TSTP Solution File: SET009-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 04:25:32 EDT 2022
% Result : Unsatisfiable 0.44s 1.03s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 08:27:41 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.44/1.02 ============================== Prover9 ===============================
% 0.44/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.02 Process 7649 was started by sandbox2 on n016.cluster.edu,
% 0.44/1.02 Sun Jul 10 08:27:41 2022
% 0.44/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7268_n016.cluster.edu".
% 0.44/1.02 ============================== end of head ===========================
% 0.44/1.02
% 0.44/1.02 ============================== INPUT =================================
% 0.44/1.02
% 0.44/1.02 % Reading from file /tmp/Prover9_7268_n016.cluster.edu
% 0.44/1.02
% 0.44/1.02 set(prolog_style_variables).
% 0.44/1.02 set(auto2).
% 0.44/1.02 % set(auto2) -> set(auto).
% 0.44/1.02 % set(auto) -> set(auto_inference).
% 0.44/1.02 % set(auto) -> set(auto_setup).
% 0.44/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.02 % set(auto) -> set(auto_limits).
% 0.44/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.02 % set(auto) -> set(auto_denials).
% 0.44/1.02 % set(auto) -> set(auto_process).
% 0.44/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.02 % set(auto2) -> assign(stats, some).
% 0.44/1.02 % set(auto2) -> clear(echo_input).
% 0.44/1.02 % set(auto2) -> set(quiet).
% 0.44/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.02 % set(auto2) -> clear(print_given).
% 0.44/1.02 assign(lrs_ticks,-1).
% 0.44/1.02 assign(sos_limit,10000).
% 0.44/1.02 assign(order,kbo).
% 0.44/1.02 set(lex_order_vars).
% 0.44/1.02 clear(print_given).
% 0.44/1.02
% 0.44/1.02 % formulas(sos). % not echoed (16 formulas)
% 0.44/1.02
% 0.44/1.02 ============================== end of input ==========================
% 0.44/1.02
% 0.44/1.02 % From the command line: assign(max_seconds, 300).
% 0.44/1.02
% 0.44/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.02
% 0.44/1.02 % Formulas that are not ordinary clauses:
% 0.44/1.02
% 0.44/1.02 ============================== end of process non-clausal formulas ===
% 0.44/1.02
% 0.44/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.02
% 0.44/1.02 ============================== PREDICATE ELIMINATION =================
% 0.44/1.02 1 -member(A,B) | -member(A,C) | -difference(D,B,C) # label(not_member_of_difference) # label(axiom). [assumption].
% 0.44/1.02 2 difference(b,a,bDa) # label(b_minus_a) # label(hypothesis). [assumption].
% 0.44/1.02 3 difference(b,d,bDd) # label(b_minus_d) # label(hypothesis). [assumption].
% 0.44/1.02 4 difference(A,B,C) | member(k(A,B,C),A) | member(k(A,B,C),C) # label(difference_axiom2) # label(axiom). [assumption].
% 0.44/1.02 Derived: -member(A,a) | -member(A,bDa). [resolve(1,c,2,a)].
% 0.44/1.02 Derived: -member(A,d) | -member(A,bDd). [resolve(1,c,3,a)].
% 0.44/1.02 Derived: -member(A,B) | -member(A,C) | member(k(D,B,C),D) | member(k(D,B,C),C). [resolve(1,c,4,a)].
% 0.44/1.02 5 -difference(A,B,C) | -member(D,C) | member(D,A) # label(member_of_difference) # label(axiom). [assumption].
% 0.44/1.02 Derived: -member(A,bDa) | member(A,b). [resolve(5,a,2,a)].
% 0.44/1.02 Derived: -member(A,bDd) | member(A,b). [resolve(5,a,3,a)].
% 0.44/1.02 Derived: -member(A,B) | member(A,C) | member(k(C,D,B),C) | member(k(C,D,B),B). [resolve(5,a,4,a)].
% 0.44/1.02 6 -member(A,B) | -difference(B,C,D) | member(A,D) | member(A,C) # label(member_of_difference_or_set2) # label(axiom). [assumption].
% 0.44/1.02 Derived: -member(A,b) | member(A,bDa) | member(A,a). [resolve(6,b,2,a)].
% 0.44/1.02 Derived: -member(A,b) | member(A,bDd) | member(A,d). [resolve(6,b,3,a)].
