27/1.52 Process 9480 was started by sandbox on n019.cluster.edu,
% 1.27/1.52 Mon May 30 22:19:56 2022
% 1.27/1.52 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_9326_n019.cluster.edu".
% 1.27/1.52 ============================== end of head ===========================
% 1.27/1.52
% 1.27/1.52 ============================== INPUT =================================
% 1.27/1.52
% 1.27/1.52 % Reading from file /tmp/Prover9_9326_n019.cluster.edu
% 1.27/1.52
% 1.27/1.52 set(prolog_style_variables).
% 1.27/1.52 set(auto2).
% 1.27/1.52 % set(auto2) -> set(auto).
% 1.27/1.52 % set(auto) -> set(auto_inference).
% 1.27/1.52 % set(auto) -> set(auto_setup).
% 1.27/1.52 % set(auto_setup) -> set(predicate_elim).
% 1.27/1.52 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.27/1.52 % set(auto) -> set(auto_limits).
% 1.27/1.52 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.27/1.52 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.27/1.52 % set(auto) -> set(auto_denials).
% 1.27/1.52 % set(auto) -> set(auto_process).
% 1.27/1.52 % set(auto2) -> assign(new_constants, 1).
% 1.27/1.52 % set(auto2) -> assign(fold_denial_max, 3).
% 1.27/1.52 % set(auto2) -> assign(max_weight, "200.000").
% 1.27/1.52 % set(auto2) -> assign(max_hours, 1).
% 1.27/1.52 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.27/1.52 % set(auto2) -> assign(max_seconds, 0).
% 1.27/1.52 % set(auto2) -> assign(max_minutes, 5).
% 1.27/1.52 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.27/1.52 % set(auto2) -> set(sort_initial_sos).
% 1.27/1.52 % set(auto2) -> assign(sos_limit, -1).
% 1.27/1.52 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.27/1.52 % set(auto2) -> assign(max_megs, 400).
% 1.27/1.52 % set(auto2) -> assign(stats, some).
% 1.27/1.52 % set(auto2) -> clear(echo_input).
% 1.27/1.52 % set(auto2) -> set(quiet).
% 1.27/1.52 % set(auto2) -> clear(print_initial_clauses).
% 1.27/1.52 % set(auto2) -> clear(print_given).
% 1.27/1.52 assign(lrs_ticks,-1).
% 1.27/1.52 assign(sos_limit,10000).
% 1.27/1.52 assign(order,kbo).
% 1.27/1.52 set(lex_order_vars).
% 1.27/1.52 clear(print_given).
% 1.27/1.52
% 1.27/1.52 % formulas(sos). % not echoed (22 formulas)
% 1.27/1.52
% 1.27/1.52 ============================== end of input ==========================
% 1.27/1.52
% 1.27/1.52 % From the command line: assign(max_seconds, 300).
% 1.27/1.52
% 1.27/1.52 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.27/1.52
% 1.27/1.52 % Formulas that are not ordinary clauses:
% 1.27/1.52
% 1.27/1.52 ============================== end of process non-clausal formulas ===
% 1.27/1.52
% 1.27/1.52 ============================== PROCESS INITIAL CLAUSES ===============
% 1.27/1.52
% 1.27/1.52 ============================== PREDICATE ELIMINATION =================
% 1.27/1.52
% 1.27/1.52 ============================== end predicate elimination =============
% 1.27/1.52
% 1.27/1.52 Auto_denials:
% 1.27/1.52 % copying label prove_c_equals_d to answer in negative clause
% 1.27/1.52
% 1.27/1.52 Term ordering decisions:
% 1.27/1.52
% 1.27/1.52 % Assigning unary symbol additive_inverse kb_weight 0 and highest precedence (11).
% 1.27/1.52 Function symbol KB weights: additive_identity=1. a=1. b=1. c=1. d=1. add=1. multiply=1. additive_inverse=0.
% 1.27/1.52
% 1.27/1.52 ============================== end of process initial clauses ========
% 1.27/1.52
% 1.27/1.52 ============================== CLAUSES FOR SEARCH ====================
% 1.27/1.52
% 1.27/1.52 ============================== end of clauses for search =============
% 1.27/1.52
% 1.27/1.52 ============================== SEARCH ================================
% 1.27/1.52
% 1.27/1.52 % Starting search at 0.01 seconds.
% 1.27/1.52
% 1.27/1.52 ============================== PROOF =================================
% 1.27/1.52 % SZS status Unsatisfiable
% 1.27/1.52 % SZS output start Refutation
% 1.27/1.52
% 1.27/1.52 % Proof 1 at 0.49 (+ 0.02) seconds: prove_c_equals_d.
% 1.27/1.52 % Length of proof is 37.
% 1.27/1.52 % Level of proof is 6.
% 1.27/1.52 % Maximum clause weight is 20.000.
% 1.27/1.52 % Given clauses 110.
% 1.27/1.52
% 1.27/1.52 1 sum(additive_identity,A,A) # label(additive_identity1) # label(axiom). [assumption].
% 1.27/1.52 2 sum(A,additive_identity,A) # label(additive_identity2) # label(axiom). [assumption].
% 1.27/1.52 3 product(a,b,c) # label(a_times_b) # label(hypothesis). [assumption].
% 1.27/1.52 4 sum(additive_inverse(A),A,additive_identity) # label(left_inverse) # label(axiom). [assumption].
% 1.27/1.52 5 sum(A,additive_inverse(A),additive_identity) # label(right_inverse) # label(axiom). [assumption].
% 1.27/1.52 6 product(A,B,multiply(A,B)) # label(closure_of_multiplication) # label(axiom). [assumption].
