TSTP Solution File: ALG002-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 17:53:33 EDT 2022
% Result : Unsatisfiable 0.71s 1.04s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ALG002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n028.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 8 11:25:01 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.71/1.04 ============================== Prover9 ===============================
% 0.71/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.71/1.04 Process 13803 was started by sandbox2 on n028.cluster.edu,
% 0.71/1.04 Wed Jun 8 11:25:02 2022
% 0.71/1.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_13572_n028.cluster.edu".
% 0.71/1.04 ============================== end of head ===========================
% 0.71/1.04
% 0.71/1.04 ============================== INPUT =================================
% 0.71/1.04
% 0.71/1.04 % Reading from file /tmp/Prover9_13572_n028.cluster.edu
% 0.71/1.04
% 0.71/1.04 set(prolog_style_variables).
% 0.71/1.04 set(auto2).
% 0.71/1.04 % set(auto2) -> set(auto).
% 0.71/1.04 % set(auto) -> set(auto_inference).
% 0.71/1.04 % set(auto) -> set(auto_setup).
% 0.71/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.71/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/1.04 % set(auto) -> set(auto_limits).
% 0.71/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/1.04 % set(auto) -> set(auto_denials).
% 0.71/1.04 % set(auto) -> set(auto_process).
% 0.71/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.71/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.71/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.71/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.71/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.71/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.71/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.71/1.04 % set(auto2) -> assign(stats, some).
% 0.71/1.04 % set(auto2) -> clear(echo_input).
% 0.71/1.04 % set(auto2) -> set(quiet).
% 0.71/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.71/1.04 % set(auto2) -> clear(print_given).
% 0.71/1.04 assign(lrs_ticks,-1).
% 0.71/1.04 assign(sos_limit,10000).
% 0.71/1.04 assign(order,kbo).
% 0.71/1.04 set(lex_order_vars).
% 0.71/1.04 clear(print_given).
% 0.71/1.04
% 0.71/1.04 % formulas(sos). % not echoed (14 formulas)
% 0.71/1.04
% 0.71/1.04 ============================== end of input ==========================
% 0.71/1.04
% 0.71/1.04 % From the command line: assign(max_seconds, 300).
% 0.71/1.04
% 0.71/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/1.04
% 0.71/1.04 % Formulas that are not ordinary clauses:
% 0.71/1.04
% 0.71/1.04 ============================== end of process non-clausal formulas ===
% 0.71/1.04
% 0.71/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.71/1.04
% 0.71/1.04 ============================== PREDICATE ELIMINATION =================
% 0.71/1.04
% 0.71/1.04 ============================== end predicate elimination =============
% 0.71/1.04
% 0.71/1.04 Auto_denials: (non-Horn, no changes).
% 0.71/1.04
% 0.71/1.04 Term ordering decisions:
% 0.71/1.04 Function symbol KB weights: additive_identity=1. multiplicative_identity=1. a=1. additive_inverse=1. multiplicative_inverse=1.
% 0.71/1.04
% 0.71/1.04 ============================== end of process initial clauses ========
% 0.71/1.04
% 0.71/1.04 ============================== CLAUSES FOR SEARCH ====================
% 0.71/1.04
% 0.71/1.04 ============================== end of clauses for search =============
% 0.71/1.04
% 0.71/1.04 ============================== SEARCH ================================
% 0.71/1.04
% 0.71/1.04 % Starting search at 0.01 seconds.
% 0.71/1.04
% 0.71/1.04 ============================== PROOF =================================
% 0.71/1.04 % SZS status Unsatisfiable
% 0.71/1.04 % SZS output start Refutation
% 0.71/1.04
% 0.71/1.04 % Proof 1 at 0.07 (+ 0.01) seconds.
% 0.71/1.04 % Length of proof is 34.
% 0.71/1.04 % Level of proof is 7.
% 0.71/1.04 % Maximum clause weight is 12.000.
% 0.71/1.04 % Given clauses 124.
% 0.71/1.04
% 0.71/1.04 1 greater_than_0(a) # label(a_greater_than_0) # label(hypothesis). [assumption].
% 0.71/1.04 2 product(A,multiplicative_identity,A) # label(right_identity) # label(axiom). [assumption].
% 0.71/1.04 3 product(A,multiplicative_inverse(A),multiplicative_identity) | product(A,A,additive_identity) # label(inverse_and_identity) # label(axiom). [assumption].
% 0.71/1.04 4 greater_than_0(A) | product(A,A,additive_identity) | greater_than_0(additive_inverse(A)) # label(product_and_inverse) # label(axiom). [assumption].
% 0.71/1.04 5 -greater_than_0(multiplicative_inverse(a)) # label(prove_a_inverse_greater_than_0) # label(negated_conjecture). [assumption].
% 0.71/1.04 6 -product(multiplicative_identity,multiplicative_identity,additive_identity) # label(not_abelian) # label(axiom). [assumption].
% 0.71/1.04 7 -greater_than_0(A) | -greater_than_0(additive_inverse(A)) # label(inverse_greater_than_0) # label(axiom). [assumption].
% 0.71/1.04 8 -greater_than_0(A) | -product(A,A,additive_identity) # label(greater_than_0_square) # label(axiom). [assumption].
% 0.71/1.04 9 -product(A,B,C) | product(B,A,C) # label(commutativity_of_product) # label(axiom). [assumption].
