TSTP Solution File: SET974+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET974+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 04:33:47 EDT 2022
% Result : Theorem 0.42s 0.98s
% Output : Refutation 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET974+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n029.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 15:13:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/0.98 ============================== Prover9 ===============================
% 0.42/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.98 Process 24165 was started by sandbox2 on n029.cluster.edu,
% 0.42/0.98 Sun Jul 10 15:13:02 2022
% 0.42/0.98 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24010_n029.cluster.edu".
% 0.42/0.98 ============================== end of head ===========================
% 0.42/0.98
% 0.42/0.98 ============================== INPUT =================================
% 0.42/0.98
% 0.42/0.98 % Reading from file /tmp/Prover9_24010_n029.cluster.edu
% 0.42/0.98
% 0.42/0.98 set(prolog_style_variables).
% 0.42/0.98 set(auto2).
% 0.42/0.98 % set(auto2) -> set(auto).
% 0.42/0.98 % set(auto) -> set(auto_inference).
% 0.42/0.98 % set(auto) -> set(auto_setup).
% 0.42/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.98 % set(auto) -> set(auto_limits).
% 0.42/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.98 % set(auto) -> set(auto_denials).
% 0.42/0.98 % set(auto) -> set(auto_process).
% 0.42/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.98 % set(auto2) -> assign(stats, some).
% 0.42/0.98 % set(auto2) -> clear(echo_input).
% 0.42/0.98 % set(auto2) -> set(quiet).
% 0.42/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.98 % set(auto2) -> clear(print_given).
% 0.42/0.98 assign(lrs_ticks,-1).
% 0.42/0.98 assign(sos_limit,10000).
% 0.42/0.98 assign(order,kbo).
% 0.42/0.98 set(lex_order_vars).
% 0.42/0.98 clear(print_given).
% 0.42/0.98
% 0.42/0.98 % formulas(sos). % not echoed (12 formulas)
% 0.42/0.98
% 0.42/0.98 ============================== end of input ==========================
% 0.42/0.98
% 0.42/0.98 % From the command line: assign(max_seconds, 300).
% 0.42/0.98
% 0.42/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.98
% 0.42/0.98 % Formulas that are not ordinary clauses:
% 0.42/0.98 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 3 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 4 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 5 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 6 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 7 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 8 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 9 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 10 (all A all B all C all D all E -(in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) & (all F all G -(A = ordered_pair(F,G) & in(F,set_intersection2(B,D)) & in(G,set_intersection2(C,E)))))) # label(t104_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 11 (all A all B (-(-disjoint(A,B) & (all C -in(C,set_intersection2(A,B)))) & -((exists C in(C,set_intersection2(A,B))) & disjoint(A,B)))) # label(t4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 12 -(all A all B all C all D (disjoint(A,B) | disjoint(C,D) -> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)))) # label(t127_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/0.98
% 0.42/0.98 ============================== end of process non-clausal formulas ===
% 0.42/0.98
% 0.42/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/0.98
% 0.42/0.98 ============================== PREDICATE ELIMINATION =================
% 0.42/0.98
% 0.42/0.98 ============================== end predicate elimination =============
% 0.42/0.98
% 0.42/0.98 Auto_denials: (non-Horn, no changes).
% 0.42/0.98
% 0.42/0.98 Term ordering decisions:
% 0.42/0.98
% 0.42/0.98 % Assigning unary symbol singleton kb_weight 0 and highest precedence (18).
% 0.42/0.98 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. set_intersection2=1. cartesian_product2=1. unordered_pair=1. ordered_pair=1. f3=1. f1=1. f2=1. singleton=0.
% 0.42/0.98
% 0.42/0.98 ============================== end of process initial clauses ========
% 0.42/0.98
% 0.42/0.98 ============================== CLAUSES FOR SEARCH ====================
% 0.42/0.98
% 0.42/0.98 ============================== end of clauses for search =============
% 0.42/0.98
% 0.42/0.98 ============================== SEARCH ================================
% 0.42/0.98
% 0.42/0.98 % Starting search at 0.01 seconds.
% 0.42/0.98
% 0.42/0.98 ============================== PROOF =================================
% 0.42/0.98 % SZS status Theorem
% 0.42/0.98 % SZS output start Refutation
% 0.42/0.98
% 0.42/0.98 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.42/0.98 % Length of proof is 19.
