TSTP Solution File: COL042-7 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : COL042-7 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 : Fri Jul 15 00:39:47 EDT 2022
% Result : Unsatisfiable 0.99s 1.33s
% Output : Refutation 0.99s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL042-7 : TPTP v8.1.0. Released v2.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n024.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 : Tue May 31 10:33:21 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.99/1.33 ============================== Prover9 ===============================
% 0.99/1.33 Prover9 (32) version 2009-11A, November 2009.
% 0.99/1.33 Process 31276 was started by sandbox2 on n024.cluster.edu,
% 0.99/1.33 Tue May 31 10:33:22 2022
% 0.99/1.33 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_31122_n024.cluster.edu".
% 0.99/1.33 ============================== end of head ===========================
% 0.99/1.33
% 0.99/1.33 ============================== INPUT =================================
% 0.99/1.33
% 0.99/1.33 % Reading from file /tmp/Prover9_31122_n024.cluster.edu
% 0.99/1.33
% 0.99/1.33 set(prolog_style_variables).
% 0.99/1.33 set(auto2).
% 0.99/1.33 % set(auto2) -> set(auto).
% 0.99/1.33 % set(auto) -> set(auto_inference).
% 0.99/1.33 % set(auto) -> set(auto_setup).
% 0.99/1.33 % set(auto_setup) -> set(predicate_elim).
% 0.99/1.33 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.99/1.33 % set(auto) -> set(auto_limits).
% 0.99/1.33 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.99/1.33 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.99/1.33 % set(auto) -> set(auto_denials).
% 0.99/1.33 % set(auto) -> set(auto_process).
% 0.99/1.33 % set(auto2) -> assign(new_constants, 1).
% 0.99/1.33 % set(auto2) -> assign(fold_denial_max, 3).
% 0.99/1.33 % set(auto2) -> assign(max_weight, "200.000").
% 0.99/1.33 % set(auto2) -> assign(max_hours, 1).
% 0.99/1.33 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.99/1.33 % set(auto2) -> assign(max_seconds, 0).
% 0.99/1.33 % set(auto2) -> assign(max_minutes, 5).
% 0.99/1.33 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.99/1.33 % set(auto2) -> set(sort_initial_sos).
% 0.99/1.33 % set(auto2) -> assign(sos_limit, -1).
% 0.99/1.33 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.99/1.33 % set(auto2) -> assign(max_megs, 400).
% 0.99/1.33 % set(auto2) -> assign(stats, some).
% 0.99/1.33 % set(auto2) -> clear(echo_input).
% 0.99/1.33 % set(auto2) -> set(quiet).
% 0.99/1.33 % set(auto2) -> clear(print_initial_clauses).
% 0.99/1.33 % set(auto2) -> clear(print_given).
% 0.99/1.33 assign(lrs_ticks,-1).
% 0.99/1.33 assign(sos_limit,10000).
% 0.99/1.33 assign(order,kbo).
% 0.99/1.33 set(lex_order_vars).
% 0.99/1.33 clear(print_given).
% 0.99/1.33
% 0.99/1.33 % formulas(sos). % not echoed (4 formulas)
% 0.99/1.33
% 0.99/1.33 ============================== end of input ==========================
% 0.99/1.33
% 0.99/1.33 % From the command line: assign(max_seconds, 300).
% 0.99/1.33
% 0.99/1.33 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.99/1.33
% 0.99/1.33 % Formulas that are not ordinary clauses:
% 0.99/1.33
% 0.99/1.33 ============================== end of process non-clausal formulas ===
% 0.99/1.33
% 0.99/1.33 ============================== PROCESS INITIAL CLAUSES ===============
% 0.99/1.33
% 0.99/1.33 ============================== PREDICATE ELIMINATION =================
% 0.99/1.33
% 0.99/1.33 ============================== end predicate elimination =============
% 0.99/1.33
% 0.99/1.33 Auto_denials:
% 0.99/1.33 % copying label prove_strong_fixed_point to answer in negative clause
% 0.99/1.33
% 0.99/1.33 Term ordering decisions:
% 0.99/1.33 Function symbol KB weights: b=1. w1=1. strong_fixed_point=1. fixed_pt=1. apply=1.
