TSTP Solution File: SET012-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET012-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 : Tue Jul 19 04:25:37 EDT 2022
% Result : Unsatisfiable 0.46s 1.01s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET012-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n009.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 : Sun Jul 10 19:39:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/1.01 ============================== Prover9 ===============================
% 0.46/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.01 Process 25791 was started by sandbox2 on n009.cluster.edu,
% 0.46/1.01 Sun Jul 10 19:39:07 2022
% 0.46/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_25546_n009.cluster.edu".
% 0.46/1.01 ============================== end of head ===========================
% 0.46/1.01
% 0.46/1.01 ============================== INPUT =================================
% 0.46/1.01
% 0.46/1.01 % Reading from file /tmp/Prover9_25546_n009.cluster.edu
% 0.46/1.01
% 0.46/1.01 set(prolog_style_variables).
% 0.46/1.01 set(auto2).
% 0.46/1.01 % set(auto2) -> set(auto).
% 0.46/1.01 % set(auto) -> set(auto_inference).
% 0.46/1.01 % set(auto) -> set(auto_setup).
% 0.46/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.01 % set(auto) -> set(auto_limits).
% 0.46/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.01 % set(auto) -> set(auto_denials).
% 0.46/1.01 % set(auto) -> set(auto_process).
% 0.46/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.01 % set(auto2) -> assign(stats, some).
% 0.46/1.01 % set(auto2) -> clear(echo_input).
% 0.46/1.01 % set(auto2) -> set(quiet).
% 0.46/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.01 % set(auto2) -> clear(print_given).
% 0.46/1.01 assign(lrs_ticks,-1).
% 0.46/1.01 assign(sos_limit,10000).
% 0.46/1.01 assign(order,kbo).
% 0.46/1.01 set(lex_order_vars).
% 0.46/1.01 clear(print_given).
% 0.46/1.01
% 0.46/1.01 % formulas(sos). % not echoed (11 formulas)
% 0.46/1.01
% 0.46/1.01 ============================== end of input ==========================
% 0.46/1.01
% 0.46/1.01 % From the command line: assign(max_seconds, 300).
% 0.46/1.01
% 0.46/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.01
% 0.46/1.01 % Formulas that are not ordinary clauses:
% 0.46/1.01
% 0.46/1.01 ============================== end of process non-clausal formulas ===
% 0.46/1.01
% 0.46/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.01
% 0.46/1.01 ============================== PREDICATE ELIMINATION =================
% 0.46/1.01 1 member(A,universal_set) | -little_set(A) # label(universal_set) # label(axiom). [assumption].
% 0.46/1.01 2 little_set(f1(A,B)) | A = B # label(extensionality1) # label(axiom). [assumption].
% 0.46/1.01 3 -member(A,B) | little_set(A) # label(a2) # label(axiom). [assumption].
% 0.46/1.01 Derived: member(f1(A,B),universal_set) | A = B. [resolve(1,b,2,a)].
% 0.46/1.01 Derived: member(A,universal_set) | -member(A,B). [resolve(1,b,3,b)].
% 0.46/1.01 4 member(A,complement(B)) | -little_set(A) | member(A,B) # label(complement2) # label(axiom). [assumption].
% 0.46/1.01 Derived: member(f1(A,B),complement(C)) | member(f1(A,B),C) | A = B. [resolve(4,b,2,a)].
% 0.46/1.01 Derived: member(A,complement(B)) | member(A,B) | -member(A,C). [resolve(4,b,3,b)].
% 0.46/1.01
% 0.46/1.01 ============================== end predicate elimination =============
% 0.46/1.01
% 0.46/1.01 Auto_denials: (non-Horn, no changes).
% 0.46/1.01
% 0.46/1.01 Term ordering decisions:
% 0.46/1.01
% 0.46/1.01 % Assigning unary symbol complement kb_weight 0 and highest precedence (9).
% 0.46/1.01 Function symbol KB weights: bs=1. universal_set=1. as=1. cs=1. empty_set=1. f1=1. complement=0.
% 0.46/1.01
% 0.46/1.01 ============================== end of process initial clauses ========
% 0.46/1.01
% 0.46/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.46/1.01
% 0.46/1.01 ============================== end of clauses for search =============
% 0.46/1.01
% 0.46/1.01 ============================== SEARCH ================================
% 0.46/1.01
% 0.46/1.01 % Starting search at 0.01 seconds.
