TSTP Solution File: SET921+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET921+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 04:33:25 EDT 2022
% Result : Theorem 0.73s 1.01s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET921+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 : n007.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 20:43:32 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.73/1.01 ============================== Prover9 ===============================
% 0.73/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.01 Process 3597 was started by sandbox2 on n007.cluster.edu,
% 0.73/1.01 Sun Jul 10 20:43:33 2022
% 0.73/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3444_n007.cluster.edu".
% 0.73/1.01 ============================== end of head ===========================
% 0.73/1.01
% 0.73/1.01 ============================== INPUT =================================
% 0.73/1.01
% 0.73/1.01 % Reading from file /tmp/Prover9_3444_n007.cluster.edu
% 0.73/1.01
% 0.73/1.01 set(prolog_style_variables).
% 0.73/1.01 set(auto2).
% 0.73/1.01 % set(auto2) -> set(auto).
% 0.73/1.01 % set(auto) -> set(auto_inference).
% 0.73/1.01 % set(auto) -> set(auto_setup).
% 0.73/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.73/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.01 % set(auto) -> set(auto_limits).
% 0.73/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.01 % set(auto) -> set(auto_denials).
% 0.73/1.01 % set(auto) -> set(auto_process).
% 0.73/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.73/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.73/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.73/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.73/1.01 % set(auto2) -> assign(stats, some).
% 0.73/1.01 % set(auto2) -> clear(echo_input).
% 0.73/1.01 % set(auto2) -> set(quiet).
% 0.73/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.01 % set(auto2) -> clear(print_given).
% 0.73/1.01 assign(lrs_ticks,-1).
% 0.73/1.01 assign(sos_limit,10000).
% 0.73/1.01 assign(order,kbo).
% 0.73/1.01 set(lex_order_vars).
% 0.73/1.01 clear(print_given).
% 0.73/1.01
% 0.73/1.01 % formulas(sos). % not echoed (6 formulas)
% 0.73/1.01
% 0.73/1.01 ============================== end of input ==========================
% 0.73/1.01
% 0.73/1.01 % From the command line: assign(max_seconds, 300).
% 0.73/1.01
% 0.73/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.01
% 0.73/1.01 % Formulas that are not ordinary clauses:
% 0.73/1.01 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.01 2 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.01 3 (all A all B all C (C = set_difference(A,B) <-> (all D (in(D,C) <-> in(D,A) & -in(D,B))))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.01 4 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.01 5 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.01 6 -(all A all B all C (in(A,set_difference(B,singleton(C))) <-> in(A,B) & A != C)) # label(t64_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.01
% 0.73/1.01 ============================== end of process non-clausal formulas ===
% 0.73/1.01
% 0.73/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.01
% 0.73/1.01 ============================== PREDICATE ELIMINATION =================
% 0.73/1.01
% 0.73/1.01 ============================== end predicate elimination =============
% 0.73/1.01
% 0.73/1.01 Auto_denials: (non-Horn, no changes).
% 0.73/1.01
% 0.73/1.01 Term ordering decisions:
% 0.73/1.01
% 0.73/1.01 % Assigning unary symbol singleton kb_weight 0 and highest precedence (12).
% 0.73/1.01 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. set_difference=1. f1=1. f2=1. singleton=0.
% 0.73/1.01
% 0.73/1.01 ============================== end of process initial clauses ========
% 0.73/1.01
% 0.73/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.01
% 0.73/1.01 ============================== end of clauses for search =============
% 0.73/1.01
% 0.73/1.01 ============================== SEARCH ================================
% 0.73/1.01
% 0.73/1.01 % Starting search at 0.01 seconds.
% 0.73/1.01
% 0.73/1.01 ============================== PROOF =================================
% 0.73/1.01 % SZS status Theorem
% 0.73/1.01 % SZS output start Refutation
% 0.73/1.01
% 0.73/1.01 % Proof 1 at 0.04 (+ 0.00) seconds.
% 0.73/1.01 % Length of proof is 23.
% 0.73/1.01 % Level of proof is 9.
% 0.73/1.01 % Maximum clause weight is 14.000.
% 0.73/1.01 % Given clauses 82.
