TSTP Solution File: SET928+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET928+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 04:33:30 EDT 2022
% Result : Theorem 0.43s 0.99s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET928+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n018.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 18:50:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.43/0.98 ============================== Prover9 ===============================
% 0.43/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.98 Process 16923 was started by sandbox on n018.cluster.edu,
% 0.43/0.98 Sun Jul 10 18:50:43 2022
% 0.43/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16770_n018.cluster.edu".
% 0.43/0.98 ============================== end of head ===========================
% 0.43/0.98
% 0.43/0.98 ============================== INPUT =================================
% 0.43/0.98
% 0.43/0.98 % Reading from file /tmp/Prover9_16770_n018.cluster.edu
% 0.43/0.98
% 0.43/0.98 set(prolog_style_variables).
% 0.43/0.98 set(auto2).
% 0.43/0.98 % set(auto2) -> set(auto).
% 0.43/0.98 % set(auto) -> set(auto_inference).
% 0.43/0.98 % set(auto) -> set(auto_setup).
% 0.43/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.98 % set(auto) -> set(auto_limits).
% 0.43/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.98 % set(auto) -> set(auto_denials).
% 0.43/0.98 % set(auto) -> set(auto_process).
% 0.43/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.98 % set(auto2) -> assign(stats, some).
% 0.43/0.98 % set(auto2) -> clear(echo_input).
% 0.43/0.98 % set(auto2) -> set(quiet).
% 0.43/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.98 % set(auto2) -> clear(print_given).
% 0.43/0.98 assign(lrs_ticks,-1).
% 0.43/0.98 assign(sos_limit,10000).
% 0.43/0.98 assign(order,kbo).
% 0.43/0.98 set(lex_order_vars).
% 0.43/0.98 clear(print_given).
% 0.43/0.98
% 0.43/0.98 % formulas(sos). % not echoed (9 formulas)
% 0.43/0.98
% 0.43/0.98 ============================== end of input ==========================
% 0.43/0.98
% 0.43/0.98 % From the command line: assign(max_seconds, 300).
% 0.43/0.98
% 0.43/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.98
% 0.43/0.98 % Formulas that are not ordinary clauses:
% 0.43/0.98 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 3 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 4 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 5 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 6 (all A all B all C -(disjoint(unordered_pair(A,B),C) & in(A,C))) # label(t55_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 7 (all A all B all C -(-in(A,B) & -in(C,B) & -disjoint(unordered_pair(A,C),B))) # label(t57_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 8 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 9 -(all A all B all C (set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) <-> -in(A,C) & -in(B,C))) # label(t72_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/0.98
% 0.43/0.98 ============================== end of process non-clausal formulas ===
% 0.43/0.98
% 0.43/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/0.98
% 0.43/0.98 ============================== PREDICATE ELIMINATION =================
% 0.43/0.98
% 0.43/0.98 ============================== end predicate elimination =============
% 0.43/0.98
% 0.43/0.98 Auto_denials: (non-Horn, no changes).
% 0.43/0.98
% 0.43/0.98 Term ordering decisions:
% 0.43/0.98 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. unordered_pair=1. set_difference=1.
% 0.43/0.98
% 0.43/0.98 ============================== end of process initial clauses ========
% 0.43/0.98
% 0.43/0.98 ============================== CLAUSES FOR SEARCH ====================
% 0.43/0.98
% 0.43/0.98 ============================== end of clauses for search =============
% 0.43/0.98
% 0.43/0.98 ============================== SEARCH ================================
% 0.43/0.98
% 0.43/0.98 % Starting search at 0.01 seconds.
% 0.43/0.99
% 0.43/0.99 ============================== PROOF =================================
% 0.43/0.99 % SZS status Theorem
% 0.43/0.99 % SZS output start Refutation
% 0.43/0.99
% 0.43/0.99 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.43/0.99 % Length of proof is 23.
% 0.43/0.99 % Level of proof is 8.
% 0.43/0.99 % Maximum clause weight is 21.000.
% 0.43/0.99 % Given clauses 42.
