TSTP Solution File: SYN353+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SYN353+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 21 11:18:30 EDT 2022
% Result : Theorem 1.84s 2.17s
% Output : Refutation 1.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN353+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n021.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 : Mon Jul 11 14:03:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.84/2.17 ============================== Prover9 ===============================
% 1.84/2.17 Prover9 (32) version 2009-11A, November 2009.
% 1.84/2.17 Process 12242 was started by sandbox on n021.cluster.edu,
% 1.84/2.17 Mon Jul 11 14:03:39 2022
% 1.84/2.17 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12089_n021.cluster.edu".
% 1.84/2.17 ============================== end of head ===========================
% 1.84/2.17
% 1.84/2.17 ============================== INPUT =================================
% 1.84/2.17
% 1.84/2.17 % Reading from file /tmp/Prover9_12089_n021.cluster.edu
% 1.84/2.17
% 1.84/2.17 set(prolog_style_variables).
% 1.84/2.17 set(auto2).
% 1.84/2.17 % set(auto2) -> set(auto).
% 1.84/2.17 % set(auto) -> set(auto_inference).
% 1.84/2.17 % set(auto) -> set(auto_setup).
% 1.84/2.17 % set(auto_setup) -> set(predicate_elim).
% 1.84/2.17 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.84/2.17 % set(auto) -> set(auto_limits).
% 1.84/2.17 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.84/2.17 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.84/2.17 % set(auto) -> set(auto_denials).
% 1.84/2.17 % set(auto) -> set(auto_process).
% 1.84/2.17 % set(auto2) -> assign(new_constants, 1).
% 1.84/2.17 % set(auto2) -> assign(fold_denial_max, 3).
% 1.84/2.17 % set(auto2) -> assign(max_weight, "200.000").
% 1.84/2.17 % set(auto2) -> assign(max_hours, 1).
% 1.84/2.17 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.84/2.17 % set(auto2) -> assign(max_seconds, 0).
% 1.84/2.17 % set(auto2) -> assign(max_minutes, 5).
% 1.84/2.17 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.84/2.17 % set(auto2) -> set(sort_initial_sos).
% 1.84/2.17 % set(auto2) -> assign(sos_limit, -1).
% 1.84/2.17 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.84/2.17 % set(auto2) -> assign(max_megs, 400).
% 1.84/2.17 % set(auto2) -> assign(stats, some).
% 1.84/2.17 % set(auto2) -> clear(echo_input).
% 1.84/2.17 % set(auto2) -> set(quiet).
% 1.84/2.17 % set(auto2) -> clear(print_initial_clauses).
% 1.84/2.17 % set(auto2) -> clear(print_given).
% 1.84/2.17 assign(lrs_ticks,-1).
% 1.84/2.17 assign(sos_limit,10000).
% 1.84/2.17 assign(order,kbo).
% 1.84/2.17 set(lex_order_vars).
% 1.84/2.17 clear(print_given).
% 1.84/2.17
% 1.84/2.17 % formulas(sos). % not echoed (1 formulas)
% 1.84/2.17
% 1.84/2.17 ============================== end of input ==========================
% 1.84/2.17
% 1.84/2.17 % From the command line: assign(max_seconds, 300).
% 1.84/2.17
% 1.84/2.17 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.84/2.17
% 1.84/2.17 % Formulas that are not ordinary clauses:
% 1.84/2.17 1 -(all X exists Y1 exists Y2 exists Y3 all Z ((big_f(Y1,Y2,Y3) -> (big_f(X,X,Z) -> big_f(Y2,Y3,Y1) | big_f(Y3,Y1,Y2))) -> (((big_f(Y3,Y1,Y2) -> big_f(Y1,Y2,Y3) & big_f(Y2,Y3,Y1)) <-> big_f(Y2,Y1,Z)) -> (((big_f(Y2,Y3,Y1) -> big_f(Y1,Y2,Y3) & big_f(Y3,Y1,Y2)) <-> big_f(Y1,Z,Y2)) -> ((((big_f(Y3,Y1,Y2) -> -big_f(Y2,Y3,Y1)) -> big_f(Y1,Y2,Y3)) <-> big_f(Z,Y2,Y1)) -> (big_f(Y1,Y2,Y3) & big_f(Y2,Y3,Y1) & big_f(Y3,Y1,Y2) <-> big_f(Z,Z,Z))))))) # label(church_46_18_5) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.84/2.17
% 1.84/2.17 ============================== end of process non-clausal formulas ===
% 1.84/2.17
% 1.84/2.17 ============================== PROCESS INITIAL CLAUSES ===============
% 1.84/2.17
% 1.84/2.17 ============================== PREDICATE ELIMINATION =================
% 1.84/2.17
% 1.84/2.17 ============================== end predicate elimination =============
% 1.84/2.17
% 1.84/2.17 Auto_denials: (non-Horn, no changes).
