TSTP Solution File: SET918+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET918+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 04:33:24 EDT 2022
% Result : Theorem 0.67s 1.00s
% Output : Refutation 0.67s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET918+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 23:10:43 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.67/0.97 ============================== Prover9 ===============================
% 0.67/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.67/0.97 Process 15182 was started by sandbox on n028.cluster.edu,
% 0.67/0.97 Sun Jul 10 23:10:43 2022
% 0.67/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15029_n028.cluster.edu".
% 0.67/0.97 ============================== end of head ===========================
% 0.67/0.97
% 0.67/0.97 ============================== INPUT =================================
% 0.67/0.97
% 0.67/0.97 % Reading from file /tmp/Prover9_15029_n028.cluster.edu
% 0.67/0.97
% 0.67/0.97 set(prolog_style_variables).
% 0.67/0.97 set(auto2).
% 0.67/0.97 % set(auto2) -> set(auto).
% 0.67/0.97 % set(auto) -> set(auto_inference).
% 0.67/0.97 % set(auto) -> set(auto_setup).
% 0.67/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.67/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.67/0.97 % set(auto) -> set(auto_limits).
% 0.67/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.67/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.67/0.97 % set(auto) -> set(auto_denials).
% 0.67/0.97 % set(auto) -> set(auto_process).
% 0.67/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.67/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.67/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.67/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.67/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.67/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.67/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.67/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.67/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.67/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.67/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.67/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.67/0.97 % set(auto2) -> assign(stats, some).
% 0.67/0.97 % set(auto2) -> clear(echo_input).
% 0.67/0.97 % set(auto2) -> set(quiet).
% 0.67/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.67/0.97 % set(auto2) -> clear(print_given).
% 0.67/0.97 assign(lrs_ticks,-1).
% 0.67/0.97 assign(sos_limit,10000).
% 0.67/0.97 assign(order,kbo).
% 0.67/0.97 set(lex_order_vars).
% 0.67/0.97 clear(print_given).
% 0.67/0.97
% 0.67/0.97 % formulas(sos). % not echoed (10 formulas)
% 0.67/0.97
% 0.67/0.97 ============================== end of input ==========================
% 0.67/0.97
% 0.67/0.97 % From the command line: assign(max_seconds, 300).
% 0.67/0.97
% 0.67/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.67/0.97
% 0.67/0.97 % Formulas that are not ordinary clauses:
% 0.67/0.97 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 3 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 4 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 5 (all A all B all C (C = unordered_pair(A,B) <-> (all D (in(D,C) <-> D = A | D = B)))) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 6 (all A all B all C (C = set_intersection2(A,B) <-> (all D (in(D,C) <-> in(D,A) & in(D,B))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 7 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 8 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 9 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.97 10 -(all A all B all C -(set_intersection2(unordered_pair(A,B),C) = singleton(A) & in(B,C) & A != B)) # label(t59_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.67/0.97
% 0.67/0.97 ============================== end of process non-clausal formulas ===
% 0.67/0.97
% 0.67/0.97 ============================== PROCESS INITIAL CLAUSES ===============
% 0.67/0.97
% 0.67/0.97 ============================== PREDICATE ELIMINATION =================
% 0.67/0.97
% 0.67/0.97 ============================== end predicate elimination =============
% 0.67/0.97
% 0.67/0.97 Auto_denials: (non-Horn, no changes).
% 0.67/0.97
% 0.67/0.97 Term ordering decisions:
% 0.67/0.97
% 0.67/0.97 % Assigning unary symbol singleton kb_weight 0 and highest precedence (14).
% 0.67/0.97 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. set_intersection2=1. unordered_pair=1. f1=1. f2=1. f3=1. singleton=0.
% 0.67/0.97
% 0.67/0.97 ============================== end of process initial clauses ========
% 0.67/1.00
% 0.67/1.00 ============================== CLAUSES FOR SEARCH ====================
% 0.67/1.00
% 0.67/1.00 ============================== end of clauses for search =============
% 0.67/1.00
% 0.67/1.00 ============================== SEARCH ================================
% 0.67/1.00
% 0.67/1.00 % Starting search at 0.01 seconds.