% 0.44/1.02 Derived: -member(A,B) | member(A,C) | member(A,D) | member(k(B,D,C),B) | member(k(B,D,C),C). [resolve(6,b,4,a)].
% 0.44/1.02 7 -member(k(A,B,C),B) | member(k(A,B,C),C) | difference(A,B,C) # label(difference_axiom1) # label(axiom). [assumption].
% 0.44/1.02 Derived: -member(k(A,B,C),B) | member(k(A,B,C),C) | -member(D,B) | -member(D,C). [resolve(7,c,1,c)].
% 0.44/1.02 Derived: -member(k(A,B,C),B) | member(k(A,B,C),C) | -member(D,C) | member(D,A). [resolve(7,c,5,a)].
% 0.44/1.02 Derived: -member(k(A,B,C),B) | member(k(A,B,C),C) | -member(D,A) | member(D,C) | member(D,B). [resolve(7,c,6,b)].
% 0.44/1.03 8 -member(k(A,B,C),C) | -member(k(A,B,C),A) | member(k(A,B,C),B) | difference(A,B,C) # label(difference_axiom3) # label(axiom). [assumption].
% 0.44/1.03 Derived: -member(k(A,B,C),C) | -member(k(A,B,C),A) | member(k(A,B,C),B) | -member(D,B) | -member(D,C). [resolve(8,d,1,c)].
% 0.44/1.03 Derived: -member(k(A,B,C),C) | -member(k(A,B,C),A) | member(k(A,B,C),B) | -member(D,C) | member(D,A). [resolve(8,d,5,a)].
% 0.44/1.03 Derived: -member(k(A,B,C),C) | -member(k(A,B,C),A) | member(k(A,B,C),B) | -member(D,A) | member(D,C) | member(D,B). [resolve(8,d,6,b)].
% 0.44/1.03 9 -subset(A,B) | -subset(B,A) | equal_sets(B,A) # label(subsets_are_set_equal_sets) # label(axiom). [assumption].
% 0.44/1.03 10 -equal_sets(A,B) | subset(A,B) # label(set_equal_sets_are_subsets1) # label(axiom). [assumption].
% 0.44/1.03 11 -equal_sets(A,B) | subset(B,A) # label(set_equal_sets_are_subsets2) # label(axiom). [assumption].
% 0.44/1.03 12 -subset(bDa,bDd) # label(prove_bDa_is_a_subset_of_bDd) # label(negated_conjecture). [assumption].
% 0.44/1.03 13 subset(d,a) # label(d_is_a_subset_of_a) # label(hypothesis). [assumption].
% 0.44/1.03 14 subset(A,B) | member(member_of_1_not_of_2(A,B),A) # label(subsets_axiom1) # label(axiom). [assumption].
% 0.44/1.03 Derived: member(member_of_1_not_of_2(bDa,bDd),bDa). [resolve(12,a,14,a)].
% 0.44/1.03 15 -member(member_of_1_not_of_2(A,B),B) | subset(A,B) # label(subsets_axiom2) # label(axiom). [assumption].
% 0.44/1.03 Derived: -member(member_of_1_not_of_2(bDa,bDd),bDd). [resolve(15,b,12,a)].
% 0.44/1.03 16 -member(A,B) | -subset(B,C) | member(A,C) # label(membership_in_subsets) # label(axiom). [assumption].
% 0.44/1.03 Derived: -member(A,d) | member(A,a). [resolve(16,b,13,a)].
% 0.44/1.03 Derived: -member(A,B) | member(A,C) | member(member_of_1_not_of_2(B,C),B). [resolve(16,b,14,a)].
% 0.44/1.03 Derived: -member(A,B) | member(A,C) | -member(member_of_1_not_of_2(B,C),C). [resolve(16,b,15,b)].
% 0.44/1.03
% 0.44/1.03 ============================== end predicate elimination =============
% 0.44/1.03
% 0.44/1.03 Auto_denials: (non-Horn, no changes).
% 0.44/1.03
% 0.44/1.03 Term ordering decisions:
% 0.44/1.03 Function symbol KB weights: b=1. bDa=1. bDd=1. a=1. d=1. member_of_1_not_of_2=1. k=1.
% 0.44/1.03
% 0.44/1.03 ============================== end of process initial clauses ========
% 0.44/1.03
% 0.44/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.44/1.03
% 0.44/1.03 ============================== end of clauses for search =============
% 0.44/1.03
% 0.44/1.03 ============================== SEARCH ================================
% 0.44/1.03
% 0.44/1.03 % Starting search at 0.01 seconds.
