TSTP Solution File: ALG074+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG074+1 : TPTP v8.1.0. Released v2.7.0.
% 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 : Thu Jul 14 17:53:45 EDT 2022
% Result : Theorem 2.79s 3.16s
% Output : Refutation 2.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ALG074+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.12 % 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 : Thu Jun 9 04:18:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.09/1.38 ============================== Prover9 ===============================
% 1.09/1.38 Prover9 (32) version 2009-11A, November 2009.
% 1.09/1.38 Process 13562 was started by sandbox on n020.cluster.edu,
% 1.09/1.38 Thu Jun 9 04:18:37 2022
% 1.09/1.38 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13403_n020.cluster.edu".
% 1.09/1.38 ============================== end of head ===========================
% 1.09/1.38
% 1.09/1.38 ============================== INPUT =================================
% 1.09/1.38
% 1.09/1.38 % Reading from file /tmp/Prover9_13403_n020.cluster.edu
% 1.09/1.38
% 1.09/1.38 set(prolog_style_variables).
% 1.09/1.38 set(auto2).
% 1.09/1.38 % set(auto2) -> set(auto).
% 1.09/1.38 % set(auto) -> set(auto_inference).
% 1.09/1.38 % set(auto) -> set(auto_setup).
% 1.09/1.38 % set(auto_setup) -> set(predicate_elim).
% 1.09/1.38 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.09/1.38 % set(auto) -> set(auto_limits).
% 1.09/1.38 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.09/1.38 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.09/1.38 % set(auto) -> set(auto_denials).
% 1.09/1.38 % set(auto) -> set(auto_process).
% 1.09/1.38 % set(auto2) -> assign(new_constants, 1).
% 1.09/1.38 % set(auto2) -> assign(fold_denial_max, 3).
% 1.09/1.38 % set(auto2) -> assign(max_weight, "200.000").
% 1.09/1.38 % set(auto2) -> assign(max_hours, 1).
% 1.09/1.38 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.09/1.38 % set(auto2) -> assign(max_seconds, 0).
% 1.09/1.38 % set(auto2) -> assign(max_minutes, 5).
% 1.09/1.38 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.09/1.38 % set(auto2) -> set(sort_initial_sos).
% 1.09/1.38 % set(auto2) -> assign(sos_limit, -1).
% 1.09/1.38 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.09/1.38 % set(auto2) -> assign(max_megs, 400).
% 1.09/1.38 % set(auto2) -> assign(stats, some).
% 1.09/1.38 % set(auto2) -> clear(echo_input).
% 1.09/1.38 % set(auto2) -> set(quiet).
% 1.09/1.38 % set(auto2) -> clear(print_initial_clauses).
% 1.09/1.38 % set(auto2) -> clear(print_given).
% 1.09/1.38 assign(lrs_ticks,-1).
% 1.09/1.38 assign(sos_limit,10000).
% 1.09/1.38 assign(order,kbo).
% 1.09/1.38 set(lex_order_vars).
% 1.09/1.38 clear(print_given).
% 1.09/1.38
% 1.09/1.38 % formulas(sos). % not echoed (5 formulas)
% 1.09/1.38
% 1.09/1.38 ============================== end of input ==========================
% 1.09/1.38
% 1.09/1.38 % From the command line: assign(max_seconds, 300).
% 1.09/1.38
% 1.09/1.38 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.09/1.38
% 1.09/1.38 % Formulas that are not ordinary clauses:
% 1.09/1.38 1 (all U (sorti1(U) -> (all V (sorti1(V) -> sorti1(op1(U,V)))))) # label(ax1) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.38 2 (all U (sorti2(U) -> (all V (sorti2(V) -> sorti2(op2(U,V)))))) # label(ax2) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.38 3 (exists U (sorti1(U) & (exists V (sorti1(V) & op1(V,U) != op1(U,V) & op1(op1(U,V),V) = U & op1(op1(U,V),U) != V)))) # label(ax3) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.38 4 -(exists U (sorti2(U) & (exists V (sorti2(V) & op2(V,U) != op2(U,V) & op2(op2(U,V),V) = U & op2(op2(U,V),U) != V)))) # label(ax4) # label(axiom) # label(non_clause). [assumption].
% 1.09/1.38 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].
% 1.09/1.38
% 1.09/1.38 ============================== end of process non-clausal formulas ===
% 1.09/1.38
% 1.09/1.38 ============================== PROCESS INITIAL CLAUSES ===============
% 1.09/1.38
% 1.09/1.38 ============================== PREDICATE ELIMINATION =================
% 1.09/1.38
% 1.09/1.38 ============================== end predicate elimination =============
% 1.09/1.38
% 1.09/1.38 Auto_denials: (non-Horn, no changes).
