TSTP Solution File: SET906+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET906+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 04:33:18 EDT 2022
% Result : Theorem 0.73s 1.04s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET906+1 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n017.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 22:06:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/0.99 ============================== Prover9 ===============================
% 0.43/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.99 Process 17983 was started by sandbox on n017.cluster.edu,
% 0.43/0.99 Sun Jul 10 22:06:34 2022
% 0.43/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_17830_n017.cluster.edu".
% 0.43/0.99 ============================== end of head ===========================
% 0.43/0.99
% 0.43/0.99 ============================== INPUT =================================
% 0.43/0.99
% 0.43/0.99 % Reading from file /tmp/Prover9_17830_n017.cluster.edu
% 0.43/0.99
% 0.43/0.99 set(prolog_style_variables).
% 0.43/0.99 set(auto2).
% 0.43/0.99 % set(auto2) -> set(auto).
% 0.43/0.99 % set(auto) -> set(auto_inference).
% 0.43/0.99 % set(auto) -> set(auto_setup).
% 0.43/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.99 % set(auto) -> set(auto_limits).
% 0.43/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.99 % set(auto) -> set(auto_denials).
% 0.43/0.99 % set(auto) -> set(auto_process).
% 0.43/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.99 % set(auto2) -> assign(stats, some).
% 0.43/0.99 % set(auto2) -> clear(echo_input).
% 0.43/0.99 % set(auto2) -> set(quiet).
% 0.43/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.99 % set(auto2) -> clear(print_given).
% 0.43/0.99 assign(lrs_ticks,-1).
% 0.43/0.99 assign(sos_limit,10000).
% 0.43/0.99 assign(order,kbo).
% 0.43/0.99 set(lex_order_vars).
% 0.43/0.99 clear(print_given).
% 0.43/0.99
% 0.43/0.99 % formulas(sos). % not echoed (13 formulas)
% 0.43/0.99
% 0.43/0.99 ============================== end of input ==========================
% 0.43/0.99
% 0.43/0.99 % From the command line: assign(max_seconds, 300).
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.99
% 0.43/0.99 % Formulas that are not ordinary clauses:
% 0.43/0.99 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 3 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 4 (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].
% 0.43/0.99 5 (all A all B all C (C = set_union2(A,B) <-> (all D (in(D,C) <-> in(D,A) | in(D,B))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 6 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 7 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 8 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 9 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 10 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 11 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 12 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 13 -(all A all B all C (subset(set_union2(unordered_pair(A,B),C),C) -> in(A,C))) # label(t47_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/0.99
% 0.43/0.99 ============================== end of process non-clausal formulas ===
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/0.99
% 0.43/0.99 ============================== PREDICATE ELIMINATION =================
% 0.43/0.99 14 -subset(A,B) | -in(C,A) | in(C,B) # label(d3_tarski) # label(axiom). [clausify(6)].
% 0.73/1.04 15 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(12)].
% 0.73/1.04 16 subset(set_union2(unordered_pair(c3,c4),c5),c5) # label(t47_zfmisc_1) # label(negated_conjecture). [clausify(13)].
% 0.73/1.04 17 subset(A,B) | in(f3(A,B),A) # label(d3_tarski) # label(axiom). [clausify(6)].
% 0.73/1.04 18 subset(A,B) | -in(f3(A,B),B) # label(d3_tarski) # label(axiom). [clausify(6)].
% 0.73/1.04 Derived: -in(A,set_union2(unordered_pair(c3,c4),c5)) | in(A,c5). [resolve(14,a,16,a)].
% 0.73/1.04 Derived: -in(A,B) | in(A,C) | in(f3(B,C),B). [resolve(14,a,17,a)].
% 0.73/1.04 Derived: -in(A,B) | in(A,C) | -in(f3(B,C),C). [resolve(14,a,18,a)].
% 0.73/1.04
% 0.73/1.04 ============================== end predicate elimination =============
% 0.73/1.04
% 0.73/1.04 Auto_denials: (non-Horn, no changes).
% 0.73/1.04
% 0.73/1.04 Term ordering decisions:
% 0.73/1.04 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. set_union2=1. unordered_pair=1. f3=1. f1=1. f2=1.
