TSTP Solution File: PUZ133+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : PUZ133+1 : 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 1.02s 1.30s
% Output : Refutation 1.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : PUZ133+1 : TPTP v8.1.0. Released v4.1.0.
% 0.00/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n026.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 : Sat May 28 23:00:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/0.98 ============================== Prover9 ===============================
% 0.41/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.41/0.98 Process 26359 was started by sandbox on n026.cluster.edu,
% 0.41/0.98 Sat May 28 23:00:24 2022
% 0.41/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26205_n026.cluster.edu".
% 0.41/0.98 ============================== end of head ===========================
% 0.41/0.98
% 0.41/0.98 ============================== INPUT =================================
% 0.41/0.98
% 0.41/0.98 % Reading from file /tmp/Prover9_26205_n026.cluster.edu
% 0.41/0.98
% 0.41/0.98 set(prolog_style_variables).
% 0.41/0.98 set(auto2).
% 0.41/0.98 % set(auto2) -> set(auto).
% 0.41/0.98 % set(auto) -> set(auto_inference).
% 0.41/0.98 % set(auto) -> set(auto_setup).
% 0.41/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.41/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/0.98 % set(auto) -> set(auto_limits).
% 0.41/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/0.98 % set(auto) -> set(auto_denials).
% 0.41/0.98 % set(auto) -> set(auto_process).
% 0.41/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.41/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.41/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.41/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.41/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.41/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.41/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.41/0.98 % set(auto2) -> assign(stats, some).
% 0.41/0.98 % set(auto2) -> clear(echo_input).
% 0.41/0.98 % set(auto2) -> set(quiet).
% 0.41/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.41/0.98 % set(auto2) -> clear(print_given).
% 0.41/0.98 assign(lrs_ticks,-1).
% 0.41/0.98 assign(sos_limit,10000).
% 0.41/0.98 assign(order,kbo).
% 0.41/0.98 set(lex_order_vars).
% 0.41/0.98 clear(print_given).
% 0.41/0.98
% 0.41/0.98 % formulas(sos). % not echoed (10 formulas)
% 0.41/0.98
% 0.41/0.98 ============================== end of input ==========================
% 0.41/0.98
% 0.41/0.98 % From the command line: assign(max_seconds, 300).
% 0.41/0.98
% 0.41/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/0.98
% 0.41/0.98 % Formulas that are not ordinary clauses:
% 0.41/0.98 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].
% 0.41/0.98 2 (all I perm(I) = minus(s(n),I)) # label(permutation) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 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].
% 0.41/0.98 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].
% 0.41/0.98 5 (all J all I minus(I,J) = minus(perm(J),perm(I))) # label(permutation_another_one) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 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].
% 0.41/0.98 7 (all X le(X,s(X))) # label(succ_le) # label(axiom) # label(non_clause). [assumption].
% 0.41/0.98 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].
% 0.41/0.98 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].
% 0.41/0.98 10 -(queens_p & (all I q(I) = p(perm(I))) -> queens_q) # label(queens_sym) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.41/0.98
% 0.41/0.98 ============================== end of process non-clausal formulas ===
% 0.41/0.98
% 0.41/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/0.98
% 0.41/0.98 ============================== PREDICATE ELIMINATION =================
% 0.41/0.98
% 0.41/0.98 ============================== end predicate elimination =============
% 0.41/0.98
% 0.41/0.98 Auto_denials: (non-Horn, no changes).
% 0.41/0.98
% 0.41/0.98 Term ordering decisions:
% 0.41/0.98 Function symbol KB weights: n=1. n0=1. c1=1. c2=1. minus=1. plus=1. s=1. perm=1. q=1. p=1.
% 1.02/1.30
% 1.02/1.30 ============================== end of process initial clauses ========
% 1.02/1.30
% 1.02/1.30 ============================== CLAUSES FOR SEARCH ====================
% 1.02/1.30
% 1.02/1.30 ============================== end of clauses for search =============
% 1.02/1.30
% 1.02/1.30 ============================== SEARCH ================================
% 1.02/1.30
% 1.02/1.30 % Starting search at 0.01 seconds.
