TSTP Solution File: ALG071+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG071+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 17:53:44 EDT 2022
% Result : Theorem 3.41s 3.69s
% Output : Refutation 3.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG071+1 : TPTP v8.1.0. Released v2.7.0.
% 0.12/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n027.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 : Wed Jun 8 05:25:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.82/1.16 ============================== Prover9 ===============================
% 0.82/1.16 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.16 Process 30590 was started by sandbox on n027.cluster.edu,
% 0.82/1.16 Wed Jun 8 05:25:57 2022
% 0.82/1.16 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30324_n027.cluster.edu".
% 0.82/1.16 ============================== end of head ===========================
% 0.82/1.16
% 0.82/1.16 ============================== INPUT =================================
% 0.82/1.16
% 0.82/1.16 % Reading from file /tmp/Prover9_30324_n027.cluster.edu
% 0.82/1.16
% 0.82/1.16 set(prolog_style_variables).
% 0.82/1.16 set(auto2).
% 0.82/1.16 % set(auto2) -> set(auto).
% 0.82/1.16 % set(auto) -> set(auto_inference).
% 0.82/1.16 % set(auto) -> set(auto_setup).
% 0.82/1.16 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.16 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.16 % set(auto) -> set(auto_limits).
% 0.82/1.16 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.16 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.16 % set(auto) -> set(auto_denials).
% 0.82/1.16 % set(auto) -> set(auto_process).
% 0.82/1.16 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.16 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.16 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.16 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.16 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.16 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.16 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.16 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.16 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.16 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.16 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.16 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.16 % set(auto2) -> assign(stats, some).
% 0.82/1.16 % set(auto2) -> clear(echo_input).
% 0.82/1.16 % set(auto2) -> set(quiet).
% 0.82/1.16 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.16 % set(auto2) -> clear(print_given).
% 0.82/1.16 assign(lrs_ticks,-1).
% 0.82/1.16 assign(sos_limit,10000).
% 0.82/1.16 assign(order,kbo).
% 0.82/1.16 set(lex_order_vars).
% 0.82/1.16 clear(print_given).
% 0.82/1.16
% 0.82/1.16 % formulas(sos). % not echoed (5 formulas)
% 0.82/1.16
% 0.82/1.16 ============================== end of input ==========================
% 0.82/1.16
% 0.82/1.16 % From the command line: assign(max_seconds, 300).
% 0.82/1.16
% 0.82/1.16 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.16
% 0.82/1.16 % Formulas that are not ordinary clauses:
% 0.82/1.16 1 (all U (sorti1(U) -> (all V (sorti1(V) -> sorti1(op1(U,V)))))) # label(ax1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.16 2 (all U (sorti2(U) -> (all V (sorti2(V) -> sorti2(op2(U,V)))))) # label(ax2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.16 3 (all U (sorti1(U) -> (exists V (sorti1(V) & op1(V,op1(V,U)) != U & op1(U,op1(V,U)) = V)))) # label(ax3) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.16 4 -(all U (sorti2(U) -> (exists V (sorti2(V) & op2(V,op2(V,U)) != U & op2(U,op2(V,U)) = V)))) # label(ax4) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.16 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].
% 0.82/1.16
% 0.82/1.16 ============================== end of process non-clausal formulas ===
% 0.82/1.16
% 0.82/1.16 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.16
% 0.82/1.16 ============================== PREDICATE ELIMINATION =================
% 0.82/1.16
% 0.82/1.16 ============================== end predicate elimination =============
% 0.82/1.16
% 0.82/1.16 Auto_denials:
% 0.82/1.16 % copying label ax3 to answer in negative clause
% 0.82/1.16
% 0.82/1.16 Term ordering decisions:
% 0.82/1.16 Function symbol KB weights: c1=1. op2=1. op1=1. h=1. j=1. f1=1.
% 0.82/1.16
% 0.82/1.16 ============================== end of process initial clauses ========
% 0.82/1.16
% 0.82/1.16 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.16
% 0.82/1.16 ============================== end of clauses for search =============
% 0.82/1.16
% 0.82/1.16 ============================== SEARCH ================================
% 0.82/1.16
% 0.82/1.16 % Starting search at 0.01 seconds.
