TSTP Solution File: PUZ133+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : PUZ133+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 : Mon Jul 18 18:24:05 EDT 2022
% Result : Theorem 0.93s 1.19s
% Output : Refutation 0.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ133+2 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n026.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun May 29 02:01:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.77/1.03 ============================== Prover9 ===============================
% 0.77/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.77/1.03 Process 29304 was started by sandbox on n026.cluster.edu,
% 0.77/1.03 Sun May 29 02:01:54 2022
% 0.77/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29151_n026.cluster.edu".
% 0.77/1.03 ============================== end of head ===========================
% 0.77/1.03
% 0.77/1.03 ============================== INPUT =================================
% 0.77/1.03
% 0.77/1.03 % Reading from file /tmp/Prover9_29151_n026.cluster.edu
% 0.77/1.03
% 0.77/1.03 set(prolog_style_variables).
% 0.77/1.03 set(auto2).
% 0.77/1.03 % set(auto2) -> set(auto).
% 0.77/1.03 % set(auto) -> set(auto_inference).
% 0.77/1.03 % set(auto) -> set(auto_setup).
% 0.77/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.77/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.77/1.03 % set(auto) -> set(auto_limits).
% 0.77/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.77/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.77/1.03 % set(auto) -> set(auto_denials).
% 0.77/1.03 % set(auto) -> set(auto_process).
% 0.77/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.77/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.77/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.77/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.77/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.77/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.77/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.77/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.77/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.77/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.77/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.77/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.77/1.03 % set(auto2) -> assign(stats, some).
% 0.77/1.03 % set(auto2) -> clear(echo_input).
% 0.77/1.03 % set(auto2) -> set(quiet).
% 0.77/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.77/1.03 % set(auto2) -> clear(print_given).
% 0.77/1.03 assign(lrs_ticks,-1).
% 0.77/1.03 assign(sos_limit,10000).
% 0.77/1.03 assign(order,kbo).
% 0.77/1.03 set(lex_order_vars).
% 0.77/1.03 clear(print_given).
% 0.77/1.03
% 0.77/1.03 % formulas(sos). % not echoed (10 formulas)
% 0.77/1.03
% 0.77/1.03 ============================== end of input ==========================
% 0.77/1.03
% 0.77/1.03 % From the command line: assign(max_seconds, 300).
% 0.77/1.03
% 0.77/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.77/1.03
% 0.77/1.03 % Formulas that are not ordinary clauses:
% 0.77/1.03 1 queens_p -> (all I all J (le(s(n0),I) & le(I,n) & le(s(I),J) & le(J,n) -> p(I) != p(J) & plus(p(I),I) != plus(p(J),J) & minus(p(I),I) != minus(p(J),J))) # label(queens_p) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.03 2 (all I (le(s(n0),I) & le(I,n) -> perm(I) = minus(s(n),I))) # label(permutation) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.03 3 (all I all J (le(s(n0),I) & le(I,n) & le(s(I),J) & le(J,n) & (le(s(I),J) <-> le(s(perm(J)),perm(I))) -> q(I) != q(J) & plus(q(I),I) != plus(q(J),J) & minus(q(I),I) != minus(q(J),J))) -> queens_q # label(queens_q) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.03 4 (all I (le(s(n0),I) & le(I,n) -> le(s(n0),perm(I)) & le(perm(I),n))) # label(permutation_range) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.03 5 (all J all I minus(I,J) = minus(perm(J),perm(I))) # label(permutation_another_one) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.03 6 (all X all Y all Z (le(X,Y) & le(Y,Z) -> le(X,Z))) # label(le_trans) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.03 7 (all X le(X,s(X))) # label(succ_le) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.03 8 (all I all J all K all L (plus(I,J) = plus(K,L) <-> minus(I,K) = minus(L,J))) # label(plus1) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.03 9 (all I all J all K all L (minus(I,J) = minus(K,L) <-> minus(I,K) = minus(J,L))) # label(minus1) # label(axiom) # label(non_clause). [assumption].
% 0.77/1.03 10 -(queens_p & (all I q(I) = p(perm(I))) -> queens_q) # label(queens_sym) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.77/1.03
% 0.77/1.03 ============================== end of process non-clausal formulas ===
% 0.77/1.03
% 0.77/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.77/1.03
% 0.77/1.03 ============================== PREDICATE ELIMINATION =================
% 0.77/1.03
% 0.77/1.03 ============================== end predicate elimination =============
% 0.77/1.03
% 0.77/1.03 Auto_denials: (non-Horn, no changes).