% 1.84/2.17
% 1.84/2.17 Term ordering decisions:
% 1.84/2.17 Function symbol KB weights: c1=1. f1=1.
% 1.84/2.17
% 1.84/2.17 ============================== end of process initial clauses ========
% 1.84/2.17
% 1.84/2.17 ============================== CLAUSES FOR SEARCH ====================
% 1.84/2.17
% 1.84/2.17 ============================== end of clauses for search =============
% 1.84/2.17
% 1.84/2.17 ============================== SEARCH ================================
% 1.84/2.17
% 1.84/2.17 % Starting search at 0.01 seconds.
% 1.84/2.17
% 1.84/2.17 ============================== PROOF =================================
% 1.84/2.17 % SZS status Theorem
% 1.84/2.17 % SZS output start Refutation
% 1.84/2.17
% 1.84/2.17 % Proof 1 at 1.19 (+ 0.01) seconds.
% 1.84/2.17 % Length of proof is 53.
% 1.84/2.17 % Level of proof is 26.
% 1.84/2.17 % Maximum clause weight is 40.000.
% 1.84/2.17 % Given clauses 401.
% 1.84/2.17
% 1.84/2.17 1 -(all X exists Y1 exists Y2 exists Y3 all Z ((big_f(Y1,Y2,Y3) -> (big_f(X,X,Z) -> big_f(Y2,Y3,Y1) | big_f(Y3,Y1,Y2))) -> (((big_f(Y3,Y1,Y2) -> big_f(Y1,Y2,Y3) & big_f(Y2,Y3,Y1)) <-> big_f(Y2,Y1,Z)) -> (((big_f(Y2,Y3,Y1) -> big_f(Y1,Y2,Y3) & big_f(Y3,Y1,Y2)) <-> big_f(Y1,Z,Y2)) -> ((((big_f(Y3,Y1,Y2) -> -big_f(Y2,Y3,Y1)) -> big_f(Y1,Y2,Y3)) <-> big_f(Z,Y2,Y1)) -> (big_f(Y1,Y2,Y3) & big_f(Y2,Y3,Y1) & big_f(Y3,Y1,Y2) <-> big_f(Z,Z,Z))))))) # label(church_46_18_5) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.84/2.17 2 big_f(A,B,C) | big_f(C,B,f1(B,C,A)) # label(church_46_18_5) # label(negated_conjecture). [clausify(1)].
% 1.84/2.17 3 big_f(A,B,C) | big_f(C,f1(C,A,B),A) # label(church_46_18_5) # label(negated_conjecture). [clausify(1)].
% 1.84/2.17 7 -big_f(A,B,C) | -big_f(B,C,A) | -big_f(C,A,B) | -big_f(f1(A,B,C),f1(A,B,C),f1(A,B,C)) # label(church_46_18_5) # label(negated_conjecture). [clausify(1)].
% 1.84/2.17 10 -big_f(A,B,C) | big_f(B,C,A) | -big_f(C,B,f1(B,C,A)) # label(church_46_18_5) # label(negated_conjecture). [clausify(1)].
% 1.84/2.17 11 -big_f(A,B,C) | big_f(C,A,B) | -big_f(C,B,f1(B,C,A)) # label(church_46_18_5) # label(negated_conjecture). [clausify(1)].
% 1.84/2.17 13 -big_f(A,B,C) | big_f(C,A,B) | -big_f(C,f1(C,A,B),A) # label(church_46_18_5) # label(negated_conjecture). [clausify(1)].
% 1.84/2.17 14 -big_f(A,B,C) | big_f(B,C,A) | -big_f(C,f1(C,A,B),A) # label(church_46_18_5) # label(negated_conjecture). [clausify(1)].
% 1.84/2.17 15 -big_f(A,B,C) | -big_f(C,A,B) | big_f(f1(B,C,A),C,B) # label(church_46_18_5) # label(negated_conjecture). [clausify(1)].
% 1.91/2.17 16 big_f(A,B,C) | big_f(B,C,A) | -big_f(f1(B,C,A),C,B) # label(church_46_18_5) # label(negated_conjecture). [clausify(1)].
% 1.91/2.17 17 big_f(A,B,C) | big_f(C,A,B) | -big_f(f1(C,A,B),A,C) # label(church_46_18_5) # label(negated_conjecture). [clausify(1)].
% 1.91/2.17 18 -big_f(A,B,C) | -big_f(c1,c1,f1(A,B,C)) | big_f(B,C,A) | big_f(C,A,B) # label(church_46_18_5) # label(negated_conjecture). [clausify(1)].
% 1.91/2.17 22 big_f(A,A,A) | -big_f(f1(A,A,A),A,A). [factor(16,a,b)].