% 0.82/1.16
% 0.82/1.16 Low Water (keep): wt=38.000, iters=4826
% 0.82/1.16
% 0.82/1.16 Low Water (keep): wt=36.000, iters=4686
% 0.82/1.16
% 0.82/1.16 Low Water (keep): wt=34.000, iters=4182
% 0.82/1.16
% 0.82/1.16 Low Water (keep): wt=32.000, iters=3718
% 0.82/1.16
% 0.82/1.16 Low Water (keep): wt=31.000, iters=3609
% 0.82/1.16
% 0.82/1.16 Low Water (keep): wt=30.000, iters=3397
% 3.41/3.69
% 3.41/3.69 Low Water (keep): wt=29.000, iters=3569
% 3.41/3.69
% 3.41/3.69 Low Water (keep): wt=28.000, iters=3520
% 3.41/3.69
% 3.41/3.69 Low Water (keep): wt=27.000, iters=3670
% 3.41/3.69
% 3.41/3.69 Low Water (keep): wt=25.000, iters=3443
% 3.41/3.69
% 3.41/3.69 Low Water (keep): wt=24.000, iters=3454
% 3.41/3.69
% 3.41/3.69 Low Water (keep): wt=19.000, iters=3498
% 3.41/3.69
% 3.41/3.69 Low Water (keep): wt=18.000, iters=3479
% 3.41/3.69
% 3.41/3.69 Low Water (keep): wt=17.000, iters=3682
% 3.41/3.69
% 3.41/3.69 Low Water (keep): wt=16.000, iters=3340
% 3.41/3.69
% 3.41/3.69 Low Water (displace): id=5304, wt=38.000
% 3.41/3.69
% 3.41/3.69 Low Water (displace): id=5318, wt=37.000
% 3.41/3.69
% 3.41/3.69 Low Water (displace): id=5608, wt=36.000
% 3.41/3.69
% 3.41/3.69 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 1.00 sec).
% 3.41/3.69
% 3.41/3.69 Low Water (displace): id=5880, wt=35.000
% 3.41/3.69
% 3.41/3.69 Low Water (displace): id=6148, wt=34.000
% 3.41/3.69
% 3.41/3.69 Low Water (displace): id=11820, wt=16.000
% 3.41/3.69
% 3.41/3.69 Low Water (displace): id=11937, wt=14.000
% 3.41/3.69
% 3.41/3.69 ============================== PROOF =================================
% 3.41/3.69 % SZS status Theorem
% 3.41/3.69 % SZS output start Refutation
% 3.41/3.69
% 3.41/3.69 % Proof 1 at 2.59 (+ 0.13) seconds: ax3.
% 3.41/3.69 % Length of proof is 35.
% 3.41/3.69 % Level of proof is 7.
% 3.41/3.69 % Maximum clause weight is 23.000.
% 3.41/3.69 % Given clauses 853.
% 3.41/3.69
% 3.41/3.69 1 (all U (sorti1(U) -> (all V (sorti1(V) -> sorti1(op1(U,V)))))) # label(ax1) # label(axiom) # label(non_clause). [assumption].
% 3.41/3.69 2 (all U (sorti2(U) -> (all V (sorti2(V) -> sorti2(op2(U,V)))))) # label(ax2) # label(axiom) # label(non_clause). [assumption].
% 3.41/3.69 3 (all U (sorti1(U) -> (exists V (sorti1(V) & op1(V,op1(V,U)) != U & op1(U,op1(V,U)) = V)))) # label(ax3) # label(axiom) # label(non_clause). [assumption].
% 3.41/3.69 4 -(all U (sorti2(U) -> (exists V (sorti2(V) & op2(V,op2(V,U)) != U & op2(U,op2(V,U)) = V)))) # label(ax4) # label(axiom) # label(non_clause). [assumption].
% 3.41/3.69 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].
% 3.41/3.69 6 sorti2(c1) # label(ax4) # label(axiom). [clausify(4)].
% 3.41/3.69 7 -sorti1(A) | op1(f1(A),op1(f1(A),A)) != A # label(ax3) # label(axiom) # answer(ax3). [clausify(3)].
% 3.41/3.69 8 -sorti1(A) | sorti1(f1(A)) # label(ax3) # label(axiom). [clausify(3)].
% 3.41/3.69 9 -sorti1(A) | sorti2(h(A)) # label(co1) # label(negated_conjecture). [clausify(5)].
% 3.41/3.69 10 -sorti2(A) | sorti1(j(A)) # label(co1) # label(negated_conjecture). [clausify(5)].
% 3.41/3.69 11 -sorti2(A) | h(j(A)) = A # label(co1) # label(negated_conjecture). [clausify(5)].
% 3.41/3.69 12 -sorti1(A) | j(h(A)) = A # label(co1) # label(negated_conjecture). [clausify(5)].
% 3.41/3.69 13 -sorti1(A) | -sorti1(B) | sorti1(op1(A,B)) # label(ax1) # label(axiom). [clausify(1)].
% 3.41/3.69 14 -sorti2(A) | -sorti2(B) | sorti2(op2(A,B)) # label(ax2) # label(axiom). [clausify(2)].
