TSTP Solution File: ALG073+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : ALG073+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 0.75s 1.05s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG073+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n025.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 : Wed Jun 8 06:13:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.75/1.05 ============================== Prover9 ===============================
% 0.75/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.05 Process 5191 was started by sandbox2 on n025.cluster.edu,
% 0.75/1.05 Wed Jun 8 06:13:35 2022
% 0.75/1.05 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_5037_n025.cluster.edu".
% 0.75/1.05 ============================== end of head ===========================
% 0.75/1.05
% 0.75/1.05 ============================== INPUT =================================
% 0.75/1.05
% 0.75/1.05 % Reading from file /tmp/Prover9_5037_n025.cluster.edu
% 0.75/1.05
% 0.75/1.05 set(prolog_style_variables).
% 0.75/1.05 set(auto2).
% 0.75/1.05 % set(auto2) -> set(auto).
% 0.75/1.05 % set(auto) -> set(auto_inference).
% 0.75/1.05 % set(auto) -> set(auto_setup).
% 0.75/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.05 % set(auto) -> set(auto_limits).
% 0.75/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.05 % set(auto) -> set(auto_denials).
% 0.75/1.05 % set(auto) -> set(auto_process).
% 0.75/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.05 % set(auto2) -> assign(stats, some).
% 0.75/1.05 % set(auto2) -> clear(echo_input).
% 0.75/1.05 % set(auto2) -> set(quiet).
% 0.75/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.05 % set(auto2) -> clear(print_given).
% 0.75/1.05 assign(lrs_ticks,-1).
% 0.75/1.05 assign(sos_limit,10000).
% 0.75/1.05 assign(order,kbo).
% 0.75/1.05 set(lex_order_vars).
% 0.75/1.05 clear(print_given).
% 0.75/1.05
% 0.75/1.05 % formulas(sos). % not echoed (5 formulas)
% 0.75/1.05
% 0.75/1.05 ============================== end of input ==========================
% 0.75/1.05
% 0.75/1.05 % From the command line: assign(max_seconds, 300).
% 0.75/1.05
% 0.75/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.05
% 0.75/1.05 % Formulas that are not ordinary clauses:
% 0.75/1.05 1 (all U (sorti1(U) -> (all V (sorti1(V) -> sorti1(op1(U,V)))))) # label(ax1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.05 2 (all U (sorti2(U) -> (all V (sorti2(V) -> sorti2(op2(U,V)))))) # label(ax2) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.05 3 (exists U (sorti1(U) & (exists V (sorti1(V) & op1(U,U) = V & op1(V,V) = U & op1(U,V) != U)))) # label(ax3) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.05 4 -(exists U (sorti2(U) & (exists V (sorti2(V) & op2(U,U) = V & op2(V,V) = U & op2(U,V) != U)))) # label(ax4) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.05 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].
% 0.75/1.05
% 0.75/1.05 ============================== end of process non-clausal formulas ===
% 0.75/1.05
% 0.75/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.05
% 0.75/1.05 ============================== PREDICATE ELIMINATION =================
% 0.75/1.05
% 0.75/1.05 ============================== end predicate elimination =============
% 0.75/1.05
% 0.75/1.05 Auto_denials:
% 0.75/1.05 % copying label ax3 to answer in negative clause
% 0.75/1.05
% 0.75/1.05 Term ordering decisions:
% 0.75/1.05 Function symbol KB weights: c1=1. c2=1. op2=1. op1=1. h=1. j=1.
% 0.75/1.05
% 0.75/1.05 ============================== end of process initial clauses ========
% 0.75/1.05
% 0.75/1.05 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.05
% 0.75/1.05 ============================== end of clauses for search =============
% 0.75/1.05
% 0.75/1.05 ============================== SEARCH ================================
% 0.75/1.05
% 0.75/1.05 % Starting search at 0.01 seconds.
% 0.75/1.05
% 0.75/1.05 ============================== PROOF =================================
% 0.75/1.05 % SZS status Theorem
% 0.75/1.05 % SZS output start Refutation
% 0.75/1.05
% 0.75/1.05 % Proof 1 at 0.04 (+ 0.00) seconds: ax3.
% 0.75/1.05 % Length of proof is 26.
% 0.75/1.05 % Level of proof is 6.
% 0.75/1.05 % Maximum clause weight is 19.000.
% 0.75/1.05 % Given clauses 40.
% 0.75/1.05
% 0.75/1.05 3 (exists U (sorti1(U) & (exists V (sorti1(V) & op1(U,U) = V & op1(V,V) = U & op1(U,V) != U)))) # label(ax3) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.05 4 -(exists U (sorti2(U) & (exists V (sorti2(V) & op2(U,U) = V & op2(V,V) = U & op2(U,V) != U)))) # label(ax4) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.05 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].
