TSTP Solution File: GRP194+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 : Sat Jul 16 11:18:06 EDT 2022
% Result : Theorem 0.72s 1.06s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n018.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 : Mon Jun 13 12:10:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.72/1.06 ============================== Prover9 ===============================
% 0.72/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.72/1.06 Process 20653 was started by sandbox2 on n018.cluster.edu,
% 0.72/1.06 Mon Jun 13 12:10:58 2022
% 0.72/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_20470_n018.cluster.edu".
% 0.72/1.06 ============================== end of head ===========================
% 0.72/1.06
% 0.72/1.06 ============================== INPUT =================================
% 0.72/1.06
% 0.72/1.06 % Reading from file /tmp/Prover9_20470_n018.cluster.edu
% 0.72/1.06
% 0.72/1.06 set(prolog_style_variables).
% 0.72/1.06 set(auto2).
% 0.72/1.06 % set(auto2) -> set(auto).
% 0.72/1.06 % set(auto) -> set(auto_inference).
% 0.72/1.06 % set(auto) -> set(auto_setup).
% 0.72/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.72/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/1.06 % set(auto) -> set(auto_limits).
% 0.72/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/1.06 % set(auto) -> set(auto_denials).
% 0.72/1.06 % set(auto) -> set(auto_process).
% 0.72/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.72/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.72/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.72/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.72/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.72/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.72/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.72/1.06 % set(auto2) -> assign(stats, some).
% 0.72/1.06 % set(auto2) -> clear(echo_input).
% 0.72/1.06 % set(auto2) -> set(quiet).
% 0.72/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.72/1.06 % set(auto2) -> clear(print_given).
% 0.72/1.06 assign(lrs_ticks,-1).
% 0.72/1.06 assign(sos_limit,10000).
% 0.72/1.06 assign(order,kbo).
% 0.72/1.06 set(lex_order_vars).
% 0.72/1.06 clear(print_given).
% 0.72/1.06
% 0.72/1.06 % formulas(sos). % not echoed (8 formulas)
% 0.72/1.06
% 0.72/1.06 ============================== end of input ==========================
% 0.72/1.06
% 0.72/1.06 % From the command line: assign(max_seconds, 300).
% 0.72/1.06
% 0.72/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/1.06
% 0.72/1.06 % Formulas that are not ordinary clauses:
% 0.72/1.06 1 (all G all X all Y (group_member(X,G) & group_member(Y,G) -> group_member(multiply(G,X,Y),G))) # label(total_function) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 2 (all G all X all Y all Z (group_member(X,G) & group_member(Y,G) & group_member(Z,G) -> multiply(G,multiply(G,X,Y),Z) = multiply(G,X,multiply(G,Y,Z)))) # label(associativity) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 3 (all X (group_member(X,f) -> group_member(phi(X),h))) # label(homomorphism1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 4 (all X all Y (group_member(X,f) & group_member(Y,f) -> multiply(h,phi(X),phi(Y)) = phi(multiply(f,X,Y)))) # label(homomorphism2) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 5 (all X (group_member(X,h) -> (exists Y (group_member(Y,f) & phi(Y) = X)))) # label(surjective) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 6 (all G all X (left_zero(G,X) <-> group_member(X,G) & (all Y (group_member(Y,G) -> multiply(G,X,Y) = X)))) # label(left_zero) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06
% 0.72/1.06 ============================== end of process non-clausal formulas ===
% 0.72/1.06
% 0.72/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/1.06
% 0.72/1.06 ============================== PREDICATE ELIMINATION =================
% 0.72/1.06
% 0.72/1.06 ============================== end predicate elimination =============
% 0.72/1.06
% 0.72/1.06 Auto_denials: (non-Horn, no changes).
% 0.72/1.06
% 0.72/1.06 Term ordering decisions:
% 0.72/1.06 Function symbol KB weights: f=1. h=1. f_left_zero=1. f2=1. phi=1. f1=1. multiply=1.
% 0.72/1.06
% 0.72/1.06 ============================== end of process initial clauses ========
% 0.72/1.06
% 0.72/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.72/1.06
% 0.72/1.06 ============================== end of clauses for search =============
% 0.72/1.06
% 0.72/1.06 ============================== SEARCH ================================
% 0.72/1.06
% 0.72/1.06 % Starting search at 0.01 seconds.
% 0.72/1.06
% 0.72/1.06 ============================== PROOF =================================
% 0.72/1.06 % SZS status Theorem
% 0.72/1.06 % SZS output start Refutation
% 0.72/1.06
% 0.72/1.06 % Proof 1 at 0.08 (+ 0.00) seconds.
% 0.72/1.06 % Length of proof is 25.
% 0.72/1.06 % Level of proof is 7.
% 0.72/1.06 % Maximum clause weight is 18.000.
% 0.72/1.06 % Given clauses 70.