% 0.67/1.00
% 0.67/1.00 ============================== PROOF =================================
% 0.67/1.00 % SZS status Theorem
% 0.67/1.00 % SZS output start Refutation
% 0.67/1.00
% 0.67/1.00 % Proof 1 at 0.05 (+ 0.00) seconds.
% 0.67/1.00 % Length of proof is 22.
% 0.67/1.00 % Level of proof is 5.
% 0.67/1.00 % Maximum clause weight is 14.000.
% 0.67/1.00 % Given clauses 58.
% 0.67/1.00
% 0.67/1.00 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.67/1.00 3 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/1.00 4 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.67/1.00 5 (all A all B all C (C = unordered_pair(A,B) <-> (all D (in(D,C) <-> D = A | D = B)))) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.67/1.00 6 (all A all B all C (C = set_intersection2(A,B) <-> (all D (in(D,C) <-> in(D,A) & in(D,B))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/1.00 7 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/1.00 10 -(all A all B all C -(set_intersection2(unordered_pair(A,B),C) = singleton(A) & in(B,C) & A != B)) # label(t59_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.67/1.00 12 in(c4,c5) # label(t59_zfmisc_1) # label(negated_conjecture). [clausify(10)].
% 0.67/1.00 13 set_intersection2(A,A) = A # label(idempotence_k3_xboole_0) # label(axiom). [clausify(7)].
% 0.67/1.00 14 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(2)].
% 0.67/1.00 15 set_intersection2(A,B) = set_intersection2(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(3)].
% 0.67/1.00 16 singleton(c3) = set_intersection2(unordered_pair(c3,c4),c5) # label(t59_zfmisc_1) # label(negated_conjecture). [clausify(10)].
% 0.67/1.00 17 set_intersection2(c5,unordered_pair(c3,c4)) = singleton(c3). [copy(16),rewrite([15(7)]),flip(a)].
% 0.67/1.00 23 c4 != c3 # label(t59_zfmisc_1) # label(negated_conjecture). [clausify(10)].
% 0.67/1.00 25 singleton(A) != B | -in(C,B) | C = A # label(d1_tarski) # label(axiom). [clausify(4)].
% 0.67/1.00 27 unordered_pair(A,B) != C | in(D,C) | D != A # label(d2_tarski) # label(axiom). [clausify(5)].
% 0.67/1.00 33 set_intersection2(A,B) != C | in(D,C) | -in(D,A) | -in(D,B) # label(d3_xboole_0) # label(axiom). [clausify(6)].
% 0.67/1.00 65 -in(c4,singleton(c3)). [ur(25,a,17,a(flip),c,23,a),rewrite([17(6)])].
% 0.67/1.00 77 in(A,unordered_pair(B,C)) | A != C. [resolve(27,a,14,a)].
% 0.67/1.00 295 in(A,unordered_pair(A,B)). [resolve(77,b,13,a),rewrite([13(1),14(1)])].
% 0.67/1.00 356 set_intersection2(c5,unordered_pair(A,c4)) != singleton(c3). [ur(33,b,65,a,c,12,a,d,295,a),rewrite([14(3)])].
% 0.67/1.00 357 $F. [resolve(356,a,17,a)].
% 0.67/1.00
% 0.67/1.00 % SZS output end Refutation
% 0.67/1.00 ============================== end of proof ==========================
% 0.67/1.00
% 0.67/1.00 ============================== STATISTICS ============================
% 0.67/1.00
% 0.67/1.00 Given=58. Generated=1161. Kept=345. proofs=1.
% 0.67/1.00 Usable=55. Sos=229. Demods=4. Limbo=31, Disabled=54. Hints=0.
% 0.67/1.00 Megabytes=0.26.
% 0.67/1.00 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.67/1.00
% 0.67/1.00 ============================== end of statistics =====================
% 0.67/1.00
% 0.67/1.00 ============================== end of search =========================
% 0.67/1.00
% 0.67/1.00 THEOREM PROVED
% 0.67/1.00 % SZS status Theorem
% 0.67/1.00
% 0.67/1.00 Exiting with 1 proof.
% 0.67/1.00
% 0.67/1.00 Process 15182 exit (max_proofs) Sun Jul 10 23:10:43 2022
% 0.67/1.00 Prover9 interrupted
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