% 0.44/1.03
% 0.44/1.03 ============================== PROOF =================================
% 0.44/1.03 % SZS status Unsatisfiable
% 0.44/1.03 % SZS output start Refutation
% 0.44/1.03
% 0.44/1.03 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.44/1.03 % Length of proof is 20.
% 0.44/1.03 % Level of proof is 4.
% 0.44/1.03 % Maximum clause weight is 9.000.
% 0.44/1.03 % Given clauses 29.
% 0.44/1.03
% 0.44/1.03 1 -member(A,B) | -member(A,C) | -difference(D,B,C) # label(not_member_of_difference) # label(axiom). [assumption].
% 0.44/1.03 2 difference(b,a,bDa) # label(b_minus_a) # label(hypothesis). [assumption].
% 0.44/1.03 3 difference(b,d,bDd) # label(b_minus_d) # label(hypothesis). [assumption].
% 0.44/1.03 5 -difference(A,B,C) | -member(D,C) | member(D,A) # label(member_of_difference) # label(axiom). [assumption].
% 0.44/1.03 6 -member(A,B) | -difference(B,C,D) | member(A,D) | member(A,C) # label(member_of_difference_or_set2) # label(axiom). [assumption].
% 0.44/1.03 12 -subset(bDa,bDd) # label(prove_bDa_is_a_subset_of_bDd) # label(negated_conjecture). [assumption].
% 0.44/1.03 13 subset(d,a) # label(d_is_a_subset_of_a) # label(hypothesis). [assumption].
% 0.44/1.03 14 subset(A,B) | member(member_of_1_not_of_2(A,B),A) # label(subsets_axiom1) # label(axiom). [assumption].
% 0.44/1.03 15 -member(member_of_1_not_of_2(A,B),B) | subset(A,B) # label(subsets_axiom2) # label(axiom). [assumption].
% 0.44/1.03 16 -member(A,B) | -subset(B,C) | member(A,C) # label(membership_in_subsets) # label(axiom). [assumption].
% 0.44/1.03 17 -member(A,a) | -member(A,bDa). [resolve(1,c,2,a)].
% 0.44/1.03 20 -member(A,bDa) | member(A,b). [resolve(5,a,2,a)].
% 0.44/1.03 24 -member(A,b) | member(A,bDd) | member(A,d). [resolve(6,b,3,a)].
% 0.44/1.03 32 member(member_of_1_not_of_2(bDa,bDd),bDa). [resolve(12,a,14,a)].
% 0.44/1.03 33 -member(member_of_1_not_of_2(bDa,bDd),bDd). [resolve(15,b,12,a)].
% 0.44/1.03 34 -member(A,d) | member(A,a). [resolve(16,b,13,a)].
% 0.44/1.03 52 member(member_of_1_not_of_2(bDa,bDd),b). [resolve(32,a,20,a)].
% 0.44/1.03 55 -member(member_of_1_not_of_2(bDa,bDd),a). [ur(17,b,32,a)].
% 0.44/1.03 66 -member(member_of_1_not_of_2(bDa,bDd),d). [ur(34,b,55,a)].
% 0.44/1.03 69 $F. [ur(24,b,33,a,c,66,a),unit_del(a,52)].
% 0.44/1.03
% 0.44/1.03 % SZS output end Refutation
% 0.44/1.03 ============================== end of proof ==========================
% 0.44/1.03
% 0.44/1.03 ============================== STATISTICS ============================
% 0.44/1.03
% 0.44/1.03 Given=29. Generated=108. Kept=52. proofs=1.
% 0.44/1.03 Usable=29. Sos=22. Demods=0. Limbo=1, Disabled=36. Hints=0.
% 0.44/1.03 Megabytes=0.08.
% 0.44/1.03 User_CPU=0.02, System_CPU=0.00, Wall_clock=1.
% 0.44/1.03
% 0.44/1.03 ============================== end of statistics =====================
% 0.44/1.03
% 0.44/1.03 ============================== end of search =========================
% 0.44/1.03
% 0.44/1.03 THEOREM PROVED
% 0.44/1.03 % SZS status Unsatisfiable
% 0.44/1.03
% 0.44/1.03 Exiting with 1 proof.
% 0.44/1.03
% 0.44/1.03 Process 7649 exit (max_proofs) Sun Jul 10 08:27:42 2022
% 0.44/1.03 Prover9 interrupted
%------------------------------------------------------------------------------