% 0.42/0.98 % Level of proof is 6.
% 0.42/0.98 % Maximum clause weight is 19.000.
% 0.42/0.98 % Given clauses 33.
% 0.42/0.98
% 0.42/0.98 3 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 10 (all A all B all C all D all E -(in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) & (all F all G -(A = ordered_pair(F,G) & in(F,set_intersection2(B,D)) & in(G,set_intersection2(C,E)))))) # label(t104_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 11 (all A all B (-(-disjoint(A,B) & (all C -in(C,set_intersection2(A,B)))) & -((exists C in(C,set_intersection2(A,B))) & disjoint(A,B)))) # label(t4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 12 -(all A all B all C all D (disjoint(A,B) | disjoint(C,D) -> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)))) # label(t127_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/0.98 15 disjoint(c3,c4) | disjoint(c5,c6) # label(t127_zfmisc_1) # label(negated_conjecture). [clausify(12)].
% 0.42/0.98 17 set_intersection2(A,B) = set_intersection2(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(3)].
% 0.42/0.98 20 disjoint(A,B) | in(f3(A,B),set_intersection2(A,B)) # label(t4_xboole_0) # label(axiom). [clausify(11)].
% 0.42/0.98 25 -disjoint(cartesian_product2(c3,c5),cartesian_product2(c4,c6)) # label(t127_zfmisc_1) # label(negated_conjecture). [clausify(12)].
% 0.42/0.98 26 -in(A,set_intersection2(B,C)) | -disjoint(B,C) # label(t4_xboole_0) # label(axiom). [clausify(11)].
% 0.42/0.98 28 -in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) | in(f1(A,B,C,D,E),set_intersection2(B,D)) # label(t104_zfmisc_1) # label(axiom). [clausify(10)].
% 0.42/0.98 29 -in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) | in(f2(A,B,C,D,E),set_intersection2(C,E)) # label(t104_zfmisc_1) # label(axiom). [clausify(10)].
% 0.42/0.98 33 in(f3(cartesian_product2(c3,c5),cartesian_product2(c4,c6)),set_intersection2(cartesian_product2(c3,c5),cartesian_product2(c4,c6))). [resolve(25,a,20,a)].
% 0.42/0.98 35 -in(A,set_intersection2(c5,c6)) | disjoint(c3,c4). [resolve(26,b,15,b)].
% 0.42/0.98 40 -in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E))) | in(f1(A,D,E,B,C),set_intersection2(B,D)). [para(17(a,1),28(a,2)),rewrite([17(6)])].
% 0.42/0.98 46 in(f2(f3(cartesian_product2(c3,c5),cartesian_product2(c4,c6)),c3,c5,c4,c6),set_intersection2(c5,c6)). [resolve(33,a,29,a)].
% 0.42/0.98 58 in(f1(f3(cartesian_product2(c3,c5),cartesian_product2(c4,c6)),c4,c6,c3,c5),set_intersection2(c3,c4)). [resolve(40,a,33,a)].
% 0.42/0.98 61 disjoint(c3,c4). [resolve(46,a,35,a)].
% 0.42/0.98 66 -in(A,set_intersection2(c3,c4)). [resolve(61,a,26,b)].
% 0.42/0.98 67 $F. [resolve(66,a,58,a)].
% 0.42/0.98
% 0.42/0.98 % SZS output end Refutation
% 0.42/0.98 ============================== end of proof ==========================
% 0.42/0.98
% 0.42/0.98 ============================== STATISTICS ============================
% 0.42/0.98
% 0.42/0.98 Given=33. Generated=98. Kept=51. proofs=1.
% 0.42/0.98 Usable=30. Sos=16. Demods=6. Limbo=1, Disabled=19. Hints=0.
% 0.42/0.98 Megabytes=0.13.
% 0.42/0.98 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.42/0.98
% 0.42/0.98 ============================== end of statistics =====================
% 0.42/0.98
% 0.42/0.98 ============================== end of search =========================
% 0.42/0.98
% 0.42/0.98 THEOREM PROVED
% 0.42/0.98 % SZS status Theorem
% 0.42/0.98
% 0.42/0.98 Exiting with 1 proof.
% 0.42/0.98
% 0.42/0.98 Process 24165 exit (max_proofs) Sun Jul 10 15:13:02 2022
% 0.42/0.98 Prover9 interrupted
%------------------------------------------------------------------------------