% 1.27/1.52 7 sum(A,B,add(A,B)) # label(closure_of_addition) # label(axiom). [assumption].
% 1.27/1.52 8 product(additive_inverse(a),additive_inverse(b),d) # label(a_inverse_times_b_inverse) # label(hypothesis). [assumption].
% 1.27/1.52 9 c != d # label(prove_c_equals_d) # label(negated_conjecture) # answer(prove_c_equals_d). [assumption].
% 1.27/1.52 10 d != c # answer(prove_c_equals_d). [copy(9),flip(a)].
% 1.27/1.52 11 -sum(A,B,C) | sum(B,A,C) # label(commutativity_of_addition) # label(axiom). [assumption].
% 1.27/1.52 12 -sum(A,B,C) | -sum(A,B,D) | C = D # label(addition_is_well_defined) # label(axiom). [assumption].
% 1.27/1.52 13 -product(A,B,C) | -product(A,B,D) | C = D # label(multiplication_is_well_defined) # label(axiom). [assumption].
% 1.27/1.52 14 -sum(A,B,C) | -sum(A,D,C) | B = D # label(cancellation1) # label(axiom). [assumption].
% 1.27/1.52 15 -sum(A,B,C) | -sum(D,B,C) | A = D # label(cancellation2) # label(axiom). [assumption].
% 1.27/1.52 17 -sum(A,B,C) | -sum(B,D,E) | -sum(A,E,F) | sum(C,D,F) # label(associativity_of_addition2) # label(axiom). [assumption].
% 1.27/1.52 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].
% 1.27/1.52 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].
% 1.27/1.52 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].
% 1.27/1.52 24 sum(A,B,add(B,A)). [hyper(11,a,7,a)].
% 1.27/1.52 27 add(A,additive_identity) = A. [hyper(12,a,7,a,b,2,a)].
% 1.27/1.52 35 multiply(a,b) = c. [hyper(13,a,6,a,b,3,a)].
% 1.27/1.52 41 -sum(additive_inverse(c),d,additive_identity) # answer(prove_c_equals_d). [ur(14,b,4,a,c,10,a)].
% 1.27/1.52 56 sum(add(A,additive_inverse(B)),B,A). [hyper(17,a,7,a,b,4,a,c,7,a),rewrite([27(4)])].
% 1.27/1.52 80 sum(c,multiply(a,additive_identity),c). [hyper(20,a,6,a,b,6,a,c,2,a,d,3,a),rewrite([35(3)])].
% 1.27/1.52 86 sum(c,multiply(a,additive_inverse(b)),multiply(a,additive_identity)). [hyper(20,a,3,a,b,6,a,c,5,a,d,6,a)].
% 1.27/1.52 110 sum(d,multiply(additive_identity,additive_inverse(b)),d). [hyper(22,a,8,a,b,6,a,c,2,a,d,8,a)].
% 1.27/1.52 203 add(A,B) = add(B,A). [hyper(12,a,7,a,b,24,a)].
% 1.27/1.52 266 multiply(a,additive_identity) = additive_identity. [hyper(14,a,2,a,b,80,a),flip(a)].
% 1.27/1.52 270 sum(c,multiply(a,additive_inverse(b)),additive_identity). [back_rewrite(86),rewrite([266(8)])].
% 1.27/1.52 1739 add(additive_identity,additive_inverse(A)) = additive_inverse(A). [hyper(15,a,4,a,b,56,a),flip(a)].
% 1.27/1.52 2405 multiply(additive_identity,additive_inverse(b)) = additive_identity. [hyper(14,a,2,a,b,110,a),flip(a)].
% 1.27/1.52 2860 product(additive_identity,additive_inverse(b),additive_identity). [para(2405(a,1),6(a,3))].
% 1.27/1.52 2924 -product(a,additive_inverse(b),additive_inverse(c)) # answer(prove_c_equals_d). [ur(22,b,8,a,c,5,a,d,2860,a,e,41,a)].
% 1.27/1.52 4086 -sum(additive_identity,multiply(a,additive_inverse(b)),additive_inverse(c)) # answer(prove_c_equals_d). [ur(23,a,2860,a,b,6,a,c,1,a,e,2924,a)].
% 1.27/1.52 4318 sum(additive_identity,multiply(a,additive_inverse(b)),additive_inverse(c)). [hyper(17,a,4,a,b,270,a,c,7,a),rewrite([203(9),1739(9)])].
% 1.27/1.52 4319 $F # answer(prove_c_equals_d). [resolve(4318,a,4086,a)].
% 1.27/1.52
% 1.27/1.52 % SZS output end Refutation
% 1.27/1.52 ============================== end of proof ==========================
% 1.27/1.52
% 1.27/1.52 ============================== STATISTICS ============================
% 1.27/1.52
% 1.27/1.52 Given=110. Generated=19506. Kept=4317. proofs=1.
% 1.27/1.52 Usable=98. Sos=2373. Demods=34. Limbo=32, Disabled=1835. Hints=0.
% 1.27/1.52 Megabytes=2.85.
% 1.27/1.52 User_CPU=0.49, System_CPU=0.02, Wall_clock=1.
% 1.27/1.52
% 1.27/1.52 ============================== end of statistics =====================
% 1.27/1.52
% 1.27/1.52 ============================== end of search =========================
% 1.27/1.52
% 1.27/1.52 THEOREM PROVED
% 1.27/1.52 % SZS status Unsatisfiable
% 1.27/1.52
% 1.27/1.52 Exiting with 1 proof.
% 1.27/1.52
% 1.27/1.52 Process 9480 exit (max_proofs) Mon May 30 22:19:57 2022
% 1.27/1.52 Prover9 interrupted
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