% 0.43/0.99
% 0.43/0.99 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 6 (all A all B all C -(disjoint(unordered_pair(A,B),C) & in(A,C))) # label(t55_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 7 (all A all B all C -(-in(A,B) & -in(C,B) & -disjoint(unordered_pair(A,C),B))) # label(t57_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 8 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 9 -(all A all B all C (set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) <-> -in(A,C) & -in(B,C))) # label(t72_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/0.99 11 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(2)].
% 0.43/0.99 12 in(A,B) | in(C,B) | disjoint(unordered_pair(A,C),B) # label(t57_zfmisc_1) # label(axiom). [clausify(7)].
% 0.43/0.99 15 -disjoint(unordered_pair(A,B),C) | -in(A,C) # label(t55_zfmisc_1) # label(axiom). [clausify(6)].
% 0.43/0.99 17 -disjoint(A,B) | set_difference(A,B) = A # label(t83_xboole_1) # label(axiom). [clausify(8)].
% 0.43/0.99 18 disjoint(A,B) | set_difference(A,B) != A # label(t83_xboole_1) # label(axiom). [clausify(8)].
% 0.43/0.99 19 set_difference(unordered_pair(c3,c4),c5) = unordered_pair(c3,c4) | -in(c3,c5) # label(t72_zfmisc_1) # label(negated_conjecture). [clausify(9)].
% 0.43/0.99 20 set_difference(unordered_pair(c3,c4),c5) = unordered_pair(c3,c4) | -in(c4,c5) # label(t72_zfmisc_1) # label(negated_conjecture). [clausify(9)].
% 0.43/0.99 21 set_difference(unordered_pair(c3,c4),c5) != unordered_pair(c3,c4) | in(c3,c5) | in(c4,c5) # label(t72_zfmisc_1) # label(negated_conjecture). [clausify(9)].
% 0.43/0.99 24 -disjoint(unordered_pair(A,B),C) | -in(B,C). [para(11(a,1),15(a,1))].
% 0.43/0.99 27 set_difference(unordered_pair(A,B),C) = unordered_pair(A,B) | in(A,C) | in(B,C). [resolve(17,a,12,c)].
% 0.43/0.99 53 set_difference(unordered_pair(A,c4),c5) = unordered_pair(A,c4) | in(A,c5) | set_difference(unordered_pair(c3,c4),c5) = unordered_pair(c3,c4). [resolve(27,b,20,b),rewrite([11(2),11(6)])].
% 0.43/0.99 60 set_difference(unordered_pair(c3,c4),c5) = unordered_pair(c3,c4) | in(c3,c5). [factor(53,a,c)].
% 0.43/0.99 83 set_difference(unordered_pair(c3,c4),c5) = unordered_pair(c3,c4). [resolve(60,b,19,b),merge(b)].
% 0.43/0.99 84 in(c3,c5) | in(c4,c5). [back_rewrite(21),rewrite([83(5)]),xx(a)].
% 0.43/0.99 90 disjoint(unordered_pair(c3,c4),c5). [resolve(83,a,18,b)].
% 0.43/0.99 116 -in(c4,c5). [resolve(90,a,24,a)].
% 0.43/0.99 118 -in(c3,c5). [resolve(90,a,15,a)].
% 0.43/0.99 119 $F. [back_unit_del(84),unit_del(a,118),unit_del(b,116)].
% 0.43/0.99
% 0.43/0.99 % SZS output end Refutation
% 0.43/0.99 ============================== end of proof ==========================
% 0.43/0.99
% 0.43/0.99 ============================== STATISTICS ============================
% 0.43/0.99
% 0.43/0.99 Given=42. Generated=285. Kept=109. proofs=1.
% 0.43/0.99 Usable=36. Sos=46. Demods=14. Limbo=3, Disabled=36. Hints=0.
% 0.43/0.99 Megabytes=0.13.
% 0.43/0.99 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.43/0.99
% 0.43/0.99 ============================== end of statistics =====================
% 0.43/0.99
% 0.43/0.99 ============================== end of search =========================
% 0.43/0.99
% 0.43/0.99 THEOREM PROVED
% 0.43/0.99 % SZS status Theorem
% 0.43/0.99
% 0.43/0.99 Exiting with 1 proof.
% 0.43/0.99
% 0.43/0.99 Process 16923 exit (max_proofs) Sun Jul 10 18:50:43 2022
% 0.43/0.99 Prover9 interrupted
%------------------------------------------------------------------------------