% 1.02/1.30
% 1.02/1.30 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 412 (0.00 of 0.11 sec).
% 1.02/1.30
% 1.02/1.30 ============================== PROOF =================================
% 1.02/1.30 % SZS status Theorem
% 1.02/1.30 % SZS output start Refutation
% 1.02/1.30
% 1.02/1.30 % Proof 1 at 0.33 (+ 0.01) seconds.
% 1.02/1.30 % Length of proof is 66.
% 1.02/1.30 % Level of proof is 10.
% 1.02/1.30 % Maximum clause weight is 42.000.
% 1.02/1.30 % Given clauses 1070.
% 1.02/1.30
% 1.02/1.30 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].
% 1.02/1.30 2 (all I perm(I) = minus(s(n),I)) # label(permutation) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.30 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].
% 1.02/1.30 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].
% 1.02/1.30 5 (all J all I minus(I,J) = minus(perm(J),perm(I))) # label(permutation_another_one) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.30 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].
% 1.02/1.30 7 (all X le(X,s(X))) # label(succ_le) # label(axiom) # label(non_clause). [assumption].
% 1.02/1.30 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].
% 1.02/1.30 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].
% 1.02/1.30 10 -(queens_p & (all I q(I) = p(perm(I))) -> queens_q) # label(queens_sym) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.02/1.30 11 queens_p # label(queens_sym) # label(negated_conjecture). [clausify(10)].
% 1.02/1.30 12 le(c1,n) | queens_q # label(queens_q) # label(axiom). [clausify(3)].
% 1.02/1.30 13 le(c2,n) | queens_q # label(queens_q) # label(axiom). [clausify(3)].
% 1.02/1.30 14 le(A,s(A)) # label(succ_le) # label(axiom). [clausify(7)].
% 1.02/1.30 15 le(s(n0),c1) | queens_q # label(queens_q) # label(axiom). [clausify(3)].
% 1.02/1.30 16 le(s(c1),c2) | queens_q # label(queens_q) # label(axiom). [clausify(3)].
% 1.02/1.30 17 q(A) = p(perm(A)) # label(queens_sym) # label(negated_conjecture). [clausify(10)].
% 1.02/1.30 18 perm(A) = minus(s(n),A) # label(permutation) # label(axiom). [clausify(2)].
% 1.02/1.30 19 minus(perm(A),perm(B)) = minus(B,A) # label(permutation_another_one) # label(axiom). [clausify(5)].
% 1.02/1.30 20 minus(minus(s(n),A),minus(s(n),B)) = minus(B,A). [copy(19),rewrite([18(1),18(4)])].
% 1.02/1.30 21 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)].
% 1.02/1.30 22 p(minus(s(n),c2)) = p(minus(s(n),c1)) | plus(p(minus(s(n),c2)),c2) = plus(p(minus(s(n),c1)),c1) | minus(p(minus(s(n),c2)),c2) = minus(p(minus(s(n),c1)),c1) | queens_q. [copy(21),rewrite([17(2),18(2),17(7),18(7),17(13),18(13),17(20),18(20),17(28),18(28),17(35),18(35)])].
% 1.02/1.30 23 -queens_q # label(queens_sym) # label(negated_conjecture). [clausify(10)].
% 1.02/1.30 24 -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)].
% 1.02/1.30 25 -le(s(n0),A) | -le(A,n) | -le(s(A),B) | -le(B,n) | p(B) != p(A). [copy(24),unit_del(a,11)].
% 1.02/1.30 26 -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)].
% 1.02/1.30 27 -le(s(n0),A) | -le(A,n) | -le(s(A),B) | -le(B,n) | plus(p(B),B) != plus(p(A),A). [copy(26),unit_del(a,11)].
% 1.02/1.30 28 -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)].