% 1.91/2.17 36 -big_f(A,B,f1(B,A,C)) | big_f(f1(f1(B,A,C),A,B),A,f1(B,A,C)) | big_f(A,C,B). [resolve(15,a,3,b)].
% 1.91/2.17 38 -big_f(f1(A,B,C),B,A) | big_f(f1(B,A,f1(A,B,C)),A,B) | big_f(B,C,A). [resolve(15,b,3,b)].
% 1.91/2.17 40 -big_f(c1,c1,A) | big_f(c1,A,c1) | big_f(A,c1,c1). [resolve(18,b,2,b),merge(d)].
% 1.91/2.17 54 big_f(c1,f1(c1,c1,A),c1) | big_f(f1(c1,c1,A),c1,c1) | big_f(A,c1,c1). [resolve(40,a,2,b)].
% 1.91/2.17 69 big_f(c1,f1(c1,c1,A),c1) | big_f(A,c1,c1) | big_f(c1,c1,A). [resolve(54,b,16,c),merge(c)].
% 1.91/2.17 80 big_f(A,c1,c1) | big_f(c1,c1,A) | -big_f(c1,A,c1). [resolve(69,a,14,c),merge(d)].
% 1.91/2.17 84 big_f(f1(c1,c1,A),c1,c1) | big_f(c1,c1,f1(c1,c1,A)) | big_f(c1,A,c1). [resolve(80,c,3,b)].
% 1.91/2.17 85 big_f(c1,c1,f1(c1,c1,A)) | big_f(c1,A,c1) | big_f(c1,c1,A). [resolve(84,a,17,c),merge(c)].
% 1.91/2.17 90 big_f(c1,A,c1) | big_f(c1,c1,A) | -big_f(A,c1,c1). [resolve(85,a,11,c),merge(d)].
% 1.91/2.17 156 big_f(f1(c1,c1,f1(c1,c1,A)),c1,c1) | big_f(c1,A,c1) | big_f(c1,c1,f1(c1,c1,A)). [resolve(38,a,84,a),merge(d)].
% 1.91/2.17 215 big_f(c1,A,c1) | big_f(c1,c1,f1(c1,c1,A)) | big_f(c1,f1(c1,c1,f1(c1,c1,A)),c1) | big_f(c1,c1,f1(c1,c1,f1(c1,c1,A))). [resolve(156,a,90,c)].
% 1.91/2.17 702 big_f(c1,A,c1) | big_f(c1,c1,f1(c1,c1,A)) | big_f(c1,c1,f1(c1,c1,f1(c1,c1,A))) | -big_f(c1,f1(c1,c1,A),c1). [resolve(215,c,13,c),merge(e)].
% 1.91/2.17 710 big_f(c1,A,c1) | big_f(c1,c1,f1(c1,c1,A)) | big_f(c1,c1,f1(c1,c1,f1(c1,c1,A))). [resolve(702,d,3,b),merge(d)].
% 1.91/2.17 718 big_f(c1,A,c1) | big_f(c1,c1,f1(c1,c1,A)) | -big_f(f1(c1,c1,A),c1,c1). [resolve(710,c,10,c),merge(d)].
% 1.91/2.17 726 big_f(c1,A,c1) | big_f(c1,c1,f1(c1,c1,A)). [resolve(718,c,84,a),merge(c),merge(d)].
% 1.91/2.17 733 big_f(c1,A,c1) | -big_f(A,c1,c1). [resolve(726,b,11,c),merge(c)].
% 1.91/2.17 739 big_f(c1,f1(c1,c1,A),c1) | big_f(A,c1,c1). [resolve(733,b,54,b),merge(b)].
% 1.91/2.17 751 big_f(A,c1,c1) | -big_f(c1,A,c1). [resolve(739,a,14,c),merge(c)].
% 1.91/2.17 755 big_f(f1(c1,c1,A),c1,c1) | big_f(A,c1,c1). [resolve(751,b,739,a)].
% 1.91/2.17 762 big_f(A,c1,c1) | big_f(c1,c1,A). [resolve(755,a,16,c),merge(b)].
% 1.91/2.17 787 big_f(A,c1,c1) | big_f(c1,A,c1). [resolve(762,b,40,a),merge(c)].
% 1.91/2.17 799 big_f(c1,A,c1). [resolve(787,a,733,b),merge(b)].
% 1.91/2.17 800 big_f(A,c1,c1). [resolve(787,b,751,b),merge(b)].
% 1.91/2.17 803 big_f(c1,c1,A). [resolve(799,a,13,c),unit_del(a,799)].
% 1.91/2.17 809 -big_f(A,B,C) | big_f(B,C,A) | big_f(C,A,B). [back_unit_del(18),unit_del(b,803)].