% 0.77/1.03
% 0.77/1.03 Term ordering decisions:
% 0.77/1.03 Function symbol KB weights: n=1. n0=1. c1=1. c2=1. minus=1. plus=1. s=1. perm=1. q=1. p=1.
% 0.93/1.19
% 0.93/1.19 ============================== end of process initial clauses ========
% 0.93/1.19
% 0.93/1.19 ============================== CLAUSES FOR SEARCH ====================
% 0.93/1.19
% 0.93/1.19 ============================== end of clauses for search =============
% 0.93/1.19
% 0.93/1.19 ============================== SEARCH ================================
% 0.93/1.19
% 0.93/1.19 % Starting search at 0.01 seconds.
% 0.93/1.19
% 0.93/1.19 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 293 (0.00 of 0.10 sec).
% 0.93/1.19
% 0.93/1.19 ============================== PROOF =================================
% 0.93/1.19 % SZS status Theorem
% 0.93/1.19 % SZS output start Refutation
% 0.93/1.19
% 0.93/1.19 % Proof 1 at 0.16 (+ 0.00) seconds.
% 0.93/1.19 % Length of proof is 65.
% 0.93/1.19 % Level of proof is 11.
% 0.93/1.19 % Maximum clause weight is 30.000.
% 0.93/1.19 % Given clauses 749.
% 0.93/1.19
% 0.93/1.19 1 queens_p -> (all I all J (le(s(n0),I) & le(I,n) & le(s(I),J) & le(J,n) -> p(I) != p(J) & plus(p(I),I) != plus(p(J),J) & minus(p(I),I) != minus(p(J),J))) # label(queens_p) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 3 (all I all J (le(s(n0),I) & le(I,n) & le(s(I),J) & le(J,n) & (le(s(I),J) <-> le(s(perm(J)),perm(I))) -> q(I) != q(J) & plus(q(I),I) != plus(q(J),J) & minus(q(I),I) != minus(q(J),J))) -> queens_q # label(queens_q) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 4 (all I (le(s(n0),I) & le(I,n) -> le(s(n0),perm(I)) & le(perm(I),n))) # label(permutation_range) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 5 (all J all I minus(I,J) = minus(perm(J),perm(I))) # label(permutation_another_one) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 6 (all X all Y all Z (le(X,Y) & le(Y,Z) -> le(X,Z))) # label(le_trans) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 7 (all X le(X,s(X))) # label(succ_le) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 8 (all I all J all K all L (plus(I,J) = plus(K,L) <-> minus(I,K) = minus(L,J))) # label(plus1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 9 (all I all J all K all L (minus(I,J) = minus(K,L) <-> minus(I,K) = minus(J,L))) # label(minus1) # label(axiom) # label(non_clause). [assumption].
% 0.93/1.19 10 -(queens_p & (all I q(I) = p(perm(I))) -> queens_q) # label(queens_sym) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.93/1.19 11 queens_p # label(queens_sym) # label(negated_conjecture). [clausify(10)].
% 0.93/1.19 12 le(c1,n) | queens_q # label(queens_q) # label(axiom). [clausify(3)].
% 0.93/1.19 13 le(c2,n) | queens_q # label(queens_q) # label(axiom). [clausify(3)].
% 0.93/1.19 14 le(A,s(A)) # label(succ_le) # label(axiom). [clausify(7)].
% 0.93/1.19 15 le(s(n0),c1) | queens_q # label(queens_q) # label(axiom). [clausify(3)].
% 0.93/1.19 16 le(s(c1),c2) | queens_q # label(queens_q) # label(axiom). [clausify(3)].
% 0.93/1.19 17 q(A) = p(perm(A)) # label(queens_sym) # label(negated_conjecture). [clausify(10)].
% 0.93/1.19 18 minus(perm(A),perm(B)) = minus(B,A) # label(permutation_another_one) # label(axiom). [clausify(5)].
% 0.93/1.19 19 q(c2) = q(c1) | plus(q(c2),c2) = plus(q(c1),c1) | minus(q(c2),c2) = minus(q(c1),c1) | queens_q # label(queens_q) # label(axiom). [clausify(3)].
% 0.93/1.19 20 p(perm(c2)) = p(perm(c1)) | plus(p(perm(c2)),c2) = plus(p(perm(c1)),c1) | minus(p(perm(c2)),c2) = minus(p(perm(c1)),c1) | queens_q. [copy(19),rewrite([17(2),17(5),17(9),17(14),17(20),17(25)])].