% 1.02/1.31 29 -le(s(n0),A) | -le(A,n) | -le(s(A),B) | -le(B,n) | minus(p(B),B) != minus(p(A),A). [copy(28),unit_del(a,11)].
% 1.02/1.31 30 -le(A,B) | -le(B,C) | le(A,C) # label(le_trans) # label(axiom). [clausify(6)].
% 1.02/1.31 31 -le(s(c1),c2) | le(s(perm(c2)),perm(c1)) | queens_q # label(queens_q) # label(axiom). [clausify(3)].
% 1.02/1.31 32 -le(s(c1),c2) | le(s(minus(s(n),c2)),minus(s(n),c1)). [copy(31),rewrite([18(6),18(11)]),unit_del(c,23)].
% 1.02/1.31 33 -le(s(n0),A) | -le(A,n) | le(perm(A),n) # label(permutation_range) # label(axiom). [clausify(4)].
% 1.02/1.31 34 -le(s(n0),A) | -le(A,n) | le(minus(s(n),A),n). [copy(33),rewrite([18(6)])].
% 1.02/1.31 35 -le(s(n0),A) | -le(A,n) | le(s(n0),perm(A)) # label(permutation_range) # label(axiom). [clausify(4)].
% 1.02/1.31 36 -le(s(n0),A) | -le(A,n) | le(s(n0),minus(s(n),A)). [copy(35),rewrite([18(8)])].
% 1.02/1.31 37 plus(A,B) != plus(C,D) | minus(B,D) = minus(C,A) # label(plus1) # label(axiom). [clausify(8)].
% 1.02/1.31 38 plus(A,B) = plus(C,D) | minus(B,D) != minus(C,A) # label(plus1) # label(axiom). [clausify(8)].
% 1.02/1.31 39 minus(A,B) != minus(C,D) | minus(D,B) = minus(C,A) # label(minus1) # label(axiom). [clausify(9)].
% 1.02/1.31 41 p(minus(s(n),c2)) = p(minus(s(n),c1)) | plus(p(minus(s(n),c2)),c2) = plus(p(minus(s(n),c1)),c1) | minus(p(minus(s(n),c2)),c2) = minus(p(minus(s(n),c1)),c1). [back_unit_del(22),unit_del(d,23)].
% 1.02/1.31 42 le(s(c1),c2). [back_unit_del(16),unit_del(b,23)].
% 1.02/1.31 43 le(s(n0),c1). [back_unit_del(15),unit_del(b,23)].
% 1.02/1.31 44 le(c2,n). [back_unit_del(13),unit_del(b,23)].
% 1.02/1.31 45 le(c1,n). [back_unit_del(12),unit_del(b,23)].
% 1.02/1.31 51 le(s(minus(s(n),c2)),minus(s(n),c1)). [back_unit_del(32),unit_del(a,42)].
% 1.02/1.31 59 -le(s(A),B) | le(A,B). [resolve(30,a,14,a)].
% 1.02/1.31 67 plus(A,B) = plus(B,A). [xx_res(38,b)].
% 1.02/1.31 73 p(minus(s(n),c2)) = p(minus(s(n),c1)) | plus(c2,p(minus(s(n),c2))) = plus(c1,p(minus(s(n),c1))) | minus(p(minus(s(n),c2)),c2) = minus(p(minus(s(n),c1)),c1). [back_rewrite(41),rewrite([67(18),67(25)])].
% 1.02/1.31 74 -le(s(n0),A) | -le(A,n) | -le(s(A),B) | -le(B,n) | plus(B,p(B)) != plus(A,p(A)). [back_rewrite(27),rewrite([67(11),67(13)])].
% 1.02/1.31 77 minus(A,B) != minus(C,D) | minus(D,minus(s(n),A)) = minus(C,minus(s(n),B)). [para(20(a,1),39(a,1))].
% 1.02/1.31 84 le(minus(s(n),c1),n). [resolve(43,a,34,a),unit_del(a,45)].
