TSTP Solution File: SET031-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET031-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 04:26:07 EDT 2022
% Result : Timeout 300.03s 300.29s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET031-4 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.33 % Computer : n009.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Sat Jul 9 22:23:52 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.74/1.00 ============================== Prover9 ===============================
% 0.74/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.00 Process 30669 was started by sandbox2 on n009.cluster.edu,
% 0.74/1.00 Sat Jul 9 22:23:52 2022
% 0.74/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30514_n009.cluster.edu".
% 0.74/1.00 ============================== end of head ===========================
% 0.74/1.00
% 0.74/1.00 ============================== INPUT =================================
% 0.74/1.00
% 0.74/1.00 % Reading from file /tmp/Prover9_30514_n009.cluster.edu
% 0.74/1.00
% 0.74/1.00 set(prolog_style_variables).
% 0.74/1.00 set(auto2).
% 0.74/1.00 % set(auto2) -> set(auto).
% 0.74/1.00 % set(auto) -> set(auto_inference).
% 0.74/1.00 % set(auto) -> set(auto_setup).
% 0.74/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.00 % set(auto) -> set(auto_limits).
% 0.74/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.00 % set(auto) -> set(auto_denials).
% 0.74/1.00 % set(auto) -> set(auto_process).
% 0.74/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.00 % set(auto2) -> assign(stats, some).
% 0.74/1.00 % set(auto2) -> clear(echo_input).
% 0.74/1.00 % set(auto2) -> set(quiet).
% 0.74/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.00 % set(auto2) -> clear(print_given).
% 0.74/1.00 assign(lrs_ticks,-1).
% 0.74/1.00 assign(sos_limit,10000).
% 0.74/1.00 assign(order,kbo).
% 0.74/1.00 set(lex_order_vars).
% 0.74/1.00 clear(print_given).
% 0.74/1.00
% 0.74/1.00 % formulas(sos). % not echoed (142 formulas)
% 0.74/1.00
% 0.74/1.00 ============================== end of input ==========================
% 0.74/1.00
% 0.74/1.00 % From the command line: assign(max_seconds, 300).
% 0.74/1.00
% 0.74/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.00
% 0.74/1.00 % Formulas that are not ordinary clauses:
% 0.74/1.00
% 0.74/1.00 ============================== end of process non-clausal formulas ===
% 0.74/1.00
% 0.74/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.00
% 0.74/1.00 ============================== PREDICATE ELIMINATION =================
% 0.74/1.00 1 proper_subset(A,B) | -subset(A,B) | A = B # label(proper_subset3) # label(axiom). [assumption].
% 0.74/1.00 2 -proper_subset(A,B) | subset(A,B) # label(proper_subset1) # label(axiom). [assumption].
% 0.74/1.00 3 -proper_subset(A,B) | A != B # label(proper_subset2) # label(axiom). [assumption].
% 0.74/1.00 4 single_valued_set(A) | little_set(f19(A)) # label(single_valued_set2) # label(axiom). [assumption].
% 0.74/1.00 5 -single_valued_set(A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D # label(single_valued_set1) # label(axiom). [assumption].
% 0.74/1.00 Derived: little_set(f19(A)) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(4,a,5,a)].
% 0.74/1.00 6 single_valued_set(A) | little_set(f20(A)) # label(single_valued_set3) # label(axiom). [assumption].
% 0.74/1.00 Derived: little_set(f20(A)) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(6,a,5,a)].
% 0.74/1.00 7 single_valued_set(A) | little_set(f21(A)) # label(single_valued_set4) # label(axiom). [assumption].
% 0.74/1.00 Derived: little_set(f21(A)) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(7,a,5,a)].
% 0.74/1.00 8 single_valued_set(A) | member(ordered_pair(f19(A),f20(A)),A) # label(single_valued_set5) # label(axiom). [assumption].
% 0.74/1.00 Derived: member(ordered_pair(f19(A),f20(A)),A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(8,a,5,a)].
% 0.74/1.00 9 single_valued_set(A) | member(ordered_pair(f19(A),f21(A)),A) # label(single_valued_set6) # label(axiom). [assumption].
% 0.74/1.00 Derived: member(ordered_pair(f19(A),f21(A)),A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(9,a,5,a)].
% 0.74/1.01 10 single_valued_set(A) | f20(A) != f21(A) # label(single_valued_set7) # label(axiom). [assumption].
% 0.74/1.01 Derived: f20(A) != f21(A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(10,a,5,a)].
% 0.74/1.01 11 -function(A) | single_valued_set(A) # label(function2) # label(axiom). [assumption].
% 0.74/1.01 Derived: -function(A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(11,b,5,a)].
% 0.74/1.01 12 function(A) | -relation(A) | -single_valued_set(A) # label(function3) # label(axiom). [assumption].