% 0.93/1.19 21 -queens_q # label(queens_sym) # label(negated_conjecture). [clausify(10)].
% 0.93/1.19 22 -queens_p | -le(s(n0),A) | -le(A,n) | -le(s(A),B) | -le(B,n) | p(B) != p(A) # label(queens_p) # label(axiom). [clausify(1)].
% 0.93/1.19 23 -le(s(n0),A) | -le(A,n) | -le(s(A),B) | -le(B,n) | p(B) != p(A). [copy(22),unit_del(a,11)].
% 0.93/1.19 24 -queens_p | -le(s(n0),A) | -le(A,n) | -le(s(A),B) | -le(B,n) | plus(p(B),B) != plus(p(A),A) # label(queens_p) # label(axiom). [clausify(1)].
% 0.93/1.19 25 -le(s(n0),A) | -le(A,n) | -le(s(A),B) | -le(B,n) | plus(p(B),B) != plus(p(A),A). [copy(24),unit_del(a,11)].
% 0.93/1.19 26 -queens_p | -le(s(n0),A) | -le(A,n) | -le(s(A),B) | -le(B,n) | minus(p(B),B) != minus(p(A),A) # label(queens_p) # label(axiom). [clausify(1)].
% 0.93/1.19 27 -le(s(n0),A) | -le(A,n) | -le(s(A),B) | -le(B,n) | minus(p(B),B) != minus(p(A),A). [copy(26),unit_del(a,11)].
% 0.93/1.19 28 -le(A,B) | -le(B,C) | le(A,C) # label(le_trans) # label(axiom). [clausify(6)].
% 0.93/1.19 29 -le(s(c1),c2) | le(s(perm(c2)),perm(c1)) | queens_q # label(queens_q) # label(axiom). [clausify(3)].
% 0.93/1.19 30 -le(s(c1),c2) | le(s(perm(c2)),perm(c1)). [copy(29),unit_del(c,21)].
% 0.93/1.19 31 -le(s(n0),A) | -le(A,n) | le(perm(A),n) # label(permutation_range) # label(axiom). [clausify(4)].
% 0.93/1.19 32 -le(s(n0),A) | -le(A,n) | le(s(n0),perm(A)) # label(permutation_range) # label(axiom). [clausify(4)].
% 0.93/1.19 35 plus(A,B) != plus(C,D) | minus(B,D) = minus(C,A) # label(plus1) # label(axiom). [clausify(8)].
% 0.93/1.19 36 plus(A,B) = plus(C,D) | minus(B,D) != minus(C,A) # label(plus1) # label(axiom). [clausify(8)].
% 0.93/1.19 37 minus(A,B) != minus(C,D) | minus(D,B) = minus(C,A) # label(minus1) # label(axiom). [clausify(9)].
% 0.93/1.19 38 p(perm(c2)) = p(perm(c1)) | plus(p(perm(c2)),c2) = plus(p(perm(c1)),c1) | minus(p(perm(c2)),c2) = minus(p(perm(c1)),c1). [back_unit_del(20),unit_del(d,21)].
% 0.93/1.19 39 le(s(c1),c2). [back_unit_del(16),unit_del(b,21)].
% 0.93/1.19 40 le(s(n0),c1). [back_unit_del(15),unit_del(b,21)].
% 0.93/1.19 41 le(c2,n). [back_unit_del(13),unit_del(b,21)].
% 0.93/1.19 42 le(c1,n). [back_unit_del(12),unit_del(b,21)].
% 0.93/1.19 48 le(s(perm(c2)),perm(c1)). [back_unit_del(30),unit_del(a,39)].
% 0.93/1.19 56 -le(s(A),B) | le(A,B). [resolve(28,a,14,a)].
% 0.93/1.19 65 plus(A,B) = plus(B,A). [xx_res(36,b)].
% 0.93/1.19 71 p(perm(c2)) = p(perm(c1)) | plus(c2,p(perm(c2))) = plus(c1,p(perm(c1))) | minus(p(perm(c2)),c2) = minus(p(perm(c1)),c1). [back_rewrite(38),rewrite([65(12),65(17)])].
% 0.93/1.19 72 -le(s(n0),A) | -le(A,n) | -le(s(A),B) | -le(B,n) | plus(B,p(B)) != plus(A,p(A)). [back_rewrite(25),rewrite([65(11),65(13)])].
% 0.93/1.19 73 minus(A,perm(B)) = minus(B,perm(A)). [resolve(37,a,18,a)].