% 1.91/2.17 812 -big_f(f1(c1,A,c1),f1(c1,A,c1),f1(c1,A,c1)). [ur(7,a,799,a,b,800,a,c,803,a)].
% 1.91/2.17 813 -big_f(f1(A,c1,c1),f1(A,c1,c1),f1(A,c1,c1)). [ur(7,a,800,a,b,803,a,c,799,a)].
% 1.91/2.17 814 -big_f(f1(c1,c1,A),f1(c1,c1,A),f1(c1,c1,A)). [ur(7,a,803,a,b,799,a,c,800,a)].
% 1.91/2.17 833 -big_f(f1(f1(c1,A,c1),f1(c1,A,c1),f1(c1,A,c1)),f1(c1,A,c1),f1(c1,A,c1)). [ur(22,a,812,a)].
% 1.91/2.17 834 -big_f(f1(f1(A,c1,c1),f1(A,c1,c1),f1(A,c1,c1)),f1(A,c1,c1),f1(A,c1,c1)). [ur(22,a,813,a)].
% 1.91/2.17 835 -big_f(f1(f1(c1,c1,A),f1(c1,c1,A),f1(c1,c1,A)),f1(c1,c1,A),f1(c1,c1,A)). [ur(22,a,814,a)].
% 1.91/2.17 895 big_f(f1(A,B,C),B,A) | big_f(B,A,f1(A,B,C)) | big_f(B,C,A). [resolve(809,a,3,b)].
% 1.91/2.17 896 big_f(A,f1(A,B,C),B) | big_f(f1(A,B,C),B,A) | big_f(C,A,B). [resolve(809,a,2,b)].
% 1.91/2.17 1031 big_f(f1(A,c1,c1),f1(A,c1,c1),f1(f1(A,c1,c1),f1(A,c1,c1),f1(A,c1,c1))). [resolve(895,a,834,a),unit_del(b,813)].
% 1.91/2.17 1032 big_f(f1(c1,A,c1),f1(c1,A,c1),f1(f1(c1,A,c1),f1(c1,A,c1),f1(c1,A,c1))). [resolve(895,a,833,a),unit_del(b,812)].
% 1.91/2.17 1057 big_f(f1(c1,c1,A),f1(f1(c1,c1,A),f1(c1,c1,A),f1(c1,c1,A)),f1(c1,c1,A)). [resolve(896,b,835,a),unit_del(b,814)].
% 1.91/2.17 1457 big_f(f1(f1(f1(A,c1,c1),f1(A,c1,c1),f1(A,c1,c1)),f1(A,c1,c1),f1(A,c1,c1)),f1(A,c1,c1),f1(f1(A,c1,c1),f1(A,c1,c1),f1(A,c1,c1))). [resolve(1031,a,36,a),unit_del(b,813)].
% 1.91/2.17 1473 -big_f(f1(f1(c1,A,c1),f1(c1,A,c1),f1(c1,A,c1)),f1(f1(f1(c1,A,c1),f1(c1,A,c1),f1(c1,A,c1)),f1(c1,A,c1),f1(c1,A,c1)),f1(c1,A,c1)). [ur(13,a,1032,a,b,833,a)].
% 1.91/2.17 1485 -big_f(f1(c1,c1,A),f1(f1(c1,c1,A),f1(c1,c1,A),f1(c1,c1,A)),f1(f1(f1(c1,c1,A),f1(c1,c1,A),f1(c1,c1,A)),f1(c1,c1,A),f1(c1,c1,A))). [ur(10,a,1057,a,b,835,a)].
% 1.91/2.17 1523 $F. [ur(809,b,1485,a,c,1473,a),unit_del(a,1457)].
% 1.91/2.17
% 1.91/2.17 % SZS output end Refutation
% 1.91/2.17 ============================== end of proof ==========================
% 1.91/2.17
% 1.91/2.17 ============================== STATISTICS ============================
% 1.91/2.17
% 1.91/2.17 Given=401. Generated=7120. Kept=1521. proofs=1.
% 1.91/2.17 Usable=317. Sos=704. Demods=0. Limbo=0, Disabled=517. Hints=0.
% 1.91/2.17 Megabytes=2.47.
% 1.91/2.17 User_CPU=1.19, System_CPU=0.01, Wall_clock=1.
% 1.91/2.17
% 1.91/2.17 ============================== end of statistics =====================
% 1.91/2.17
% 1.91/2.17 ============================== end of search =========================
% 1.91/2.17
% 1.91/2.17 THEOREM PROVED
% 1.91/2.17 % SZS status Theorem
% 1.91/2.17
% 1.91/2.17 Exiting with 1 proof.
% 1.91/2.17
% 1.91/2.17 Process 12242 exit (max_proofs) Mon Jul 11 14:03:40 2022
% 1.91/2.18 Prover9 interrupted
%------------------------------------------------------------------------------