TSTP Solution File: SET914+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET914+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 04:33:22 EDT 2022
% Result : Theorem 0.70s 0.99s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET914+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 15:26:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.67/0.96 ============================== Prover9 ===============================
% 0.67/0.96 Prover9 (32) version 2009-11A, November 2009.
% 0.67/0.96 Process 29283 was started by sandbox2 on n018.cluster.edu,
% 0.67/0.96 Sun Jul 10 15:26:28 2022
% 0.67/0.96 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_29130_n018.cluster.edu".
% 0.67/0.96 ============================== end of head ===========================
% 0.67/0.96
% 0.67/0.96 ============================== INPUT =================================
% 0.67/0.96
% 0.67/0.96 % Reading from file /tmp/Prover9_29130_n018.cluster.edu
% 0.67/0.96
% 0.67/0.96 set(prolog_style_variables).
% 0.67/0.96 set(auto2).
% 0.67/0.96 % set(auto2) -> set(auto).
% 0.67/0.96 % set(auto) -> set(auto_inference).
% 0.67/0.96 % set(auto) -> set(auto_setup).
% 0.67/0.96 % set(auto_setup) -> set(predicate_elim).
% 0.67/0.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.67/0.96 % set(auto) -> set(auto_limits).
% 0.67/0.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.67/0.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.67/0.96 % set(auto) -> set(auto_denials).
% 0.67/0.96 % set(auto) -> set(auto_process).
% 0.67/0.96 % set(auto2) -> assign(new_constants, 1).
% 0.67/0.96 % set(auto2) -> assign(fold_denial_max, 3).
% 0.67/0.96 % set(auto2) -> assign(max_weight, "200.000").
% 0.67/0.96 % set(auto2) -> assign(max_hours, 1).
% 0.67/0.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.67/0.96 % set(auto2) -> assign(max_seconds, 0).
% 0.67/0.96 % set(auto2) -> assign(max_minutes, 5).
% 0.67/0.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.67/0.96 % set(auto2) -> set(sort_initial_sos).
% 0.67/0.96 % set(auto2) -> assign(sos_limit, -1).
% 0.67/0.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.67/0.96 % set(auto2) -> assign(max_megs, 400).
% 0.67/0.96 % set(auto2) -> assign(stats, some).
% 0.67/0.96 % set(auto2) -> clear(echo_input).
% 0.67/0.96 % set(auto2) -> set(quiet).
% 0.67/0.96 % set(auto2) -> clear(print_initial_clauses).
% 0.67/0.96 % set(auto2) -> clear(print_given).
% 0.67/0.96 assign(lrs_ticks,-1).
% 0.67/0.96 assign(sos_limit,10000).
% 0.67/0.96 assign(order,kbo).
% 0.67/0.96 set(lex_order_vars).
% 0.67/0.96 clear(print_given).
% 0.67/0.96
% 0.67/0.96 % formulas(sos). % not echoed (13 formulas)
% 0.67/0.96
% 0.67/0.96 ============================== end of input ==========================
% 0.67/0.96
% 0.67/0.96 % From the command line: assign(max_seconds, 300).
% 0.67/0.96
% 0.67/0.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.67/0.96
% 0.67/0.96 % Formulas that are not ordinary clauses:
% 0.67/0.96 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 3 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 4 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 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].
% 0.67/0.96 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].
% 0.67/0.96 7 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 8 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 9 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 10 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 11 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.67/0.96 12 -(all A all B all C -(disjoint(unordered_pair(A,B),C) & in(A,C))) # label(t55_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.67/0.96
% 0.67/0.96 ============================== end of process non-clausal formulas ===
% 0.67/0.96
% 0.67/0.96 ============================== PROCESS INITIAL CLAUSES ===============
% 0.67/0.96
% 0.67/0.96 ============================== PREDICATE ELIMINATION =================
% 0.67/0.96
% 0.67/0.96 ============================== end predicate elimination =============
% 0.67/0.96
% 0.67/0.96 Auto_denials: (non-Horn, no changes).
% 0.67/0.96
% 0.67/0.96 Term ordering decisions:
% 0.67/0.96
% 0.70/0.99 % Assigning unary symbol f1 kb_weight 0 and highest precedence (15).
% 0.70/0.99 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. set_intersection2=1. unordered_pair=1. f2=1. f3=1. f1=0.
% 0.70/0.99
% 0.70/0.99 ============================== end of process initial clauses ========
% 0.70/0.99
% 0.70/0.99 ============================== CLAUSES FOR SEARCH ====================
% 0.70/0.99
% 0.70/0.99 ============================== end of clauses for search =============
% 0.70/0.99
% 0.70/0.99 ============================== SEARCH ================================
% 0.70/0.99
% 0.70/0.99 % Starting search at 0.01 seconds.