% 0.46/1.01
% 0.46/1.01 ============================== PROOF =================================
% 0.46/1.01 % SZS status Unsatisfiable
% 0.46/1.01 % SZS output start Refutation
% 0.46/1.01
% 0.46/1.01 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.46/1.01 % Length of proof is 20.
% 0.46/1.01 % Level of proof is 5.
% 0.46/1.01 % Maximum clause weight is 19.000.
% 0.46/1.01 % Given clauses 38.
% 0.46/1.01
% 0.46/1.01 2 little_set(f1(A,B)) | A = B # label(extensionality1) # label(axiom). [assumption].
% 0.46/1.01 4 member(A,complement(B)) | -little_set(A) | member(A,B) # label(complement2) # label(axiom). [assumption].
% 0.46/1.01 5 complement(as) = bs # label(complement_of_a_is_b) # label(hypothesis). [assumption].
% 0.46/1.01 6 complement(bs) = cs # label(complement_of_b_is_c) # label(hypothesis). [assumption].
% 0.46/1.01 7 cs = complement(bs). [copy(6),flip(a)].
% 0.46/1.01 8 member(f1(A,B),A) | member(f1(A,B),B) | A = B # label(extensionality2) # label(axiom). [assumption].
% 0.46/1.01 10 as != cs # label(prove_a_equals_c) # label(negated_conjecture). [assumption].
% 0.46/1.01 11 complement(bs) != as. [copy(10),rewrite([7(2)]),flip(a)].
% 0.46/1.01 12 -member(A,complement(B)) | -member(A,B) # label(complement1) # label(axiom). [assumption].
% 0.46/1.01 13 -member(f1(A,B),A) | -member(f1(A,B),B) | A = B # label(extensionality3) # label(axiom). [assumption].
% 0.46/1.01 16 member(f1(A,B),complement(C)) | member(f1(A,B),C) | A = B. [resolve(4,b,2,a)].
% 0.46/1.01 20 -member(f1(A,complement(B)),B) | member(f1(A,complement(B)),A) | complement(B) = A. [resolve(12,a,8,b),flip(c)].
% 0.46/1.01 22 -member(A,bs) | -member(A,as). [para(5(a,1),12(a,2))].
% 0.46/1.01 25 member(f1(A,complement(B)),B) | complement(B) = A | -member(f1(A,complement(B)),A). [resolve(16,a,13,b),flip(b),flip(d),merge(d)].
% 0.46/1.01 27 member(f1(A,B),bs) | member(f1(A,B),as) | A = B. [para(5(a,1),16(a,2))].
% 0.46/1.01 39 member(f1(A,complement(complement(B))),A) | complement(complement(B)) = A | member(f1(A,complement(complement(B))),B). [resolve(20,a,16,a),flip(d),merge(d)].
% 0.46/1.01 43 member(f1(A,complement(complement(A))),A) | complement(complement(A)) = A. [factor(39,a,c)].
% 0.46/1.01 69 -member(f1(as,complement(bs)),bs). [resolve(43,a,22,b),rewrite([5(2),5(7)]),unit_del(a,11)].
% 0.46/1.01 76 member(f1(as,complement(A)),bs) | complement(A) = as | member(f1(as,complement(A)),A). [resolve(27,b,25,c),flip(b),merge(d)].
% 0.46/1.01 83 $F. [factor(76,a,c),unit_del(a,69),unit_del(b,11)].
% 0.46/1.01
% 0.46/1.01 % SZS output end Refutation
% 0.46/1.01 ============================== end of proof ==========================
% 0.46/1.01
% 0.46/1.01 ============================== STATISTICS ============================
% 0.46/1.01
% 0.46/1.01 Given=38. Generated=198. Kept=76. proofs=1.
% 0.46/1.01 Usable=38. Sos=26. Demods=4. Limbo=7, Disabled=20. Hints=0.
% 0.46/1.01 Megabytes=0.08.
% 0.46/1.01 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.46/1.01
% 0.46/1.01 ============================== end of statistics =====================
% 0.46/1.01
% 0.46/1.01 ============================== end of search =========================
% 0.46/1.01
% 0.46/1.01 THEOREM PROVED
% 0.46/1.01 % SZS status Unsatisfiable
% 0.46/1.01
% 0.46/1.01 Exiting with 1 proof.
% 0.46/1.01
% 0.46/1.01 Process 25791 exit (max_proofs) Sun Jul 10 19:39:07 2022
% 0.46/1.01 Prover9 interrupted
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