TSTP Solution File: ALG029+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG029+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 17:53:39 EDT 2022
% Result : Theorem 0.40s 0.93s
% Output : Refutation 0.66s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ALG029+1 : TPTP v8.1.0. Released v2.7.0.
% 0.12/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 9 03:41:12 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.40/0.93 ============================== Prover9 ===============================
% 0.40/0.93 Prover9 (32) version 2009-11A, November 2009.
% 0.40/0.93 Process 21246 was started by sandbox2 on n027.cluster.edu,
% 0.40/0.93 Thu Jun 9 03:41:12 2022
% 0.40/0.93 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_20864_n027.cluster.edu".
% 0.40/0.93 ============================== end of head ===========================
% 0.40/0.93
% 0.40/0.93 ============================== INPUT =================================
% 0.40/0.93
% 0.40/0.93 % Reading from file /tmp/Prover9_20864_n027.cluster.edu
% 0.40/0.93
% 0.40/0.93 set(prolog_style_variables).
% 0.40/0.93 set(auto2).
% 0.40/0.93 % set(auto2) -> set(auto).
% 0.40/0.93 % set(auto) -> set(auto_inference).
% 0.40/0.93 % set(auto) -> set(auto_setup).
% 0.40/0.93 % set(auto_setup) -> set(predicate_elim).
% 0.40/0.93 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.40/0.93 % set(auto) -> set(auto_limits).
% 0.40/0.93 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.40/0.93 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.40/0.93 % set(auto) -> set(auto_denials).
% 0.40/0.93 % set(auto) -> set(auto_process).
% 0.40/0.93 % set(auto2) -> assign(new_constants, 1).
% 0.40/0.93 % set(auto2) -> assign(fold_denial_max, 3).
% 0.40/0.93 % set(auto2) -> assign(max_weight, "200.000").
% 0.40/0.93 % set(auto2) -> assign(max_hours, 1).
% 0.40/0.93 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.40/0.93 % set(auto2) -> assign(max_seconds, 0).
% 0.40/0.93 % set(auto2) -> assign(max_minutes, 5).
% 0.40/0.93 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.40/0.93 % set(auto2) -> set(sort_initial_sos).
% 0.40/0.93 % set(auto2) -> assign(sos_limit, -1).
% 0.40/0.93 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.40/0.93 % set(auto2) -> assign(max_megs, 400).
% 0.40/0.93 % set(auto2) -> assign(stats, some).
% 0.40/0.93 % set(auto2) -> clear(echo_input).
% 0.40/0.93 % set(auto2) -> set(quiet).
% 0.40/0.93 % set(auto2) -> clear(print_initial_clauses).
% 0.40/0.93 % set(auto2) -> clear(print_given).
% 0.40/0.93 assign(lrs_ticks,-1).
% 0.40/0.93 assign(sos_limit,10000).
% 0.40/0.93 assign(order,kbo).
% 0.40/0.93 set(lex_order_vars).
% 0.40/0.93 clear(print_given).
% 0.40/0.93
% 0.40/0.93 % formulas(sos). % not echoed (5 formulas)
% 0.40/0.93
% 0.40/0.93 ============================== end of input ==========================
% 0.40/0.93
% 0.40/0.93 % From the command line: assign(max_seconds, 300).
% 0.40/0.93
% 0.40/0.93 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.40/0.93
% 0.40/0.93 % Formulas that are not ordinary clauses:
% 0.40/0.93 1 (all U (sorti1(U) -> (all V (sorti1(V) -> sorti1(op1(U,V)))))) # label(ax1) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.93 2 (all U (sorti2(U) -> (all V (sorti2(V) -> sorti2(op2(U,V)))))) # label(ax2) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.93 3 (all U (sorti1(U) -> (all V (sorti1(V) -> op1(U,V) = op1(V,U))))) # label(ax3) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.93 4 -(all U (sorti2(U) -> (all V (sorti2(V) -> op2(U,V) = op2(V,U))))) # label(ax4) # label(axiom) # label(non_clause). [assumption].
% 0.40/0.93 5 -((all U (sorti1(U) -> sorti2(h(U)))) & (all V (sorti2(V) -> sorti1(j(V)))) -> -((all W (sorti1(W) -> (all X (sorti1(X) -> h(op1(W,X)) = op2(h(W),h(X)))))) & (all Y (sorti2(Y) -> (all Z (sorti2(Z) -> j(op2(Y,Z)) = op1(j(Y),j(Z)))))) & (all X1 (sorti2(X1) -> h(j(X1)) = X1)) & (all X2 (sorti1(X2) -> j(h(X2)) = X2)))) # label(co1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.40/0.93
% 0.40/0.93 ============================== end of process non-clausal formulas ===
% 0.40/0.93
% 0.40/0.93 ============================== PROCESS INITIAL CLAUSES ===============
% 0.40/0.93
% 0.40/0.93 ============================== PREDICATE ELIMINATION =================
% 0.40/0.93
% 0.40/0.93 ============================== end predicate elimination =============
% 0.40/0.93
% 0.40/0.93 Auto_denials:
% 0.40/0.93 % copying label ax4 to answer in negative clause
% 0.40/0.93
% 0.40/0.93 Term ordering decisions:
% 0.40/0.93 Function symbol KB weights: c1=1. c2=1. op1=1. op2=1. h=1. j=1.
% 0.40/0.93
% 0.40/0.93 ============================== end of process initial clauses ========
% 0.40/0.93
% 0.40/0.93 ============================== CLAUSES FOR SEARCH ====================
% 0.40/0.93
% 0.40/0.93 ============================== end of clauses for search =============
% 0.40/0.93
% 0.40/0.93 ============================== SEARCH ================================
% 0.40/0.93
% 0.40/0.93 % Starting search at 0.01 seconds.