% 0.70/0.99
% 0.70/0.99 ============================== PROOF =================================
% 0.70/0.99 % SZS status Theorem
% 0.70/0.99 % SZS output start Refutation
% 0.70/0.99
% 0.70/0.99 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.70/0.99 % Length of proof is 28.
% 0.70/0.99 % Level of proof is 6.
% 0.70/0.99 % Maximum clause weight is 23.000.
% 0.70/0.99 % Given clauses 61.
% 0.70/0.99
% 0.70/0.99 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 3 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 4 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 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].
% 0.70/0.99 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].
% 0.70/0.99 7 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 8 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.70/0.99 12 -(all A all B all C -(disjoint(unordered_pair(A,B),C) & in(A,C))) # label(t55_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.70/0.99 15 in(c3,c5) # label(t55_zfmisc_1) # label(negated_conjecture). [clausify(12)].
% 0.70/0.99 16 set_intersection2(A,A) = A # label(idempotence_k3_xboole_0) # label(axiom). [clausify(8)].
% 0.70/0.99 17 disjoint(unordered_pair(c3,c4),c5) # label(t55_zfmisc_1) # label(negated_conjecture). [clausify(12)].
% 0.70/0.99 18 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(2)].
% 0.70/0.99 19 set_intersection2(A,B) = set_intersection2(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(3)].
% 0.70/0.99 23 unordered_pair(A,B) = C | in(f2(A,B,C),C) | f2(A,B,C) = A | f2(A,B,C) = B # label(d2_tarski) # label(axiom). [clausify(5)].
% 0.70/0.99 26 empty_set != A | -in(B,A) # label(d1_xboole_0) # label(axiom). [clausify(4)].
% 0.70/0.99 28 -disjoint(A,B) | set_intersection2(A,B) = empty_set # label(d7_xboole_0) # label(axiom). [clausify(7)].
% 0.70/0.99 30 unordered_pair(A,B) != C | in(D,C) | D != A # label(d2_tarski) # label(axiom). [clausify(5)].
% 0.70/0.99 31 unordered_pair(A,B) != C | in(D,C) | D != B # label(d2_tarski) # label(axiom). [clausify(5)].
% 0.70/0.99 35 set_intersection2(A,B) != C | in(D,C) | -in(D,A) | -in(D,B) # label(d3_xboole_0) # label(axiom). [clausify(6)].
% 0.70/0.99 64 -in(A,empty_set). [ur(26,a,16,a(flip)),rewrite([16(3)])].
% 0.70/0.99 67 set_intersection2(c5,unordered_pair(c3,c4)) = empty_set. [resolve(28,a,17,a),rewrite([19(5)])].
% 0.70/0.99 70 in(A,unordered_pair(B,C)) | A != C. [resolve(30,a,18,a)].
% 0.70/0.99 191 unordered_pair(A,B) = empty_set | f2(A,B,empty_set) = A | f2(A,B,empty_set) = B. [resolve(64,a,23,b)].
% 0.70/0.99 198 unordered_pair(A,B) != empty_set. [ur(31,b,64,a,c,16,a)].
% 0.70/0.99 199 f2(A,A,empty_set) = A. [factor(191,b,c),unit_del(a,198)].
% 0.70/0.99 254 -in(c3,unordered_pair(c3,c4)). [ur(35,a,67,a,b,64,a,c,15,a)].
% 0.70/0.99 255 in(A,unordered_pair(A,B)). [resolve(70,b,199,a),rewrite([199(2),18(1)])].
% 0.70/0.99 256 $F. [resolve(255,a,254,a)].
% 0.70/0.99
% 0.70/0.99 % SZS output end Refutation
% 0.70/0.99 ============================== end of proof ==========================
% 0.70/0.99
% 0.70/0.99 ============================== STATISTICS ============================
% 0.70/0.99
% 0.70/0.99 Given=61. Generated=1174. Kept=243. proofs=1.
% 0.70/0.99 Usable=58. Sos=166. Demods=6. Limbo=0, Disabled=44. Hints=0.
% 0.70/0.99 Megabytes=0.22.
% 0.70/0.99 User_CPU=0.04, System_CPU=0.01, Wall_clock=0.
% 0.70/0.99
% 0.70/0.99 ============================== end of statistics =====================
% 0.70/0.99
% 0.70/0.99 ============================== end of search =========================
% 0.70/0.99
% 0.70/0.99 THEOREM PROVED
% 0.70/0.99 % SZS status Theorem
% 0.70/0.99
% 0.70/0.99 Exiting with 1 proof.
% 0.70/0.99
% 0.70/0.99 Process 29283 exit (max_proofs) Sun Jul 10 15:26:28 2022
% 0.70/0.99 Prover9 interrupted
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