TSTP Solution File: SET950+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET950+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 04:33:38 EDT 2022
% Result : Theorem 9.35s 9.61s
% Output : Refutation 9.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET950+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 03:36:40 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.46/1.00 ============================== Prover9 ===============================
% 0.46/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.00 Process 30200 was started by sandbox2 on n016.cluster.edu,
% 0.46/1.00 Sun Jul 10 03:36:41 2022
% 0.46/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30046_n016.cluster.edu".
% 0.46/1.00 ============================== end of head ===========================
% 0.46/1.00
% 0.46/1.00 ============================== INPUT =================================
% 0.46/1.00
% 0.46/1.00 % Reading from file /tmp/Prover9_30046_n016.cluster.edu
% 0.46/1.00
% 0.46/1.00 set(prolog_style_variables).
% 0.46/1.00 set(auto2).
% 0.46/1.00 % set(auto2) -> set(auto).
% 0.46/1.00 % set(auto) -> set(auto_inference).
% 0.46/1.00 % set(auto) -> set(auto_setup).
% 0.46/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.00 % set(auto) -> set(auto_limits).
% 0.46/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.00 % set(auto) -> set(auto_denials).
% 0.46/1.00 % set(auto) -> set(auto_process).
% 0.46/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.00 % set(auto2) -> assign(stats, some).
% 0.46/1.00 % set(auto2) -> clear(echo_input).
% 0.46/1.00 % set(auto2) -> set(quiet).
% 0.46/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.00 % set(auto2) -> clear(print_given).
% 0.46/1.00 assign(lrs_ticks,-1).
% 0.46/1.00 assign(sos_limit,10000).
% 0.46/1.00 assign(order,kbo).
% 0.46/1.00 set(lex_order_vars).
% 0.46/1.00 clear(print_given).
% 0.46/1.00
% 0.46/1.00 % formulas(sos). % not echoed (10 formulas)
% 0.46/1.00
% 0.46/1.00 ============================== end of input ==========================
% 0.46/1.00
% 0.46/1.00 % From the command line: assign(max_seconds, 300).
% 0.46/1.00
% 0.46/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.00
% 0.46/1.00 % Formulas that are not ordinary clauses:
% 0.46/1.00 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 3 (all A all B all C (C = cartesian_product2(A,B) <-> (all D (in(D,C) <-> (exists E exists F (in(E,A) & in(F,B) & D = ordered_pair(E,F))))))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 4 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 5 (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].
% 0.46/1.00 6 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 7 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 8 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 9 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 10 -(all A all B all C all D -(subset(A,cartesian_product2(B,C)) & in(D,A) & (all E all F -(in(E,B) & in(F,C) & D = ordered_pair(E,F))))) # label(t103_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.46/1.00
% 0.46/1.00 ============================== end of process non-clausal formulas ===
% 0.46/1.00
% 0.46/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.00
% 0.46/1.00 ============================== PREDICATE ELIMINATION =================
% 0.46/1.00 11 -subset(A,B) | -in(C,A) | in(C,B) # label(d3_tarski) # label(axiom). [clausify(4)].
% 0.46/1.00 12 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(9)].
% 0.46/1.00 13 subset(c3,cartesian_product2(c4,c5)) # label(t103_zfmisc_1) # label(negated_conjecture). [clausify(10)].
% 0.46/1.00 14 subset(A,B) | in(f6(A,B),A) # label(d3_tarski) # label(axiom). [clausify(4)].
% 9.35/9.61 15 subset(A,B) | -in(f6(A,B),B) # label(d3_tarski) # label(axiom). [clausify(4)].
% 9.35/9.61 Derived: -in(A,c3) | in(A,cartesian_product2(c4,c5)). [resolve(11,a,13,a)].
% 9.35/9.61 Derived: -in(A,B) | in(A,C) | in(f6(B,C),B). [resolve(11,a,14,a)].
% 9.35/9.61 Derived: -in(A,B) | in(A,C) | -in(f6(B,C),C). [resolve(11,a,15,a)].
% 9.35/9.61
% 9.35/9.61 ============================== end predicate elimination =============
% 9.35/9.61
% 9.35/9.61 Auto_denials: (non-Horn, no changes).
% 9.35/9.61
% 9.35/9.61 Term ordering decisions:
% 9.35/9.61
% 9.35/9.61 % Assigning unary symbol singleton kb_weight 0 and highest precedence (19).
% 9.35/9.61 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. cartesian_product2=1. ordered_pair=1. unordered_pair=1. f6=1. f3=1. f4=1. f5=1. f1=1. f2=1. singleton=0.
% 9.35/9.61
% 9.35/9.61 ============================== end of process initial clauses ========
% 9.35/9.61
% 9.35/9.61 ============================== CLAUSES FOR SEARCH ====================
% 9.35/9.61
% 9.35/9.61 ============================== end of clauses for search =============
% 9.35/9.61
% 9.35/9.61 ============================== SEARCH ================================
% 9.35/9.61
% 9.35/9.61 % Starting search at 0.01 seconds.
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=63.000, iters=3445
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=60.000, iters=3403
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=57.000, iters=3336
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=50.000, iters=3399
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=49.000, iters=3368
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=48.000, iters=3362
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=47.000, iters=3427
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=46.000, iters=3343
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=45.000, iters=3398
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=44.000, iters=3349
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=43.000, iters=3377
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=42.000, iters=3364
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=41.000, iters=3363
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=40.000, iters=3394
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=39.000, iters=3381
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=38.000, iters=3359
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=37.000, iters=3438
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=36.000, iters=3340
% 9.35/9.61
% 9.35/9.61 Low Water (keep): wt=35.000, iters=3390
% 9.35/9.61
% 9.35/9.61 ============================== PROOF =================================
% 9.35/9.61 % SZS status Theorem
% 9.35/9.61 % SZS output start Refutation
% 9.35/9.61
% 9.35/9.61 % Proof 1 at 8.61 (+ 0.02) seconds.
