TSTP Solution File: SET008-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET008-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 04:25:31 EDT 2022
% Result : Unsatisfiable 0.43s 0.99s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n008.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 20:24:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/0.98 ============================== Prover9 ===============================
% 0.43/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.98 Process 26850 was started by sandbox2 on n008.cluster.edu,
% 0.43/0.98 Sun Jul 10 20:24:39 2022
% 0.43/0.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_26469_n008.cluster.edu".
% 0.43/0.98 ============================== end of head ===========================
% 0.43/0.98
% 0.43/0.98 ============================== INPUT =================================
% 0.43/0.98
% 0.43/0.98 % Reading from file /tmp/Prover9_26469_n008.cluster.edu
% 0.43/0.98
% 0.43/0.98 set(prolog_style_variables).
% 0.43/0.98 set(auto2).
% 0.43/0.98 % set(auto2) -> set(auto).
% 0.43/0.98 % set(auto) -> set(auto_inference).
% 0.43/0.98 % set(auto) -> set(auto_setup).
% 0.43/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.98 % set(auto) -> set(auto_limits).
% 0.43/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.98 % set(auto) -> set(auto_denials).
% 0.43/0.98 % set(auto) -> set(auto_process).
% 0.43/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.98 % set(auto2) -> assign(stats, some).
% 0.43/0.98 % set(auto2) -> clear(echo_input).
% 0.43/0.98 % set(auto2) -> set(quiet).
% 0.43/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.98 % set(auto2) -> clear(print_given).
% 0.43/0.98 assign(lrs_ticks,-1).
% 0.43/0.98 assign(sos_limit,10000).
% 0.43/0.98 assign(order,kbo).
% 0.43/0.98 set(lex_order_vars).
% 0.43/0.98 clear(print_given).
% 0.43/0.98
% 0.43/0.98 % formulas(sos). % not echoed (21 formulas)
% 0.43/0.98
% 0.43/0.98 ============================== end of input ==========================
% 0.43/0.98
% 0.43/0.98 % From the command line: assign(max_seconds, 300).
% 0.43/0.98
% 0.43/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.98
% 0.43/0.98 % Formulas that are not ordinary clauses:
% 0.43/0.98
% 0.43/0.98 ============================== end of process non-clausal formulas ===
% 0.43/0.98
% 0.43/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/0.98
% 0.43/0.98 ============================== PREDICATE ELIMINATION =================
% 0.43/0.98 1 -member(A,B) | -member(A,C) | -difference(D,B,C) # label(not_member_of_difference) # label(axiom). [assumption].
% 0.43/0.98 2 difference(b,a,bDa) # label(b_minus_a) # label(hypothesis). [assumption].
% 0.43/0.98 3 difference(A,B,C) | member(k(A,B,C),A) | member(k(A,B,C),C) # label(difference_axiom2) # label(axiom). [assumption].
% 0.43/0.98 Derived: -member(A,a) | -member(A,bDa). [resolve(1,c,2,a)].
% 0.43/0.98 Derived: -member(A,B) | -member(A,C) | member(k(D,B,C),D) | member(k(D,B,C),C). [resolve(1,c,3,a)].
% 0.43/0.98 4 -difference(A,B,C) | -member(D,C) | member(D,A) # label(member_of_difference) # label(axiom). [assumption].
% 0.43/0.98 Derived: -member(A,bDa) | member(A,b). [resolve(4,a,2,a)].
% 0.43/0.98 Derived: -member(A,B) | member(A,C) | member(k(C,D,B),C) | member(k(C,D,B),B). [resolve(4,a,3,a)].
% 0.43/0.98 5 -member(A,B) | -difference(B,C,D) | member(A,D) | member(A,C) # label(member_of_difference_or_set2) # label(axiom). [assumption].
% 0.43/0.98 Derived: -member(A,b) | member(A,bDa) | member(A,a). [resolve(5,b,2,a)].
% 0.43/0.98 Derived: -member(A,B) | member(A,C) | member(A,D) | member(k(B,D,C),B) | member(k(B,D,C),C). [resolve(5,b,3,a)].
% 0.43/0.98 6 -member(k(A,B,C),B) | member(k(A,B,C),C) | difference(A,B,C) # label(difference_axiom1) # label(axiom). [assumption].
% 0.43/0.98 Derived: -member(k(A,B,C),B) | member(k(A,B,C),C) | -member(D,B) | -member(D,C). [resolve(6,c,1,c)].
% 0.43/0.98 Derived: -member(k(A,B,C),B) | member(k(A,B,C),C) | -member(D,C) | member(D,A). [resolve(6,c,4,a)].