% 1.02/1.31 96 -le(s(n0),minus(s(n),c2)) | -le(minus(s(n),c2),n) | minus(p(minus(s(n),c2)),minus(s(n),c2)) != minus(p(minus(s(n),c1)),minus(s(n),c1)). [resolve(51,a,29,c),flip(d),unit_del(c,84)].
% 1.02/1.31 97 -le(s(n0),minus(s(n),c2)) | -le(minus(s(n),c2),n) | p(minus(s(n),c2)) != p(minus(s(n),c1)). [resolve(51,a,25,c),flip(d),unit_del(c,84)].
% 1.02/1.31 147 le(c1,c2). [resolve(59,a,42,a)].
% 1.02/1.31 160 -le(A,c1) | le(A,c2). [resolve(147,a,30,b)].
% 1.02/1.31 281 le(s(n0),c2). [resolve(160,a,43,a)].
% 1.02/1.31 284 le(s(n0),minus(s(n),c2)). [resolve(281,a,36,a),unit_del(a,44)].
% 1.02/1.31 285 le(minus(s(n),c2),n). [resolve(281,a,34,a),unit_del(a,44)].
% 1.02/1.31 290 p(minus(s(n),c2)) != p(minus(s(n),c1)). [back_unit_del(97),unit_del(a,284),unit_del(b,285)].
% 1.02/1.31 291 minus(p(minus(s(n),c2)),minus(s(n),c2)) != minus(p(minus(s(n),c1)),minus(s(n),c1)). [back_unit_del(96),unit_del(a,284),unit_del(b,285)].
% 1.02/1.31 292 plus(c2,p(minus(s(n),c2))) = plus(c1,p(minus(s(n),c1))) | minus(p(minus(s(n),c2)),c2) = minus(p(minus(s(n),c1)),c1). [back_unit_del(73),unit_del(a,290)].
% 1.02/1.31 445 plus(minus(s(n),c2),p(minus(s(n),c2))) != plus(minus(s(n),c1),p(minus(s(n),c1))). [resolve(74,c,51,a),flip(d),unit_del(a,284),unit_del(b,285),unit_del(c,84)].
% 1.02/1.31 1378 minus(p(minus(s(n),c2)),p(minus(s(n),c1))) != minus(c1,c2). [ur(77,b,291,a(flip)),flip(a)].
% 1.02/1.31 1406 minus(p(minus(s(n),c2)),c2) = minus(p(minus(s(n),c1)),c1). [resolve(292,a,37,a),unit_del(b,1378)].
% 1.02/1.31 2598 minus(p(minus(s(n),c2)),p(minus(s(n),c1))) != minus(c2,c1). [ur(38,a,445,a),rewrite([20(20)])].
% 1.02/1.31 2602 $F. [ur(39,b,2598,a(flip)),rewrite([1406(14)]),xx(a)].
% 1.02/1.31
% 1.02/1.31 % SZS output end Refutation
% 1.02/1.31 ============================== end of proof ==========================
% 1.02/1.31
% 1.02/1.31 ============================== STATISTICS ============================
% 1.02/1.31
% 1.02/1.31 Given=1070. Generated=11787. Kept=2583. proofs=1.
% 1.02/1.31 Usable=1064. Sos=1477. Demods=15. Limbo=2, Disabled=62. Hints=0.
% 1.02/1.31 Megabytes=2.64.
% 1.02/1.31 User_CPU=0.33, System_CPU=0.01, Wall_clock=1.
% 1.02/1.31
% 1.02/1.31 ============================== end of statistics =====================
% 1.02/1.31
% 1.02/1.31 ============================== end of search =========================
% 1.02/1.31
% 1.02/1.31 THEOREM PROVED
% 1.02/1.31 % SZS status Theorem
% 1.02/1.31
% 1.02/1.31 Exiting with 1 proof.
% 1.02/1.31
% 1.02/1.31 Process 26359 exit (max_proofs) Sat May 28 23:00:25 2022
% 1.02/1.31 Prover9 interrupted
%------------------------------------------------------------------------------