% 9.35/9.61 % Length of proof is 26.
% 9.35/9.61 % Level of proof is 8.
% 9.35/9.61 % Maximum clause weight is 28.000.
% 9.35/9.61 % Given clauses 495.
% 9.35/9.61
% 9.35/9.61 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 9.35/9.61 3 (all A all B all C (C = cartesian_product2(A,B) <-> (all D (in(D,C) <-> (exists E exists F (in(E,A) & in(F,B) & D = ordered_pair(E,F))))))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 9.35/9.61 4 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 9.35/9.61 5 (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].
% 9.35/9.61 10 -(all A all B all C all D -(subset(A,cartesian_product2(B,C)) & in(D,A) & (all E all F -(in(E,B) & in(F,C) & D = ordered_pair(E,F))))) # label(t103_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 9.35/9.61 11 -subset(A,B) | -in(C,A) | in(C,B) # label(d3_tarski) # label(axiom). [clausify(4)].
% 9.35/9.61 13 subset(c3,cartesian_product2(c4,c5)) # label(t103_zfmisc_1) # label(negated_conjecture). [clausify(10)].
% 9.35/9.61 17 in(c6,c3) # label(t103_zfmisc_1) # label(negated_conjecture). [clausify(10)].
% 9.35/9.61 18 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(2)].
% 9.35/9.61 19 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(5)].
% 9.35/9.61 20 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)). [copy(19),rewrite([18(4)])].
% 9.35/9.61 29 -in(A,c4) | -in(B,c5) | ordered_pair(A,B) != c6 # label(t103_zfmisc_1) # label(negated_conjecture). [clausify(10)].
% 9.35/9.61 30 -in(A,c4) | -in(B,c5) | unordered_pair(singleton(A),unordered_pair(A,B)) != c6. [copy(29),rewrite([20(5)])].
% 9.35/9.61 31 cartesian_product2(A,B) != C | -in(D,C) | in(f1(A,B,C,D),A) # label(d2_zfmisc_1) # label(axiom). [clausify(3)].
% 9.35/9.61 32 cartesian_product2(A,B) != C | -in(D,C) | in(f2(A,B,C,D),B) # label(d2_zfmisc_1) # label(axiom). [clausify(3)].
% 9.35/9.61 35 cartesian_product2(A,B) != C | -in(D,C) | ordered_pair(f1(A,B,C,D),f2(A,B,C,D)) = D # label(d2_zfmisc_1) # label(axiom). [clausify(3)].
% 9.35/9.61 36 cartesian_product2(A,B) != C | -in(D,C) | unordered_pair(singleton(f1(A,B,C,D)),unordered_pair(f1(A,B,C,D),f2(A,B,C,D))) = D. [copy(35),rewrite([20(6)])].
% 9.35/9.61 39 -in(A,c3) | in(A,cartesian_product2(c4,c5)). [resolve(11,a,13,a)].
% 9.35/9.61 137 in(c6,cartesian_product2(c4,c5)). [resolve(39,a,17,a)].
% 9.35/9.61 199 cartesian_product2(c4,c5) != cartesian_product2(A,B) | in(f2(A,B,cartesian_product2(c4,c5),c6),B). [resolve(137,a,32,b),flip(a)].
% 9.35/9.61 200 cartesian_product2(c4,c5) != cartesian_product2(A,B) | in(f1(A,B,cartesian_product2(c4,c5),c6),A). [resolve(137,a,31,b),flip(a)].
% 9.35/9.61 2185 in(f2(c4,c5,cartesian_product2(c4,c5),c6),c5). [xx_res(199,a)].
% 9.35/9.61 2208 -in(A,c4) | unordered_pair(singleton(A),unordered_pair(A,f2(c4,c5,cartesian_product2(c4,c5),c6))) != c6. [resolve(2185,a,30,b)].
% 9.35/9.61 2567 in(f1(c4,c5,cartesian_product2(c4,c5),c6),c4). [xx_res(200,a)].
% 9.35/9.61 2568 unordered_pair(singleton(f1(c4,c5,cartesian_product2(c4,c5),c6)),unordered_pair(f1(c4,c5,cartesian_product2(c4,c5),c6),f2(c4,c5,cartesian_product2(c4,c5),c6))) != c6. [resolve(2567,a,2208,a)].
% 9.35/9.61 6953 $F. [ur(36,b,137,a,c,2568,a),xx(a)].
% 9.35/9.61
% 9.35/9.61 % SZS output end Refutation
% 9.35/9.61 ============================== end of proof ==========================
% 9.35/9.61
% 9.35/9.61 ============================== STATISTICS ============================
% 9.35/9.61
% 9.35/9.61 Given=495. Generated=16836. Kept=6930. proofs=1.
% 9.35/9.61 Usable=495. Sos=6362. Demods=2. Limbo=0, Disabled=97. Hints=0.
% 9.35/9.61 Megabytes=11.35.
% 9.35/9.61 User_CPU=8.61, System_CPU=0.02, Wall_clock=9.
% 9.35/9.61
% 9.35/9.61 ============================== end of statistics =====================
% 9.35/9.61
% 9.35/9.61 ============================== end of search =========================
% 9.35/9.61
% 9.35/9.61 THEOREM PROVED
% 9.35/9.61 % SZS status Theorem
% 9.35/9.61
% 9.35/9.61 Exiting with 1 proof.
% 9.35/9.61
% 9.35/9.61 Process 30200 exit (max_proofs) Sun Jul 10 03:36:50 2022
% 9.35/9.61 Prover9 interrupted
%------------------------------------------------------------------------------