TSTP Solution File: SET929+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET929+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 04:33:30 EDT 2022
% Result : Theorem 0.45s 0.99s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET929+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n027.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 : Sat Jul 9 22:01:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.45/0.98 ============================== Prover9 ===============================
% 0.45/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.45/0.98 Process 12862 was started by sandbox on n027.cluster.edu,
% 0.45/0.98 Sat Jul 9 22:01:17 2022
% 0.45/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_12709_n027.cluster.edu".
% 0.45/0.98 ============================== end of head ===========================
% 0.45/0.98
% 0.45/0.98 ============================== INPUT =================================
% 0.45/0.98
% 0.45/0.98 % Reading from file /tmp/Prover9_12709_n027.cluster.edu
% 0.45/0.98
% 0.45/0.98 set(prolog_style_variables).
% 0.45/0.98 set(auto2).
% 0.45/0.98 % set(auto2) -> set(auto).
% 0.45/0.98 % set(auto) -> set(auto_inference).
% 0.45/0.98 % set(auto) -> set(auto_setup).
% 0.45/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.45/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/0.98 % set(auto) -> set(auto_limits).
% 0.45/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/0.98 % set(auto) -> set(auto_denials).
% 0.45/0.98 % set(auto) -> set(auto_process).
% 0.45/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.45/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.45/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.45/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.45/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.45/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.45/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.45/0.98 % set(auto2) -> assign(stats, some).
% 0.45/0.98 % set(auto2) -> clear(echo_input).
% 0.45/0.98 % set(auto2) -> set(quiet).
% 0.45/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.45/0.98 % set(auto2) -> clear(print_given).
% 0.45/0.98 assign(lrs_ticks,-1).
% 0.45/0.98 assign(sos_limit,10000).
% 0.45/0.98 assign(order,kbo).
% 0.45/0.98 set(lex_order_vars).
% 0.45/0.98 clear(print_given).
% 0.45/0.98
% 0.45/0.98 % formulas(sos). % not echoed (9 formulas)
% 0.45/0.98
% 0.45/0.98 ============================== end of input ==========================
% 0.45/0.98
% 0.45/0.98 % From the command line: assign(max_seconds, 300).
% 0.45/0.98
% 0.45/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/0.99
% 0.45/0.99 % Formulas that are not ordinary clauses:
% 0.45/0.99 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 3 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 4 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 5 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 6 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 7 (all A all B all C (subset(unordered_pair(A,B),C) <-> in(A,C) & in(B,C))) # label(t38_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 8 -(all A all B all C (set_difference(unordered_pair(A,B),C) = empty_set <-> in(A,C) & in(B,C))) # label(t73_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/0.99
% 0.45/0.99 ============================== end of process non-clausal formulas ===
% 0.45/0.99
% 0.45/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/0.99
% 0.45/0.99 ============================== PREDICATE ELIMINATION =================
% 0.45/0.99
% 0.45/0.99 ============================== end predicate elimination =============
% 0.45/0.99
% 0.45/0.99 Auto_denials: (non-Horn, no changes).
% 0.45/0.99
% 0.45/0.99 Term ordering decisions:
% 0.45/0.99 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. unordered_pair=1. set_difference=1.
% 0.45/0.99
% 0.45/0.99 ============================== end of process initial clauses ========
% 0.45/0.99
% 0.45/0.99 ============================== CLAUSES FOR SEARCH ====================
% 0.45/0.99
% 0.45/0.99 ============================== end of clauses for search =============
% 0.45/0.99
% 0.45/0.99 ============================== SEARCH ================================
% 0.45/0.99
% 0.45/0.99 % Starting search at 0.01 seconds.
% 0.45/0.99
% 0.45/0.99 ============================== PROOF =================================
% 0.45/0.99 % SZS status Theorem
% 0.45/0.99 % SZS output start Refutation
% 0.45/0.99
% 0.45/0.99 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.45/0.99 % Length of proof is 21.
% 0.45/0.99 % Level of proof is 7.
