TSTP Solution File: SET903+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET903+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 04:33:17 EDT 2022
% Result : Theorem 0.46s 1.02s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET903+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 9 17:33:30 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.46/1.02 ============================== Prover9 ===============================
% 0.46/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.02 Process 30286 was started by sandbox on n010.cluster.edu,
% 0.46/1.02 Sat Jul 9 17:33:31 2022
% 0.46/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30132_n010.cluster.edu".
% 0.46/1.02 ============================== end of head ===========================
% 0.46/1.02
% 0.46/1.02 ============================== INPUT =================================
% 0.46/1.02
% 0.46/1.02 % Reading from file /tmp/Prover9_30132_n010.cluster.edu
% 0.46/1.02
% 0.46/1.02 set(prolog_style_variables).
% 0.46/1.02 set(auto2).
% 0.46/1.02 % set(auto2) -> set(auto).
% 0.46/1.02 % set(auto) -> set(auto_inference).
% 0.46/1.02 % set(auto) -> set(auto_setup).
% 0.46/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.02 % set(auto) -> set(auto_limits).
% 0.46/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.02 % set(auto) -> set(auto_denials).
% 0.46/1.02 % set(auto) -> set(auto_process).
% 0.46/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.02 % set(auto2) -> assign(stats, some).
% 0.46/1.02 % set(auto2) -> clear(echo_input).
% 0.46/1.02 % set(auto2) -> set(quiet).
% 0.46/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.02 % set(auto2) -> clear(print_given).
% 0.46/1.02 assign(lrs_ticks,-1).
% 0.46/1.02 assign(sos_limit,10000).
% 0.46/1.02 assign(order,kbo).
% 0.46/1.02 set(lex_order_vars).
% 0.46/1.02 clear(print_given).
% 0.46/1.02
% 0.46/1.02 % formulas(sos). % not echoed (9 formulas)
% 0.46/1.02
% 0.46/1.02 ============================== end of input ==========================
% 0.46/1.02
% 0.46/1.02 % From the command line: assign(max_seconds, 300).
% 0.46/1.02
% 0.46/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.02
% 0.46/1.02 % Formulas that are not ordinary clauses:
% 0.46/1.02 1 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 2 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 3 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 4 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 5 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 6 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 7 (all A all B all C -(singleton(A) = set_union2(B,C) & -(B = singleton(A) & C = singleton(A)) & -(B = empty_set & C = singleton(A)) & -(B = singleton(A) & C = empty_set))) # label(t43_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 8 -(all A all B all C -(singleton(A) = set_union2(B,C) & B != C & B != empty_set & C != empty_set)) # label(t44_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.46/1.02
% 0.46/1.02 ============================== end of process non-clausal formulas ===
% 0.46/1.02
% 0.46/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.02
% 0.46/1.02 ============================== PREDICATE ELIMINATION =================
% 0.46/1.02
% 0.46/1.02 ============================== end predicate elimination =============
% 0.46/1.02
% 0.46/1.02 Auto_denials: (non-Horn, no changes).
% 0.46/1.02
% 0.46/1.02 Term ordering decisions:
% 0.46/1.02
% 0.46/1.02 % Assigning unary symbol singleton kb_weight 0 and highest precedence (10).
% 0.46/1.02 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. set_union2=1. singleton=0.
% 0.46/1.02
% 0.46/1.02 ============================== end of process initial clauses ========
% 0.46/1.02
% 0.46/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.46/1.02
% 0.46/1.02 ============================== end of clauses for search =============
% 0.46/1.02
% 0.46/1.02 ============================== SEARCH ================================
% 0.46/1.02
% 0.46/1.02 % Starting search at 0.01 seconds.
% 0.46/1.02
% 0.46/1.02 ============================== PROOF =================================
% 0.46/1.02 % SZS status Theorem
% 0.46/1.02 % SZS output start Refutation
% 0.46/1.02
% 0.46/1.02 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.46/1.02 % Length of proof is 15.
% 0.46/1.02 % Level of proof is 6.
% 0.46/1.02 % Maximum clause weight is 13.000.
% 0.46/1.02 % Given clauses 21.
% 0.46/1.02
% 0.46/1.02 7 (all A all B all C -(singleton(A) = set_union2(B,C) & -(B = singleton(A) & C = singleton(A)) & -(B = empty_set & C = singleton(A)) & -(B = singleton(A) & C = empty_set))) # label(t43_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 8 -(all A all B all C -(singleton(A) = set_union2(B,C) & B != C & B != empty_set & C != empty_set)) # label(t44_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.46/1.02 12 singleton(c3) = set_union2(c4,c5) # label(t44_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.46/1.02 13 set_union2(c4,c5) = singleton(c3). [copy(12),flip(a)].
% 0.46/1.02 16 c5 != c4 # label(t44_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.46/1.02 17 empty_set != c4 # label(t44_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.46/1.02 18 c4 != empty_set. [copy(17),flip(a)].
% 0.46/1.02 19 c5 != empty_set # label(t44_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.46/1.02 22 singleton(A) != set_union2(B,C) | singleton(A) = B | empty_set = B # label(t43_zfmisc_1) # label(axiom). [clausify(7)].
% 0.46/1.02 23 singleton(A) != set_union2(B,C) | singleton(A) = C | C = empty_set # label(t43_zfmisc_1) # label(axiom). [clausify(7)].
% 0.46/1.02 24 singleton(A) != set_union2(B,C) | singleton(A) = C | empty_set = C. [copy(23),flip(c)].
% 0.46/1.02 28 singleton(c3) = c4. [resolve(22,a,13,a(flip)),flip(b),unit_del(b,18)].
% 0.46/1.02 29 set_union2(c4,c5) = c4. [back_rewrite(13),rewrite([28(5)])].
% 0.46/1.02 38 singleton(A) != c4 | singleton(A) = c5. [para(29(a,1),24(a,2)),flip(c),unit_del(c,19)].
% 0.46/1.02 39 $F. [resolve(38,a,28,a),rewrite([28(2)]),flip(a),unit_del(a,16)].
% 0.46/1.02
% 0.46/1.02 % SZS output end Refutation
% 0.46/1.02 ============================== end of proof ==========================
% 0.46/1.02
% 0.46/1.02 ============================== STATISTICS ============================
% 0.46/1.02
% 0.46/1.02 Given=21. Generated=89. Kept=26. proofs=1.
% 0.46/1.02 Usable=20. Sos=4. Demods=4. Limbo=0, Disabled=16. Hints=0.
% 0.46/1.02 Megabytes=0.06.
% 0.46/1.02 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.46/1.02
% 0.46/1.02 ============================== end of statistics =====================
% 0.46/1.02
% 0.46/1.02 ============================== end of search =========================
% 0.46/1.02
% 0.46/1.02 THEOREM PROVED
% 0.46/1.02 % SZS status Theorem
% 0.46/1.02
% 0.46/1.02 Exiting with 1 proof.
% 0.46/1.02
% 0.46/1.02 Process 30286 exit (max_proofs) Sat Jul 9 17:33:31 2022
% 0.46/1.02 Prover9 interrupted
%------------------------------------------------------------------------------