% 0.73/1.01
% 0.73/1.01 2 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.01 3 (all A all B all C (C = set_difference(A,B) <-> (all D (in(D,C) <-> in(D,A) & -in(D,B))))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.01 6 -(all A all B all C (in(A,set_difference(B,singleton(C))) <-> in(A,B) & A != C)) # label(t64_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.01 8 in(c3,set_difference(c4,singleton(c5))) | in(c3,c4) # label(t64_zfmisc_1) # label(negated_conjecture). [clausify(6)].
% 0.73/1.01 13 set_difference(A,B) != C | -in(D,C) | -in(D,B) # label(d4_xboole_0) # label(axiom). [clausify(3)].
% 0.73/1.01 14 in(c3,set_difference(c4,singleton(c5))) | c5 != c3 # label(t64_zfmisc_1) # label(negated_conjecture). [clausify(6)].
% 0.73/1.01 15 singleton(A) != B | -in(C,B) | C = A # label(d1_tarski) # label(axiom). [clausify(2)].
% 0.73/1.01 16 singleton(A) != B | in(C,B) | C != A # label(d1_tarski) # label(axiom). [clausify(2)].
% 0.73/1.01 17 set_difference(A,B) != C | -in(D,C) | in(D,A) # label(d4_xboole_0) # label(axiom). [clausify(3)].
% 0.73/1.01 18 -in(c3,set_difference(c4,singleton(c5))) | -in(c3,c4) | c5 = c3 # label(t64_zfmisc_1) # label(negated_conjecture). [clausify(6)].
% 0.73/1.01 20 set_difference(A,B) != C | in(D,C) | -in(D,A) | in(D,B) # label(d4_xboole_0) # label(axiom). [clausify(3)].
% 0.73/1.01 45 in(A,singleton(B)) | A != B. [xx_res(16,a)].
% 0.73/1.01 50 set_difference(c4,singleton(c5)) != set_difference(A,B) | in(c3,A) | in(c3,c4). [resolve(17,b,8,a),flip(a)].
% 0.73/1.01 53 in(c3,c4). [factor(50,b,c),xx(a)].
% 0.73/1.01 54 -in(c3,set_difference(c4,singleton(c5))) | c5 = c3. [back_unit_del(18),unit_del(b,53)].
% 0.73/1.01 90 set_difference(c4,A) != B | in(c3,B) | in(c3,A). [resolve(53,a,20,c)].
% 0.73/1.01 111 in(A,singleton(A)). [xx_res(45,b)].
% 0.73/1.01 131 -in(A,set_difference(B,singleton(A))). [ur(13,a,xx,c,111,a)].
% 0.73/1.01 276 in(c3,set_difference(c4,A)) | in(c3,A). [xx_res(90,a)].
% 0.73/1.01 277 in(c3,singleton(c5)) | c5 = c3. [resolve(276,a,54,a)].
% 0.73/1.01 293 c5 = c3 | singleton(c5) != singleton(A) | c3 = A. [resolve(277,a,15,b),flip(b)].
% 0.73/1.01 377 c5 = c3. [xx_res(293,b),flip(b),merge(b)].
% 0.73/1.01 378 $F. [back_rewrite(14),rewrite([377(3),377(7)]),xx(b),unit_del(a,131)].
% 0.73/1.01
% 0.73/1.01 % SZS output end Refutation
% 0.73/1.01 ============================== end of proof ==========================
% 0.73/1.01
% 0.73/1.01 ============================== STATISTICS ============================
% 0.73/1.01
% 0.73/1.01 Given=82. Generated=721. Kept=371. proofs=1.
% 0.73/1.01 Usable=75. Sos=264. Demods=1. Limbo=1, Disabled=47. Hints=0.
% 0.73/1.01 Megabytes=0.28.
% 0.73/1.01 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.73/1.01
% 0.73/1.01 ============================== end of statistics =====================
% 0.73/1.01
% 0.73/1.01 ============================== end of search =========================
% 0.73/1.01
% 0.73/1.01 THEOREM PROVED
% 0.73/1.01 % SZS status Theorem
% 0.73/1.01
% 0.73/1.01 Exiting with 1 proof.
% 0.73/1.01
% 0.73/1.01 Process 3597 exit (max_proofs) Sun Jul 10 20:43:33 2022
% 0.73/1.01 Prover9 interrupted
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