% 0.93/1.19 75 minus(A,B) != minus(C,D) | minus(A,perm(D)) = minus(B,perm(C)). [para(18(a,1),37(a,1)),rewrite([73(5),73(7)])].
% 0.93/1.19 77 minus(A,perm(perm(B))) = minus(A,B). [back_rewrite(18),rewrite([73(3)])].
% 0.93/1.19 84 le(perm(c1),n). [resolve(40,a,31,a),unit_del(a,42)].
% 0.93/1.19 96 -le(s(n0),perm(c2)) | -le(perm(c2),n) | minus(c2,perm(p(perm(c2)))) != minus(c1,perm(p(perm(c1)))). [resolve(48,a,27,c),rewrite([73(19),73(25)]),flip(d),unit_del(c,84)].
% 0.93/1.19 97 -le(s(n0),perm(c2)) | -le(perm(c2),n) | p(perm(c2)) != p(perm(c1)). [resolve(48,a,23,c),flip(d),unit_del(c,84)].
% 0.93/1.19 170 le(c1,c2). [resolve(56,a,39,a)].
% 0.93/1.19 183 -le(A,c1) | le(A,c2). [resolve(170,a,28,b)].
% 0.93/1.19 324 plus(A,B) != plus(C,D) | minus(B,C) = minus(D,A). [para(65(a,1),35(a,2))].
% 0.93/1.19 339 le(s(n0),c2). [resolve(183,a,40,a)].
% 0.93/1.19 348 le(s(n0),perm(c2)). [resolve(339,a,32,a),unit_del(a,41)].
% 0.93/1.19 349 le(perm(c2),n). [resolve(339,a,31,a),unit_del(a,41)].
% 0.93/1.19 354 p(perm(c2)) != p(perm(c1)). [back_unit_del(97),unit_del(a,348),unit_del(b,349)].
% 0.93/1.19 355 minus(c2,perm(p(perm(c2)))) != minus(c1,perm(p(perm(c1)))). [back_unit_del(96),unit_del(a,348),unit_del(b,349)].
% 0.93/1.19 356 plus(c2,p(perm(c2))) = plus(c1,p(perm(c1))) | minus(p(perm(c2)),c2) = minus(p(perm(c1)),c1). [back_unit_del(71),unit_del(a,354)].
% 0.93/1.19 492 plus(perm(c2),p(perm(c2))) != plus(perm(c1),p(perm(c1))). [resolve(72,c,48,a),flip(d),unit_del(a,348),unit_del(b,349),unit_del(c,84)].
% 0.93/1.19 1669 minus(p(perm(c1)),p(perm(c2))) != minus(c2,c1). [ur(75,b,355,a),flip(a)].
% 0.93/1.19 1671 plus(c2,p(perm(c2))) != plus(c1,p(perm(c1))). [ur(324,b,1669,a),rewrite([65(10)]),flip(a)].
% 0.93/1.19 1674 minus(p(perm(c2)),c2) = minus(p(perm(c1)),c1). [back_unit_del(356),unit_del(a,1671)].
% 0.93/1.19 1742 minus(p(perm(c2)),p(perm(c1))) != minus(c2,c1). [ur(36,a,492,a),rewrite([73(12),77(12)])].
% 0.93/1.19 1746 $F. [ur(37,b,1742,a(flip)),rewrite([1674(10)]),xx(a)].
% 0.93/1.19
% 0.93/1.19 % SZS output end Refutation
% 0.93/1.19 ============================== end of proof ==========================
% 0.93/1.19
% 0.93/1.19 ============================== STATISTICS ============================
% 0.93/1.19
% 0.93/1.19 Given=749. Generated=6230. Kept=1729. proofs=1.
% 0.93/1.19 Usable=744. Sos=949. Demods=20. Limbo=2, Disabled=56. Hints=0.
% 0.93/1.19 Megabytes=1.50.
% 0.93/1.19 User_CPU=0.16, System_CPU=0.00, Wall_clock=1.
% 0.93/1.19
% 0.93/1.19 ============================== end of statistics =====================
% 0.93/1.19
% 0.93/1.19 ============================== end of search =========================
% 0.93/1.19
% 0.93/1.19 THEOREM PROVED
% 0.93/1.19 % SZS status Theorem
% 0.93/1.19
% 0.93/1.19 Exiting with 1 proof.
% 0.93/1.19
% 0.93/1.19 Process 29304 exit (max_proofs) Sun May 29 02:01:55 2022
% 0.93/1.19 Prover9 interrupted
%------------------------------------------------------------------------------