% 0.71/1.04 10 -product(A,B,C) | product(additive_inverse(A),additive_inverse(B),C) # label(product_of_inverses1) # label(axiom). [assumption].
% 0.71/1.04 11 product(A,B,C) | -product(additive_inverse(A),additive_inverse(B),C) # label(product_of_inverses2) # label(axiom). [assumption].
% 0.71/1.04 12 -product(A,B,C) | product(A,additive_inverse(B),additive_inverse(C)) # label(product_to_inverse) # label(axiom). [assumption].
% 0.71/1.04 13 -product(A,B,C) | -greater_than_0(A) | -greater_than_0(B) | greater_than_0(C) # label(product_and_greater_than_0) # label(axiom). [assumption].
% 0.71/1.04 14 -product(A,B,C) | -product(A,A,additive_identity) | product(C,C,additive_identity) # label(square_to_0) # label(axiom). [assumption].
% 0.71/1.04 15 -product(A,A,B) | -greater_than_0(A) | greater_than_0(B). [factor(13,b,c)].
% 0.71/1.04 17 greater_than_0(multiplicative_identity) | greater_than_0(additive_inverse(multiplicative_identity)). [resolve(6,a,4,b)].
% 0.71/1.04 19 -product(a,a,additive_identity). [ur(8,a,1,a)].
% 0.71/1.04 20 product(multiplicative_inverse(A),A,multiplicative_identity) | product(A,A,additive_identity). [resolve(9,a,3,a)].
% 0.71/1.04 24 product(additive_inverse(A),additive_inverse(multiplicative_identity),A). [resolve(10,a,2,a)].
% 0.71/1.04 25 product(A,A,additive_identity) | greater_than_0(additive_inverse(A)) | greater_than_0(additive_inverse(additive_inverse(A))). [resolve(11,b,4,b)].
% 0.71/1.04 28 product(A,additive_inverse(multiplicative_inverse(A)),additive_inverse(multiplicative_identity)) | product(A,A,additive_identity). [resolve(12,a,3,a)].
% 0.71/1.04 29 product(A,additive_inverse(multiplicative_identity),additive_inverse(A)). [resolve(12,a,2,a)].
% 0.71/1.04 39 -greater_than_0(additive_inverse(multiplicative_identity)) | greater_than_0(multiplicative_identity). [resolve(24,a,15,a)].
% 0.71/1.04 42 product(additive_inverse(additive_inverse(A)),additive_inverse(additive_inverse(multiplicative_identity)),A). [resolve(24,a,10,a)].
% 0.71/1.04 43 greater_than_0(multiplicative_identity). [resolve(39,a,17,b),merge(b)].
% 0.71/1.04 50 -greater_than_0(additive_inverse(multiplicative_identity)). [ur(7,a,43,a)].
% 0.71/1.04 51 product(A,A,additive_identity) | -product(multiplicative_inverse(A),multiplicative_inverse(A),additive_identity). [resolve(20,a,14,a),unit_del(c,6)].
% 0.71/1.04 62 product(A,multiplicative_identity,additive_inverse(additive_inverse(A))). [resolve(29,a,11,b)].
% 0.71/1.04 65 greater_than_0(additive_inverse(additive_inverse(multiplicative_identity))). [resolve(62,a,15,a),unit_del(a,43)].
% 0.71/1.04 233 -greater_than_0(additive_inverse(additive_inverse(multiplicative_inverse(a)))). [ur(13,a,42,a,c,65,a,d,5,a)].
% 0.71/1.04 502 product(A,A,additive_identity) | -greater_than_0(A) | -greater_than_0(additive_inverse(multiplicative_inverse(A))). [resolve(28,a,13,a),unit_del(d,50)].
% 0.71/1.04 532 -product(multiplicative_inverse(a),multiplicative_inverse(a),additive_identity). [ur(51,a,19,a)].
% 0.71/1.04 543 greater_than_0(additive_inverse(multiplicative_inverse(a))). [resolve(532,a,25,a),unit_del(b,233)].
% 0.71/1.04 1233 $F. [resolve(502,c,543,a),unit_del(a,19),unit_del(b,1)].
% 0.71/1.04
% 0.71/1.04 % SZS output end Refutation
% 0.71/1.04 ============================== end of proof ==========================
% 0.71/1.04
% 0.71/1.04 ============================== STATISTICS ============================
% 0.71/1.04
% 0.71/1.04 Given=124. Generated=1860. Kept=1232. proofs=1.
% 0.71/1.04 Usable=122. Sos=1104. Demods=0. Limbo=1, Disabled=19. Hints=0.
% 0.71/1.04 Megabytes=0.84.
% 0.71/1.04 User_CPU=0.07, System_CPU=0.01, Wall_clock=0.
% 0.71/1.04
% 0.71/1.04 ============================== end of statistics =====================
% 0.71/1.04
% 0.71/1.04 ============================== end of search =========================
% 0.71/1.04
% 0.71/1.04 THEOREM PROVED
% 0.71/1.04 % SZS status Unsatisfiable
% 0.71/1.04
% 0.71/1.04 Exiting with 1 proof.
% 0.71/1.04
% 0.71/1.04 Process 13803 exit (max_proofs) Wed Jun 8 11:25:02 2022
% 0.71/1.04 Prover9 interrupted
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