% 1.09/1.38
% 1.09/1.38 Term ordering decisions:
% 1.09/1.38 Function symbol KB weights: c1=1. c2=1. op2=1. op1=1. h=1. j=1.
% 1.09/1.38
% 1.09/1.38 ============================== end of process initial clauses ========
% 1.09/1.38
% 1.09/1.38 ============================== CLAUSES FOR SEARCH ====================
% 1.09/1.38
% 1.09/1.38 ============================== end of clauses for search =============
% 1.09/1.38
% 1.09/1.38 ============================== SEARCH ================================
% 1.09/1.38
% 1.09/1.38 % Starting search at 0.01 seconds.
% 1.09/1.38
% 1.09/1.38 Low Water (keep): wt=77.000, iters=3337
% 1.09/1.38
% 1.09/1.38 Low Water (keep): wt=65.000, iters=3348
% 1.09/1.38
% 1.09/1.38 Low Water (keep): wt=34.000, iters=3704
% 1.09/1.38
% 1.09/1.38 Low Water (keep): wt=30.000, iters=3609
% 1.09/1.38
% 1.09/1.38 Low Water (keep): wt=26.000, iters=3783
% 2.79/3.16
% 2.79/3.16 Low Water (keep): wt=24.000, iters=3773
% 2.79/3.16
% 2.79/3.16 Low Water (keep): wt=20.000, iters=3367
% 2.79/3.16
% 2.79/3.16 Low Water (keep): wt=16.000, iters=3343
% 2.79/3.16
% 2.79/3.16 Low Water (keep): wt=14.000, iters=3340
% 2.79/3.16
% 2.79/3.16 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.58 sec).
% 2.79/3.16
% 2.79/3.16 Low Water (displace): id=5834, wt=77.000
% 2.79/3.16
% 2.79/3.16 Low Water (displace): id=6189, wt=65.000
% 2.79/3.16
% 2.79/3.16 ============================== PROOF =================================
% 2.79/3.16 % SZS status Theorem
% 2.79/3.16 % SZS output start Refutation
% 2.79/3.16
% 2.79/3.16 % Proof 1 at 2.09 (+ 0.08) seconds.
% 2.79/3.16 % Length of proof is 39.
% 2.79/3.16 % Level of proof is 7.
% 2.79/3.16 % Maximum clause weight is 29.000.
% 2.79/3.16 % Given clauses 1434.
% 2.79/3.16
% 2.79/3.16 1 (all U (sorti1(U) -> (all V (sorti1(V) -> sorti1(op1(U,V)))))) # label(ax1) # label(axiom) # label(non_clause). [assumption].
% 2.79/3.16 3 (exists U (sorti1(U) & (exists V (sorti1(V) & op1(V,U) != op1(U,V) & op1(op1(U,V),V) = U & op1(op1(U,V),U) != V)))) # label(ax3) # label(axiom) # label(non_clause). [assumption].
% 2.79/3.16 4 -(exists U (sorti2(U) & (exists V (sorti2(V) & op2(V,U) != op2(U,V) & op2(op2(U,V),V) = U & op2(op2(U,V),U) != V)))) # label(ax4) # label(axiom) # label(non_clause). [assumption].
% 2.79/3.16 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].
% 2.79/3.16 6 sorti1(c1) # label(ax3) # label(axiom). [clausify(3)].
% 2.79/3.16 7 sorti1(c2) # label(ax3) # label(axiom). [clausify(3)].
% 2.79/3.16 8 op1(op1(c1,c2),c2) = c1 # label(ax3) # label(axiom). [clausify(3)].
% 2.79/3.16 9 op1(c2,c1) != op1(c1,c2) # label(ax3) # label(axiom). [clausify(3)].
% 2.79/3.16 10 op1(op1(c1,c2),c1) != c2 # label(ax3) # label(axiom). [clausify(3)].
% 2.79/3.16 11 -sorti1(A) | sorti2(h(A)) # label(co1) # label(negated_conjecture). [clausify(5)].
% 2.79/3.16 14 -sorti1(A) | j(h(A)) = A # label(co1) # label(negated_conjecture). [clausify(5)].
% 2.79/3.16 15 -sorti1(A) | -sorti1(B) | sorti1(op1(A,B)) # label(ax1) # label(axiom). [clausify(1)].
% 2.79/3.16 17 -sorti1(A) | -sorti1(B) | h(op1(A,B)) = op2(h(A),h(B)) # label(co1) # label(negated_conjecture). [clausify(5)].
% 2.79/3.16 18 -sorti1(A) | -sorti1(B) | op2(h(A),h(B)) = h(op1(A,B)). [copy(17),flip(c)].
% 2.79/3.16 21 -sorti2(A) | -sorti2(B) | op2(B,A) = op2(A,B) | op2(op2(A,B),B) != A | op2(op2(A,B),A) = B # label(ax4) # label(axiom). [clausify(4)].