% 0.73/1.04
% 0.73/1.04 ============================== end of process initial clauses ========
% 0.73/1.04
% 0.73/1.04 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.04
% 0.73/1.04 ============================== end of clauses for search =============
% 0.73/1.04
% 0.73/1.04 ============================== SEARCH ================================
% 0.73/1.04
% 0.73/1.04 % Starting search at 0.01 seconds.
% 0.73/1.04
% 0.73/1.04 ============================== PROOF =================================
% 0.73/1.04 % SZS status Theorem
% 0.73/1.04 % SZS output start Refutation
% 0.73/1.04
% 0.73/1.04 % Proof 1 at 0.06 (+ 0.01) seconds.
% 0.73/1.04 % Length of proof is 21.
% 0.73/1.04 % Level of proof is 5.
% 0.73/1.04 % Maximum clause weight is 11.000.
% 0.73/1.04 % Given clauses 54.
% 0.73/1.04
% 0.73/1.04 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 3 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 4 (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].
% 0.73/1.04 5 (all A all B all C (C = set_union2(A,B) <-> (all D (in(D,C) <-> in(D,A) | in(D,B))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 6 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 9 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.04 13 -(all A all B all C (subset(set_union2(unordered_pair(A,B),C),C) -> in(A,C))) # label(t47_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.04 14 -subset(A,B) | -in(C,A) | in(C,B) # label(d3_tarski) # label(axiom). [clausify(6)].
% 0.73/1.04 16 subset(set_union2(unordered_pair(c3,c4),c5),c5) # label(t47_zfmisc_1) # label(negated_conjecture). [clausify(13)].
% 0.73/1.04 20 set_union2(A,A) = A # label(idempotence_k2_xboole_0) # label(axiom). [clausify(9)].
% 0.73/1.04 21 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(2)].
% 0.73/1.04 22 set_union2(A,B) = set_union2(B,A) # label(commutativity_k2_xboole_0) # label(axiom). [clausify(3)].
% 0.73/1.04 26 -in(c3,c5) # label(t47_zfmisc_1) # label(negated_conjecture). [clausify(13)].
% 0.73/1.04 30 unordered_pair(A,B) != C | in(D,C) | D != A # label(d2_tarski) # label(axiom). [clausify(4)].
% 0.73/1.04 33 set_union2(A,B) != C | in(D,C) | -in(D,B) # label(d2_xboole_0) # label(axiom). [clausify(5)].
% 0.73/1.04 40 -in(A,set_union2(unordered_pair(c3,c4),c5)) | in(A,c5). [resolve(14,a,16,a)].
% 0.73/1.04 41 -in(A,set_union2(c5,unordered_pair(c3,c4))) | in(A,c5). [copy(40),rewrite([22(5)])].
% 0.73/1.04 64 in(A,unordered_pair(B,C)) | A != C. [resolve(30,a,21,a)].
% 0.73/1.04 179 -in(c3,set_union2(c5,unordered_pair(c3,c4))). [ur(41,b,26,a)].
% 0.73/1.04 308 in(A,unordered_pair(A,B)). [resolve(64,b,20,a),rewrite([20(1),21(1)])].
% 0.73/1.04 404 $F. [ur(33,a,xx,b,179,a),unit_del(a,308)].
% 0.73/1.04
% 0.73/1.04 % SZS output end Refutation
% 0.73/1.04 ============================== end of proof ==========================
% 0.73/1.04
% 0.73/1.04 ============================== STATISTICS ============================
% 0.73/1.04
% 0.73/1.04 Given=54. Generated=1419. Kept=383. proofs=1.
% 0.73/1.04 Usable=52. Sos=276. Demods=3. Limbo=9, Disabled=75. Hints=0.
% 0.73/1.04 Megabytes=0.34.
% 0.73/1.04 User_CPU=0.06, System_CPU=0.01, Wall_clock=0.
% 0.73/1.04
% 0.73/1.04 ============================== end of statistics =====================
% 0.73/1.04
% 0.73/1.04 ============================== end of search =========================
% 0.73/1.04
% 0.73/1.04 THEOREM PROVED
% 0.73/1.04 % SZS status Theorem
% 0.73/1.04
% 0.73/1.04 Exiting with 1 proof.
% 0.73/1.04
% 0.73/1.04 Process 17983 exit (max_proofs) Sun Jul 10 22:06:34 2022
% 0.73/1.04 Prover9 interrupted
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