% 0.45/0.99 % Maximum clause weight is 15.000.
% 0.45/0.99 % Given clauses 40.
% 0.45/0.99
% 0.45/0.99 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 6 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 7 (all A all B all C (subset(unordered_pair(A,B),C) <-> in(A,C) & in(B,C))) # label(t38_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.99 8 -(all A all B all C (set_difference(unordered_pair(A,B),C) = empty_set <-> in(A,C) & in(B,C))) # label(t73_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/0.99 12 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(2)].
% 0.45/0.99 13 set_difference(unordered_pair(c3,c4),c5) = empty_set | in(c3,c5) # label(t73_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.45/0.99 14 set_difference(unordered_pair(c3,c4),c5) = empty_set | in(c4,c5) # label(t73_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.45/0.99 17 set_difference(unordered_pair(c3,c4),c5) != empty_set | -in(c3,c5) | -in(c4,c5) # label(t73_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.45/0.99 18 set_difference(A,B) != empty_set | subset(A,B) # label(t37_xboole_1) # label(axiom). [clausify(6)].
% 0.45/0.99 19 set_difference(A,B) = empty_set | -subset(A,B) # label(t37_xboole_1) # label(axiom). [clausify(6)].
% 0.45/0.99 20 -subset(unordered_pair(A,B),C) | in(A,C) # label(t38_zfmisc_1) # label(axiom). [clausify(7)].
% 0.45/0.99 21 -subset(unordered_pair(A,B),C) | in(B,C) # label(t38_zfmisc_1) # label(axiom). [clausify(7)].
% 0.45/0.99 22 subset(unordered_pair(A,B),C) | -in(A,C) | -in(B,C) # label(t38_zfmisc_1) # label(axiom). [clausify(7)].
% 0.45/0.99 29 subset(unordered_pair(A,c4),c5) | -in(A,c5) | set_difference(unordered_pair(c3,c4),c5) = empty_set. [resolve(22,b,14,b),rewrite([12(2)])].
% 0.45/0.99 49 subset(unordered_pair(c3,c4),c5) | set_difference(unordered_pair(c3,c4),c5) = empty_set. [resolve(29,b,13,b),merge(c)].
% 0.45/0.99 50 set_difference(unordered_pair(c3,c4),c5) = empty_set. [resolve(49,a,19,b),merge(b)].
% 0.45/0.99 51 -in(c3,c5) | -in(c4,c5). [back_rewrite(17),rewrite([50(5)]),xx(a)].
% 0.45/0.99 52 subset(unordered_pair(c3,c4),c5). [resolve(50,a,18,a)].
% 0.45/0.99 53 in(c4,c5). [resolve(52,a,21,a)].
% 0.45/0.99 54 in(c3,c5). [resolve(52,a,20,a)].
% 0.45/0.99 55 $F. [back_unit_del(51),unit_del(a,54),unit_del(b,53)].
% 0.45/0.99
% 0.45/0.99 % SZS output end Refutation
% 0.45/0.99 ============================== end of proof ==========================
% 0.45/0.99
% 0.45/0.99 ============================== STATISTICS ============================
% 0.45/0.99
% 0.45/0.99 Given=40. Generated=125. Kept=46. proofs=1.
% 0.45/0.99 Usable=31. Sos=0. Demods=4. Limbo=2, Disabled=27. Hints=0.
% 0.45/0.99 Megabytes=0.07.
% 0.45/0.99 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.45/0.99
% 0.45/0.99 ============================== end of statistics =====================
% 0.45/0.99
% 0.45/0.99 ============================== end of search =========================
% 0.45/0.99
% 0.45/0.99 THEOREM PROVED
% 0.45/0.99 % SZS status Theorem
% 0.45/0.99
% 0.45/0.99 Exiting with 1 proof.
% 0.45/0.99
% 0.45/0.99 Process 12862 exit (max_proofs) Sat Jul 9 22:01:17 2022
% 0.45/0.99 Prover9 interrupted
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