% 3.41/3.69 15 -sorti1(A) | op1(A,op1(f1(A),A)) = f1(A) # label(ax3) # label(axiom). [clausify(3)].
% 3.41/3.69 16 -sorti1(A) | -sorti1(B) | h(op1(A,B)) = op2(h(A),h(B)) # label(co1) # label(negated_conjecture). [clausify(5)].
% 3.41/3.69 17 -sorti1(A) | -sorti1(B) | op2(h(A),h(B)) = h(op1(A,B)). [copy(16),flip(c)].
% 3.41/3.69 18 -sorti2(A) | -sorti2(B) | j(op2(A,B)) = op1(j(A),j(B)) # label(co1) # label(negated_conjecture). [clausify(5)].
% 3.41/3.69 19 -sorti2(A) | -sorti2(B) | op1(j(A),j(B)) = j(op2(A,B)). [copy(18),flip(c)].
% 3.41/3.69 20 -sorti2(A) | op2(A,op2(A,c1)) = c1 | op2(c1,op2(A,c1)) != A # label(ax4) # label(axiom). [clausify(4)].
% 3.41/3.69 21 sorti1(j(c1)). [hyper(10,a,6,a)].
% 3.41/3.69 22 h(j(c1)) = c1. [hyper(11,a,6,a)].
% 3.41/3.69 26 op1(j(c1),op1(f1(j(c1)),j(c1))) = f1(j(c1)). [hyper(15,a,21,a)].
% 3.41/3.69 28 sorti1(f1(j(c1))). [hyper(8,a,21,a)].
% 3.41/3.69 29 op1(f1(j(c1)),op1(f1(j(c1)),j(c1))) != j(c1) # answer(ax3). [ur(7,a,21,a)].
% 3.41/3.69 38 h(op1(f1(j(c1)),j(c1))) = op2(h(f1(j(c1))),c1). [hyper(17,a,28,a,b,21,a),rewrite([22(7)]),flip(a)].
% 3.41/3.69 42 sorti1(op1(f1(j(c1)),j(c1))). [hyper(13,a,28,a,b,21,a)].
% 3.41/3.69 43 j(h(f1(j(c1)))) = f1(j(c1)). [hyper(12,a,28,a)].
% 3.41/3.69 44 sorti2(h(f1(j(c1)))). [hyper(9,a,28,a)].
% 3.41/3.69 64 j(op2(h(f1(j(c1))),c1)) = op1(f1(j(c1)),j(c1)). [hyper(19,a,44,a,b,6,a),rewrite([43(5)]),flip(a)].
% 3.41/3.69 69 sorti2(op2(h(f1(j(c1))),c1)). [hyper(14,a,44,a,b,6,a)].
% 3.41/3.69 229 op2(c1,op2(h(f1(j(c1))),c1)) = h(f1(j(c1))). [hyper(17,a,21,a,b,42,a),rewrite([22(3),38(8),26(17)])].
% 3.41/3.69 361 j(op2(h(f1(j(c1))),op2(h(f1(j(c1))),c1))) = op1(f1(j(c1)),op1(f1(j(c1)),j(c1))). [hyper(19,a,44,a,b,69,a),rewrite([43(5),64(10)]),flip(a)].
% 3.41/3.69 11959 op2(h(f1(j(c1))),op2(h(f1(j(c1))),c1)) = c1. [hyper(20,a,44,a,c,229,a)].
% 3.41/3.69 11960 $F # answer(ax3). [back_rewrite(361),rewrite([11959(11)]),flip(a),unit_del(a,29)].
% 3.41/3.69
% 3.41/3.69 % SZS output end Refutation
% 3.41/3.69 ============================== end of proof ==========================
% 3.41/3.69
% 3.41/3.69 ============================== STATISTICS ============================
% 3.41/3.69
% 3.41/3.69 Given=853. Generated=235815. Kept=11952. proofs=1.
% 3.41/3.69 Usable=852. Sos=9992. Demods=1742. Limbo=1, Disabled=1120. Hints=0.
% 3.41/3.69 Megabytes=12.58.
% 3.41/3.69 User_CPU=2.59, System_CPU=0.13, Wall_clock=2.
% 3.41/3.69
% 3.41/3.69 ============================== end of statistics =====================
% 3.41/3.69
% 3.41/3.69 ============================== end of search =========================
% 3.41/3.69
% 3.41/3.69 THEOREM PROVED
% 3.41/3.69 % SZS status Theorem
% 3.41/3.69
% 3.41/3.69 Exiting with 1 proof.
% 3.41/3.69
% 3.41/3.69 Process 30590 exit (max_proofs) Wed Jun 8 05:25:59 2022
% 3.41/3.69 Prover9 interrupted
%------------------------------------------------------------------------------