% 0.43/0.98 Derived: -member(k(A,B,C),B) | member(k(A,B,C),C) | -member(D,A) | member(D,C) | member(D,B). [resolve(6,c,5,b)].
% 0.43/0.98 7 -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].
% 0.43/0.98 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(7,d,1,c)].
% 0.43/0.99 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(7,d,4,a)].
% 0.43/0.99 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(7,d,5,b)].
% 0.43/0.99 8 -intersection(a,bDa,aI_bDa) # label(a_intersection_bDa) # label(negated_conjecture). [assumption].
% 0.43/0.99 9 member(h(A,B,C),C) | intersection(A,B,C) | member(h(A,B,C),A) # label(intersection_axiom1) # label(axiom). [assumption].
% 0.43/0.99 10 member(h(A,B,C),C) | intersection(A,B,C) | member(h(A,B,C),B) # label(intersection_axiom2) # label(axiom). [assumption].
% 0.43/0.99 Derived: member(h(a,bDa,aI_bDa),aI_bDa) | member(h(a,bDa,aI_bDa),a). [resolve(8,a,9,b)].
% 0.43/0.99 Derived: member(h(a,bDa,aI_bDa),aI_bDa) | member(h(a,bDa,aI_bDa),bDa). [resolve(8,a,10,b)].
% 0.43/0.99 11 -intersection(A,B,C) | -member(D,C) | member(D,A) # label(member_of_intersection_is_member_of_set1) # label(axiom). [assumption].
% 0.43/0.99 Derived: -member(A,B) | member(A,C) | member(h(C,D,B),B) | member(h(C,D,B),C). [resolve(11,a,9,b)].
% 0.43/0.99 Derived: -member(A,B) | member(A,C) | member(h(C,D,B),B) | member(h(C,D,B),D). [resolve(11,a,10,b)].
% 0.43/0.99 12 -intersection(A,B,C) | -member(D,C) | member(D,B) # label(member_of_intersection_is_member_of_set2) # label(axiom). [assumption].
% 0.43/0.99 Derived: -member(A,B) | member(A,C) | member(h(D,C,B),B) | member(h(D,C,B),D). [resolve(12,a,9,b)].
% 0.43/0.99 Derived: -member(A,B) | member(A,C) | member(h(D,C,B),B) | member(h(D,C,B),C). [resolve(12,a,10,b)].
% 0.43/0.99 13 -intersection(A,B,C) | -member(D,B) | -member(D,A) | member(D,C) # label(member_of_both_is_member_of_intersection) # label(axiom). [assumption].
% 0.43/0.99 Derived: -member(A,B) | -member(A,C) | member(A,D) | member(h(C,B,D),D) | member(h(C,B,D),C). [resolve(13,a,9,b)].
% 0.43/0.99 Derived: -member(A,B) | -member(A,C) | member(A,D) | member(h(C,B,D),D) | member(h(C,B,D),B). [resolve(13,a,10,b)].
% 0.43/0.99 14 -member(h(A,B,C),C) | -member(h(A,B,C),B) | -member(h(A,B,C),A) | intersection(A,B,C) # label(intersection_axiom3) # label(axiom). [assumption].
% 0.43/0.99 Derived: -member(h(A,B,C),C) | -member(h(A,B,C),B) | -member(h(A,B,C),A) | -member(D,C) | member(D,A). [resolve(14,d,11,a)].
% 0.43/0.99 Derived: -member(h(A,B,C),C) | -member(h(A,B,C),B) | -member(h(A,B,C),A) | -member(D,C) | member(D,B). [resolve(14,d,12,a)].
% 0.43/0.99 Derived: -member(h(A,B,C),C) | -member(h(A,B,C),B) | -member(h(A,B,C),A) | -member(D,B) | -member(D,A) | member(D,C). [resolve(14,d,13,a)].
% 0.43/0.99 15 -subset(A,B) | -subset(B,A) | equal_sets(B,A) # label(subsets_are_set_equal_sets) # label(axiom). [assumption].
% 0.43/0.99 16 -equal_sets(A,B) | subset(A,B) # label(set_equal_sets_are_subsets1) # label(axiom). [assumption].
% 0.43/0.99 17 -equal_sets(A,B) | subset(B,A) # label(set_equal_sets_are_subsets2) # label(axiom). [assumption].
% 0.43/0.99 18 -member(A,B) | -subset(B,C) | member(A,C) # label(membership_in_subsets) # label(axiom). [assumption].
% 0.43/0.99 19 subset(A,B) | member(member_of_1_not_of_2(A,B),A) # label(subsets_axiom1) # label(axiom). [assumption].
% 0.43/0.99 20 -member(member_of_1_not_of_2(A,B),B) | subset(A,B) # label(subsets_axiom2) # label(axiom). [assumption].
