TSTP Solution File: SET987+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET987+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 04:33:52 EDT 2022
% Result : Theorem 0.75s 1.01s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET987+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n018.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 11:58:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.75/1.01 ============================== Prover9 ===============================
% 0.75/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.01 Process 3212 was started by sandbox2 on n018.cluster.edu,
% 0.75/1.01 Sun Jul 10 11:58:43 2022
% 0.75/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3059_n018.cluster.edu".
% 0.75/1.01 ============================== end of head ===========================
% 0.75/1.01
% 0.75/1.01 ============================== INPUT =================================
% 0.75/1.01
% 0.75/1.01 % Reading from file /tmp/Prover9_3059_n018.cluster.edu
% 0.75/1.01
% 0.75/1.01 set(prolog_style_variables).
% 0.75/1.01 set(auto2).
% 0.75/1.01 % set(auto2) -> set(auto).
% 0.75/1.01 % set(auto) -> set(auto_inference).
% 0.75/1.01 % set(auto) -> set(auto_setup).
% 0.75/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.01 % set(auto) -> set(auto_limits).
% 0.75/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.01 % set(auto) -> set(auto_denials).
% 0.75/1.01 % set(auto) -> set(auto_process).
% 0.75/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.01 % set(auto2) -> assign(stats, some).
% 0.75/1.01 % set(auto2) -> clear(echo_input).
% 0.75/1.01 % set(auto2) -> set(quiet).
% 0.75/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.01 % set(auto2) -> clear(print_given).
% 0.75/1.01 assign(lrs_ticks,-1).
% 0.75/1.01 assign(sos_limit,10000).
% 0.75/1.01 assign(order,kbo).
% 0.75/1.01 set(lex_order_vars).
% 0.75/1.01 clear(print_given).
% 0.75/1.01
% 0.75/1.01 % formulas(sos). % not echoed (10 formulas)
% 0.75/1.01
% 0.75/1.01 ============================== end of input ==========================
% 0.75/1.01
% 0.75/1.01 % From the command line: assign(max_seconds, 300).
% 0.75/1.01
% 0.75/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.01
% 0.75/1.01 % Formulas that are not ordinary clauses:
% 0.75/1.01 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 2 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 3 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 4 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 5 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 6 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 7 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 8 (all A all B set_difference(set_union2(A,B),B) = set_difference(A,B)) # label(t40_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 9 (all A all B (set_difference(A,singleton(B)) = A <-> -in(B,A))) # label(t65_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 10 -(all A all B (-in(A,B) -> set_difference(set_union2(B,singleton(A)),singleton(A)) = B)) # label(t141_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.01
% 0.75/1.01 ============================== end of process non-clausal formulas ===
% 0.75/1.01
% 0.75/1.01 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.75/1.01 ============================== PREDICATE ELIMINATION =================
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% 0.75/1.01 ============================== end predicate elimination =============
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% 0.75/1.01 Auto_denials: (non-Horn, no changes).
% 0.75/1.01
% 0.75/1.01 Term ordering decisions:
% 0.75/1.01
% 0.75/1.01 % Assigning unary symbol singleton kb_weight 0 and highest precedence (10).
% 0.75/1.01 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. set_union2=1. set_difference=1. singleton=0.
% 0.75/1.01
% 0.75/1.01 ============================== end of process initial clauses ========
% 0.75/1.01
% 0.75/1.01 ============================== CLAUSES FOR SEARCH ====================
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% 0.75/1.01 ============================== end of clauses for search =============
% 0.75/1.01
% 0.75/1.01 ============================== SEARCH ================================
% 0.75/1.01
% 0.75/1.01 % Starting search at 0.01 seconds.
% 0.75/1.01
% 0.75/1.01 ============================== PROOF =================================
% 0.75/1.01 % SZS status Theorem
% 0.75/1.01 % SZS output start Refutation
% 0.75/1.01
% 0.75/1.01 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.75/1.01 % Length of proof is 9.
% 0.75/1.01 % Level of proof is 3.
% 0.75/1.01 % Maximum clause weight is 9.000.
% 0.75/1.01 % Given clauses 7.
% 0.75/1.01
% 0.75/1.01 8 (all A all B set_difference(set_union2(A,B),B) = set_difference(A,B)) # label(t40_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 9 (all A all B (set_difference(A,singleton(B)) = A <-> -in(B,A))) # label(t65_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.01 10 -(all A all B (-in(A,B) -> set_difference(set_union2(B,singleton(A)),singleton(A)) = B)) # label(t141_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.01 14 set_difference(set_union2(A,B),B) = set_difference(A,B) # label(t40_xboole_1) # label(axiom). [clausify(8)].
% 0.75/1.01 15 set_difference(A,singleton(B)) = A | in(B,A) # label(t65_zfmisc_1) # label(axiom). [clausify(9)].
% 0.75/1.01 17 -in(c3,c4) # label(t141_zfmisc_1) # label(negated_conjecture). [clausify(10)].
% 0.75/1.01 20 set_difference(set_union2(c4,singleton(c3)),singleton(c3)) != c4 # label(t141_zfmisc_1) # label(negated_conjecture). [clausify(10)].
% 0.75/1.01 21 set_difference(c4,singleton(c3)) != c4. [copy(20),rewrite([14(7)])].
% 0.75/1.01 26 $F. [resolve(17,a,15,b),unit_del(a,21)].
% 0.75/1.01
% 0.75/1.01 % SZS output end Refutation
% 0.75/1.01 ============================== end of proof ==========================
% 0.75/1.01
% 0.75/1.01 ============================== STATISTICS ============================
% 0.75/1.01
% 0.75/1.01 Given=7. Generated=25. Kept=13. proofs=1.
% 0.75/1.01 Usable=7. Sos=6. Demods=4. Limbo=0, Disabled=12. Hints=0.
% 0.75/1.01 Megabytes=0.04.
% 0.75/1.01 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.75/1.01
% 0.75/1.01 ============================== end of statistics =====================
% 0.75/1.01
% 0.75/1.01 ============================== end of search =========================
% 0.75/1.01
% 0.75/1.01 THEOREM PROVED
% 0.75/1.01 % SZS status Theorem
% 0.75/1.01
% 0.75/1.01 Exiting with 1 proof.
% 0.75/1.01
% 0.75/1.01 Process 3212 exit (max_proofs) Sun Jul 10 11:58:43 2022
% 0.75/1.01 Prover9 interrupted
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