% 0.40/0.93
% 0.40/0.93 ============================== PROOF =================================
% 0.40/0.93 % SZS status Theorem
% 0.40/0.93 % SZS output start Refutation
% 0.40/0.93
% 0.40/0.93 % Proof 1 at 0.01 (+ 0.00) seconds: ax4.
% 0.40/0.93 % Length of proof is 24.
% 0.40/0.93 % Level of proof is 6.
% 0.40/0.93 % Maximum clause weight is 14.000.
% 0.40/0.93 % Given clauses 14.
% 0.40/0.93
% 0.40/0.93 3 (all U (sorti1(U) -> (all V (sorti1(V) -> op1(U,V) = op1(V,U))))) # label(ax3) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.93 4 -(all U (sorti2(U) -> (all V (sorti2(V) -> op2(U,V) = op2(V,U))))) # label(ax4) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.93 5 -((all U (sorti1(U) -> sorti2(h(U)))) & (all V (sorti2(V) -> sorti1(j(V)))) -> -((all W (sorti1(W) -> (all X (sorti1(X) -> h(op1(W,X)) = op2(h(W),h(X)))))) & (all Y (sorti2(Y) -> (all Z (sorti2(Z) -> j(op2(Y,Z)) = op1(j(Y),j(Z)))))) & (all X1 (sorti2(X1) -> h(j(X1)) = X1)) & (all X2 (sorti1(X2) -> j(h(X2)) = X2)))) # label(co1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.66/0.93 6 sorti2(c1) # label(ax4) # label(axiom). [clausify(4)].
% 0.66/0.93 7 sorti2(c2) # label(ax4) # label(axiom). [clausify(4)].
% 0.66/0.93 8 op2(c2,c1) != op2(c1,c2) # label(ax4) # label(axiom) # answer(ax4). [clausify(4)].
% 0.66/0.93 10 -sorti2(A) | sorti1(j(A)) # label(co1) # label(negated_conjecture). [clausify(5)].
% 0.66/0.93 11 -sorti2(A) | h(j(A)) = A # label(co1) # label(negated_conjecture). [clausify(5)].
% 0.66/0.93 15 -sorti1(A) | -sorti1(B) | op1(B,A) = op1(A,B) # label(ax3) # label(axiom). [clausify(3)].
% 0.66/0.93 16 -sorti1(A) | -sorti1(B) | h(op1(A,B)) = op2(h(A),h(B)) # label(co1) # label(negated_conjecture). [clausify(5)].
% 0.66/0.93 17 -sorti1(A) | -sorti1(B) | op2(h(A),h(B)) = h(op1(A,B)). [copy(16),flip(c)].
% 0.66/0.93 18 -sorti2(A) | -sorti2(B) | j(op2(A,B)) = op1(j(A),j(B)) # label(co1) # label(negated_conjecture). [clausify(5)].
% 0.66/0.93 19 -sorti2(A) | -sorti2(B) | op1(j(A),j(B)) = j(op2(A,B)). [copy(18),flip(c)].
% 0.66/0.93 20 sorti1(j(c2)). [hyper(10,a,7,a)].
% 0.66/0.93 21 sorti1(j(c1)). [hyper(10,a,6,a)].
% 0.66/0.93 22 h(j(c2)) = c2. [hyper(11,a,7,a)].
% 0.66/0.93 23 h(j(c1)) = c1. [hyper(11,a,6,a)].
% 0.66/0.93 29 op1(j(c2),j(c1)) = j(op2(c2,c1)). [hyper(19,a,7,a,b,6,a)].
% 0.66/0.93 30 op1(j(c1),j(c2)) = j(op2(c1,c2)). [hyper(19,a,6,a,b,7,a)].
% 0.66/0.93 35 h(j(op2(c2,c1))) = op2(c2,c1). [hyper(17,a,20,a,b,21,a),rewrite([22(3),23(4),29(8)]),flip(a)].
% 0.66/0.93 36 h(j(op2(c1,c2))) = op2(c1,c2). [hyper(17,a,21,a,b,20,a),rewrite([23(3),22(4),30(8)]),flip(a)].
% 0.66/0.93 37 j(op2(c2,c1)) = j(op2(c1,c2)). [hyper(15,a,20,a,b,21,a),rewrite([30(5),29(9)]),flip(a)].
% 0.66/0.93 40 op2(c2,c1) = op2(c1,c2). [back_rewrite(35),rewrite([37(4),36(5)]),flip(a)].
% 0.66/0.93 41 $F # answer(ax4). [resolve(40,a,8,a)].
% 0.66/0.93
% 0.66/0.93 % SZS output end Refutation
% 0.66/0.93 ============================== end of proof ==========================
% 0.66/0.93
% 0.66/0.93 ============================== STATISTICS ============================
% 0.66/0.93
% 0.66/0.93 Given=14. Generated=47. Kept=33. proofs=1.
% 0.66/0.93 Usable=14. Sos=14. Demods=10. Limbo=3, Disabled=13. Hints=0.
% 0.66/0.93 Megabytes=0.07.
% 0.66/0.93 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.66/0.93
% 0.66/0.93 ============================== end of statistics =====================
% 0.66/0.93
% 0.66/0.93 ============================== end of search =========================
% 0.66/0.93
% 0.66/0.93 THEOREM PROVED
% 0.66/0.93 % SZS status Theorem
% 0.66/0.93
% 0.66/0.93 Exiting with 1 proof.
% 0.66/0.93
% 0.66/0.93 Process 21246 exit (max_proofs) Thu Jun 9 03:41:12 2022
% 0.66/0.93 Prover9 interrupted
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