% 0.99/1.33
% 0.99/1.33 ============================== end of process initial clauses ========
% 0.99/1.33
% 0.99/1.33 ============================== CLAUSES FOR SEARCH ====================
% 0.99/1.33
% 0.99/1.33 ============================== end of clauses for search =============
% 0.99/1.33
% 0.99/1.33 ============================== SEARCH ================================
% 0.99/1.33
% 0.99/1.33 % Starting search at 0.01 seconds.
% 0.99/1.33
% 0.99/1.33 ============================== PROOF =================================
% 0.99/1.33 % SZS status Unsatisfiable
% 0.99/1.33 % SZS output start Refutation
% 0.99/1.33
% 0.99/1.33 % Proof 1 at 0.34 (+ 0.01) seconds: prove_strong_fixed_point.
% 0.99/1.33 % Length of proof is 11.
% 0.99/1.33 % Level of proof is 4.
% 0.99/1.33 % Maximum clause weight is 29.000.
% 0.99/1.33 % Given clauses 53.
% 0.99/1.33
% 0.99/1.33 1 apply(apply(w1,A),B) = apply(apply(B,A),A) # label(w1_definition) # label(axiom). [assumption].
% 0.99/1.33 2 apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)) # label(b_definition) # label(axiom). [assumption].
% 0.99/1.33 3 strong_fixed_point = apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),apply(apply(b,b),b)) # label(strong_fixed_point) # label(axiom). [assumption].
% 0.99/1.33 4 apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) # label(prove_strong_fixed_point) # label(negated_conjecture) # answer(prove_strong_fixed_point). [assumption].
% 0.99/1.33 5 apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt))))) != apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))) # answer(prove_strong_fixed_point). [copy(4),rewrite([3(1),2(19),2(16),2(15),3(15),2(33),2(30),2(29)]),flip(a)].
% 0.99/1.33 7 apply(apply(w1,A),w1) = apply(apply(A,A),A). [para(1(a,1),1(a,2))].
% 0.99/1.33 14 apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)) # answer(prove_strong_fixed_point). [para(1(a,1),5(a,1,2)),rewrite([2(12)]),flip(a)].
% 0.99/1.33 27 apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)) != apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1) # answer(prove_strong_fixed_point). [para(1(a,1),14(a,1)),rewrite([2(11)]),flip(a)].
% 0.99/1.33 30 apply(apply(A,apply(B,apply(apply(b,A),B))),apply(apply(b,A),B)) = apply(apply(w1,apply(apply(b,A),B)),w1). [para(2(a,1),7(a,2,1)),flip(a)].
% 0.99/1.33 1917 apply(A,apply(apply(w1,apply(apply(b,apply(b,A)),B)),B)) = apply(apply(w1,apply(apply(b,apply(b,A)),B)),w1). [para(30(a,1),2(a,1)),rewrite([1(21,R)]),flip(a)].
% 0.99/1.33 1918 $F # answer(prove_strong_fixed_point). [resolve(1917,a,27,a)].
% 0.99/1.33
% 0.99/1.33 % SZS output end Refutation
% 0.99/1.33 ============================== end of proof ==========================
% 0.99/1.33
% 0.99/1.33 ============================== STATISTICS ============================
% 0.99/1.33
% 0.99/1.33 Given=53. Generated=6723. Kept=1916. proofs=1.
% 0.99/1.33 Usable=53. Sos=1683. Demods=777. Limbo=3, Disabled=180. Hints=0.
% 0.99/1.33 Megabytes=2.84.
% 0.99/1.33 User_CPU=0.34, System_CPU=0.01, Wall_clock=0.
% 0.99/1.33
% 0.99/1.33 ============================== end of statistics =====================
% 0.99/1.33
% 0.99/1.33 ============================== end of search =========================
% 0.99/1.33
% 0.99/1.33 THEOREM PROVED
% 0.99/1.33 % SZS status Unsatisfiable
% 0.99/1.33
% 0.99/1.33 Exiting with 1 proof.
% 0.99/1.33
% 0.99/1.33 Process 31276 exit (max_proofs) Tue May 31 10:33:22 2022
% 0.99/1.33 Prover9 interrupted
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