% 2.79/3.16 26 sorti2(h(c2)). [resolve(11,a,7,a)].
% 2.79/3.16 27 sorti2(h(c1)). [resolve(11,a,6,a)].
% 2.79/3.16 28 j(h(c2)) = c2. [resolve(14,a,7,a)].
% 2.79/3.16 30 -sorti1(A) | sorti1(op1(c2,A)). [resolve(15,a,7,a)].
% 2.79/3.16 31 -sorti1(A) | sorti1(op1(c1,A)). [resolve(15,a,6,a)].
% 2.79/3.16 33 -sorti1(A) | sorti1(op1(A,c1)). [resolve(15,b,6,a)].
% 2.79/3.16 34 -sorti1(A) | op2(h(c2),h(A)) = h(op1(c2,A)). [resolve(18,a,7,a)].
% 2.79/3.16 35 -sorti1(A) | op2(h(c1),h(A)) = h(op1(c1,A)). [resolve(18,a,6,a)].
% 2.79/3.16 36 -sorti1(A) | op2(h(A),h(c2)) = h(op1(A,c2)). [resolve(18,b,7,a)].
% 2.79/3.16 37 -sorti1(A) | op2(h(A),h(c1)) = h(op1(A,c1)). [resolve(18,b,6,a)].
% 2.79/3.16 44 -sorti2(A) | op2(h(c2),A) = op2(A,h(c2)) | op2(op2(A,h(c2)),h(c2)) != A | op2(op2(A,h(c2)),A) = h(c2). [resolve(26,a,21,b)].
% 2.79/3.16 88 sorti1(op1(c2,c1)). [resolve(30,a,6,a)].
% 2.79/3.16 96 j(h(op1(c2,c1))) = op1(c2,c1). [resolve(88,a,14,a)].
% 2.79/3.16 101 sorti1(op1(c1,c2)). [resolve(31,a,7,a)].
% 2.79/3.16 110 j(h(op1(c1,c2))) = op1(c1,c2). [resolve(101,a,14,a)].
% 2.79/3.16 131 sorti1(op1(op1(c1,c2),c1)). [resolve(33,a,101,a)].
% 2.79/3.16 191 op2(h(c2),h(c1)) = h(op1(c2,c1)). [resolve(34,a,6,a)].
% 2.79/3.16 256 op2(h(c1),h(c2)) = h(op1(c1,c2)). [resolve(35,a,7,a)].
% 2.79/3.16 311 j(h(op1(op1(c1,c2),c1))) = op1(op1(c1,c2),c1). [resolve(131,a,14,a)].
% 2.79/3.16 319 op2(h(op1(c1,c2)),h(c2)) = h(c1). [resolve(36,a,101,a),rewrite([8(12)])].
% 2.79/3.16 383 op2(h(op1(c1,c2)),h(c1)) = h(op1(op1(c1,c2),c1)). [resolve(37,a,101,a)].
% 2.79/3.16 566 h(op1(c2,c1)) = h(op1(c1,c2)) | h(op1(op1(c1,c2),c1)) = h(c2). [resolve(44,a,27,a),rewrite([191(5),256(9),256(14),319(16),256(19),383(21)]),xx(b)].
% 2.79/3.16 11613 h(op1(c2,c1)) = h(op1(c1,c2)). [para(566(b,1),311(a,1,1)),rewrite([28(12)]),flip(b),unit_del(b,10)].
% 2.79/3.16 11619 $F. [back_rewrite(96),rewrite([11613(4),110(5)]),flip(a),unit_del(a,9)].
% 2.79/3.16
% 2.79/3.16 % SZS output end Refutation
% 2.79/3.16 ============================== end of proof ==========================
% 2.79/3.16
% 2.79/3.16 ============================== STATISTICS ============================
% 2.79/3.16
% 2.79/3.16 Given=1434. Generated=120293. Kept=11611. proofs=1.
% 2.79/3.16 Usable=1420. Sos=9224. Demods=2252. Limbo=6, Disabled=975. Hints=0.
% 2.79/3.16 Megabytes=11.25.
% 2.79/3.16 User_CPU=2.09, System_CPU=0.08, Wall_clock=2.
% 2.79/3.16
% 2.79/3.16 ============================== end of statistics =====================
% 2.79/3.16
% 2.79/3.16 ============================== end of search =========================
% 2.79/3.16
% 2.79/3.16 THEOREM PROVED
% 2.79/3.16 % SZS status Theorem
% 2.79/3.16
% 2.79/3.16 Exiting with 1 proof.
% 2.79/3.16
% 2.79/3.16 Process 13562 exit (max_proofs) Thu Jun 9 04:18:39 2022
% 2.79/3.16 Prover9 interrupted
%------------------------------------------------------------------------------