% 0.43/0.99 Derived: -member(A,B) | member(A,C) | member(member_of_1_not_of_2(B,C),B). [resolve(18,b,19,a)].
% 0.43/0.99 Derived: -member(A,B) | member(A,C) | -member(member_of_1_not_of_2(B,C),C). [resolve(18,b,20,b)].
% 0.43/0.99
% 0.43/0.99 ============================== end predicate elimination =============
% 0.43/0.99
% 0.43/0.99 Auto_denials: (non-Horn, no changes).
% 0.43/0.99
% 0.43/0.99 Term ordering decisions:
% 0.43/0.99 Function symbol KB weights: bDa=1. a=1. aI_bDa=1. b=1. member_of_1_not_of_2=1. h=1. k=1.
% 0.43/0.99
% 0.43/0.99 ============================== end of process initial clauses ========
% 0.43/0.99
% 0.43/0.99 ============================== CLAUSES FOR SEARCH ====================
% 0.43/0.99
% 0.43/0.99 ============================== end of clauses for search =============
% 0.43/0.99
% 0.43/0.99 ============================== SEARCH ================================
% 0.43/0.99
% 0.43/0.99 % Starting search at 0.02 seconds.
% 0.43/0.99
% 0.43/0.99 ============================== PROOF =================================
% 0.43/0.99 % SZS status Unsatisfiable
% 0.43/0.99 % SZS output start Refutation
% 0.43/0.99
% 0.43/0.99 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.43/0.99 % Length of proof is 12.
% 0.43/0.99 % Level of proof is 3.
% 0.43/0.99 % Maximum clause weight is 6.000.
% 0.43/0.99 % Given clauses 14.
% 0.43/0.99
% 0.43/0.99 1 -member(A,B) | -member(A,C) | -difference(D,B,C) # label(not_member_of_difference) # label(axiom). [assumption].
% 0.43/0.99 2 difference(b,a,bDa) # label(b_minus_a) # label(hypothesis). [assumption].
% 0.43/0.99 8 -intersection(a,bDa,aI_bDa) # label(a_intersection_bDa) # label(negated_conjecture). [assumption].
% 0.43/0.99 9 member(h(A,B,C),C) | intersection(A,B,C) | member(h(A,B,C),A) # label(intersection_axiom1) # label(axiom). [assumption].
% 0.43/0.99 10 member(h(A,B,C),C) | intersection(A,B,C) | member(h(A,B,C),B) # label(intersection_axiom2) # label(axiom). [assumption].
% 0.43/0.99 21 -member(A,aI_bDa) # label(prove_aI_bDa_is_empty) # label(negated_conjecture). [assumption].
% 0.43/0.99 22 -member(A,a) | -member(A,bDa). [resolve(1,c,2,a)].
% 0.43/0.99 34 member(h(a,bDa,aI_bDa),aI_bDa) | member(h(a,bDa,aI_bDa),a). [resolve(8,a,9,b)].
% 0.43/0.99 35 member(h(a,bDa,aI_bDa),a). [copy(34),unit_del(a,21)].
% 0.43/0.99 36 member(h(a,bDa,aI_bDa),aI_bDa) | member(h(a,bDa,aI_bDa),bDa). [resolve(8,a,10,b)].
% 0.43/0.99 37 member(h(a,bDa,aI_bDa),bDa). [copy(36),unit_del(a,21)].
% 0.43/0.99 73 $F. [resolve(35,a,22,a),unit_del(a,37)].
% 0.43/0.99
% 0.43/0.99 % SZS output end Refutation
% 0.43/0.99 ============================== end of proof ==========================
% 0.43/0.99
% 0.43/0.99 ============================== STATISTICS ============================
% 0.43/0.99
% 0.43/0.99 Given=14. Generated=146. Kept=50. proofs=1.
% 0.43/0.99 Usable=14. Sos=24. Demods=0. Limbo=12, Disabled=46. Hints=0.
% 0.43/0.99 Megabytes=0.08.
% 0.43/0.99 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.43/0.99
% 0.43/0.99 ============================== end of statistics =====================
% 0.43/0.99
% 0.43/0.99 ============================== end of search =========================
% 0.43/0.99
% 0.43/0.99 THEOREM PROVED
% 0.43/0.99 % SZS status Unsatisfiable
% 0.43/0.99
% 0.43/0.99 Exiting with 1 proof.
% 0.43/0.99
% 0.43/0.99 Process 26850 exit (max_proofs) Sun Jul 10 20:24:39 2022
% 0.43/0.99 Prover9 interrupted
%------------------------------------------------------------------------------