% 0.72/1.06
% 0.72/1.06 3 (all X (group_member(X,f) -> group_member(phi(X),h))) # label(homomorphism1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 4 (all X all Y (group_member(X,f) & group_member(Y,f) -> multiply(h,phi(X),phi(Y)) = phi(multiply(f,X,Y)))) # label(homomorphism2) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 5 (all X (group_member(X,h) -> (exists Y (group_member(Y,f) & phi(Y) = X)))) # label(surjective) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 6 (all G all X (left_zero(G,X) <-> group_member(X,G) & (all Y (group_member(Y,G) -> multiply(G,X,Y) = X)))) # label(left_zero) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.06 7 left_zero(f,f_left_zero) # label(left_zero_for_f) # label(hypothesis). [assumption].
% 0.72/1.06 8 -left_zero(h,phi(f_left_zero)) # label(prove_left_zero_h) # label(negated_conjecture). [assumption].
% 0.72/1.06 9 -left_zero(A,B) | group_member(B,A) # label(left_zero) # label(axiom). [clausify(6)].
% 0.72/1.06 10 -group_member(A,f) | group_member(phi(A),h) # label(homomorphism1) # label(axiom). [clausify(3)].
% 0.72/1.06 11 -group_member(A,h) | group_member(f1(A),f) # label(surjective) # label(axiom). [clausify(5)].
% 0.72/1.06 12 -group_member(A,h) | phi(f1(A)) = A # label(surjective) # label(axiom). [clausify(5)].
% 0.72/1.06 13 left_zero(A,B) | -group_member(B,A) | group_member(f2(A,B),A) # label(left_zero) # label(axiom). [clausify(6)].
% 0.72/1.06 15 -left_zero(A,B) | -group_member(C,A) | multiply(A,B,C) = B # label(left_zero) # label(axiom). [clausify(6)].
% 0.72/1.06 16 left_zero(A,B) | -group_member(B,A) | multiply(A,B,f2(A,B)) != B # label(left_zero) # label(axiom). [clausify(6)].
% 0.72/1.06 17 -group_member(A,f) | -group_member(B,f) | phi(multiply(f,A,B)) = multiply(h,phi(A),phi(B)) # label(homomorphism2) # label(axiom). [clausify(4)].
% 0.72/1.06 18 -group_member(A,f) | -group_member(B,f) | multiply(h,phi(A),phi(B)) = phi(multiply(f,A,B)). [copy(17),flip(c)].
% 0.72/1.06 26 group_member(f_left_zero,f). [resolve(9,a,7,a)].
% 0.72/1.06 27 -group_member(A,f) | multiply(f,f_left_zero,A) = f_left_zero. [resolve(15,a,7,a)].
% 0.72/1.06 41 -group_member(A,f) | multiply(h,phi(f_left_zero),phi(A)) = phi(multiply(f,f_left_zero,A)). [resolve(26,a,18,a)].
% 0.72/1.06 44 group_member(phi(f_left_zero),h). [resolve(26,a,10,a)].
% 0.72/1.06 56 multiply(h,phi(f_left_zero),f2(h,phi(f_left_zero))) != phi(f_left_zero). [resolve(44,a,16,b),unit_del(a,8)].
% 0.72/1.06 59 group_member(f2(h,phi(f_left_zero)),h). [resolve(44,a,13,b),unit_del(a,8)].
% 0.72/1.06 113 phi(f1(f2(h,phi(f_left_zero)))) = f2(h,phi(f_left_zero)). [resolve(59,a,12,a)].
% 0.72/1.06 114 group_member(f1(f2(h,phi(f_left_zero))),f). [resolve(59,a,11,a)].
% 0.72/1.06 124 multiply(f,f_left_zero,f1(f2(h,phi(f_left_zero)))) = f_left_zero. [resolve(114,a,27,a)].
% 0.72/1.06 637 $F. [resolve(41,a,114,a),rewrite([113(9),124(16)]),unit_del(a,56)].
% 0.72/1.06
% 0.72/1.06 % SZS output end Refutation
% 0.72/1.06 ============================== end of proof ==========================
% 0.72/1.06
% 0.72/1.06 ============================== STATISTICS ============================
% 0.72/1.06
% 0.72/1.06 Given=70. Generated=867. Kept=629. proofs=1.
% 0.72/1.06 Usable=66. Sos=405. Demods=91. Limbo=4, Disabled=166. Hints=0.
% 0.72/1.06 Megabytes=0.97.
% 0.72/1.06 User_CPU=0.08, System_CPU=0.00, Wall_clock=0.
% 0.72/1.06
% 0.72/1.06 ============================== end of statistics =====================
% 0.72/1.06
% 0.72/1.06 ============================== end of search =========================
% 0.72/1.06
% 0.72/1.06 THEOREM PROVED
% 0.72/1.06 % SZS status Theorem
% 0.72/1.06
% 0.72/1.06 Exiting with 1 proof.
% 0.72/1.06
% 0.72/1.06 Process 20653 exit (max_proofs) Mon Jun 13 12:10:58 2022
% 0.72/1.06 Prover9 interrupted
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