% 0.75/1.05 6 sorti1(c1) # label(ax3) # label(axiom). [clausify(3)].
% 0.75/1.05 7 sorti1(c2) # label(ax3) # label(axiom). [clausify(3)].
% 0.75/1.05 8 op1(c1,c1) = c2 # label(ax3) # label(axiom). [clausify(3)].
% 0.75/1.05 9 op1(c2,c2) = c1 # label(ax3) # label(axiom). [clausify(3)].
% 0.75/1.05 10 op1(c1,c2) != c1 # label(ax3) # label(axiom) # answer(ax3). [clausify(3)].
% 0.75/1.05 11 -sorti1(A) | sorti2(h(A)) # label(co1) # label(negated_conjecture). [clausify(5)].
% 0.75/1.05 14 -sorti1(A) | j(h(A)) = A # label(co1) # label(negated_conjecture). [clausify(5)].
% 0.75/1.05 17 -sorti1(A) | -sorti1(B) | h(op1(A,B)) = op2(h(A),h(B)) # label(co1) # label(negated_conjecture). [clausify(5)].
% 0.75/1.05 18 -sorti1(A) | -sorti1(B) | op2(h(A),h(B)) = h(op1(A,B)). [copy(17),flip(c)].
% 0.75/1.05 19 -sorti2(A) | -sorti2(B) | j(op2(A,B)) = op1(j(A),j(B)) # label(co1) # label(negated_conjecture). [clausify(5)].
% 0.75/1.05 20 -sorti2(A) | -sorti2(B) | op1(j(A),j(B)) = j(op2(A,B)). [copy(19),flip(c)].
% 0.75/1.05 21 -sorti2(A) | -sorti2(B) | op2(A,A) != B | op2(B,B) != A | op2(A,B) = A # label(ax4) # label(axiom). [clausify(4)].
% 0.75/1.05 22 sorti2(h(c2)). [hyper(11,a,7,a)].
% 0.75/1.05 23 sorti2(h(c1)). [hyper(11,a,6,a)].
% 0.75/1.05 24 j(h(c2)) = c2. [hyper(14,a,7,a)].
% 0.75/1.05 25 j(h(c1)) = c1. [hyper(14,a,6,a)].
% 0.75/1.05 28 op2(h(c2),h(c2)) = h(c1). [hyper(18,a,7,a,b,7,a),rewrite([9(8)])].
% 0.75/1.05 30 op2(h(c1),h(c2)) = h(op1(c1,c2)). [hyper(18,a,6,a,b,7,a)].
% 0.75/1.05 31 op2(h(c1),h(c1)) = h(c2). [hyper(18,a,6,a,b,6,a),rewrite([8(8)])].
% 0.75/1.05 33 j(h(op1(c1,c2))) = op1(c1,c2). [hyper(20,a,23,a,b,22,a),rewrite([25(3),24(4),30(8)]),flip(a)].
% 0.75/1.05 509 h(op1(c1,c2)) = h(c1). [hyper(21,a,23,a,b,22,a,c,31,a,d,28,a),rewrite([30(5)])].
% 0.75/1.05 548 op1(c1,c2) = c1. [back_rewrite(33),rewrite([509(4),25(3)]),flip(a)].
% 0.75/1.05 549 $F # answer(ax3). [resolve(548,a,10,a)].
% 0.75/1.05
% 0.75/1.05 % SZS output end Refutation
% 0.75/1.05 ============================== end of proof ==========================
% 0.75/1.05
% 0.75/1.05 ============================== STATISTICS ============================
% 0.75/1.05
% 0.75/1.05 Given=40. Generated=645. Kept=541. proofs=1.
% 0.75/1.05 Usable=37. Sos=415. Demods=239. Limbo=39, Disabled=63. Hints=0.
% 0.75/1.05 Megabytes=0.55.
% 0.75/1.05 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.75/1.05
% 0.75/1.05 ============================== end of statistics =====================
% 0.75/1.05
% 0.75/1.05 ============================== end of search =========================
% 0.75/1.05
% 0.75/1.05 THEOREM PROVED
% 0.75/1.05 % SZS status Theorem
% 0.75/1.05
% 0.75/1.05 Exiting with 1 proof.
% 0.75/1.05
% 0.75/1.05 Process 5191 exit (max_proofs) Wed Jun 8 06:13:35 2022
% 0.75/1.05 Prover9 interrupted
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