% 0.74/1.01 Derived: function(A) | -relation(A) | little_set(f19(A)). [resolve(12,c,4,a)].
% 0.74/1.01 Derived: function(A) | -relation(A) | little_set(f20(A)). [resolve(12,c,6,a)].
% 0.74/1.01 Derived: function(A) | -relation(A) | little_set(f21(A)). [resolve(12,c,7,a)].
% 0.74/1.01 Derived: function(A) | -relation(A) | member(ordered_pair(f19(A),f20(A)),A). [resolve(12,c,8,a)].
% 0.74/1.01 Derived: function(A) | -relation(A) | member(ordered_pair(f19(A),f21(A)),A). [resolve(12,c,9,a)].
% 0.74/1.01 Derived: function(A) | -relation(A) | f20(A) != f21(A). [resolve(12,c,10,a)].
% 0.74/1.01 13 disjoint(A,B) | member(f23(A,B),A) # label(disjoint2) # label(axiom). [assumption].
% 0.74/1.01 14 -disjoint(A,B) | -member(C,A) | -member(C,B) # label(disjoint1) # label(axiom). [assumption].
% 0.74/1.01 Derived: member(f23(A,B),A) | -member(C,A) | -member(C,B). [resolve(13,a,14,a)].
% 0.74/1.01 15 disjoint(A,B) | member(f23(A,B),B) # label(disjoint3) # label(axiom). [assumption].
% 0.74/1.01 Derived: member(f23(A,B),B) | -member(C,A) | -member(C,B). [resolve(15,a,14,a)].
% 0.74/1.01 16 A = empty_set | disjoint(f24(A),A) # label(regularity2) # label(axiom). [assumption].
% 0.74/1.01 Derived: A = empty_set | -member(B,f24(A)) | -member(B,A). [resolve(16,b,14,a)].
% 0.74/1.01 17 one_to_one_function(A) | -function(A) | -function(converse(A)) # label(one_to_one_function3) # label(axiom). [assumption].
% 0.74/1.01 18 -one_to_one_function(A) | function(A) # label(one_to_one_function1) # label(axiom). [assumption].
% 0.74/1.01 19 -one_to_one_function(A) | function(converse(A)) # label(one_to_one_function2) # label(axiom). [assumption].
% 0.74/1.01 20 function(f25) # label(choice1) # label(axiom). [assumption].
% 0.74/1.01 21 -function(A) | relation(A) # label(function1) # label(axiom). [assumption].
% 0.74/1.01 22 -little_set(A) | -function(B) | little_set(image(A,B)) # label(image_and_substitution6) # label(axiom). [assumption].
% 0.74/1.01 Derived: relation(f25). [resolve(20,a,21,a)].
% 0.74/1.01 Derived: -little_set(A) | little_set(image(A,f25)). [resolve(20,a,22,b)].
% 0.74/1.01 23 -maps(A,B,C) | function(A) # label(maps1) # label(axiom). [assumption].
% 0.74/1.01 Derived: -maps(A,B,C) | relation(A). [resolve(23,b,21,a)].
% 0.74/1.01 Derived: -maps(A,B,C) | -little_set(D) | little_set(image(D,A)). [resolve(23,b,22,b)].
% 0.74/1.01 24 maps(A,B,C) | -function(A) | domain_of(A) != B | -subset(range_of(A),C) # label(maps4) # label(axiom). [assumption].
% 0.74/1.01 Derived: maps(f25,A,B) | domain_of(f25) != A | -subset(range_of(f25),B). [resolve(24,b,20,a)].
% 0.74/1.01 Derived: maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C) | -maps(A,D,E). [resolve(24,b,23,b)].
% 0.74/1.01 25 -function(A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(11,b,5,a)].
% 0.74/1.01 Derived: -little_set(A) | -little_set(B) | -little_set(C) | -member(ordered_pair(A,B),f25) | -member(ordered_pair(A,C),f25) | B = C. [resolve(25,a,20,a)].
% 0.74/1.01 Derived: -little_set(A) | -little_set(B) | -little_set(C) | -member(ordered_pair(A,B),D) | -member(ordered_pair(A,C),D) | B = C | -maps(D,E,F). [resolve(25,a,23,b)].
% 0.74/1.01 26 function(A) | -relation(A) | little_set(f19(A)). [resolve(12,c,4,a)].
% 0.74/1.01 Derived: -relation(A) | little_set(f19(A)) | -little_set(B) | little_set(image(B,A)). [resolve(26,a,22,b)].
% 0.74/1.01 Derived: -relation(A) | little_set(f19(A)) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(26,a,24,b)].
% 0.74/1.01 Derived: -relation(A) | little_set(f19(A)) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(26,a,25,a)].
% 0.74/1.01 27 function(A) | -relation(A) | little_set(f20(A)). [resolve(12,c,6,a)].
% 0.74/1.01 Derived: -relation(A) | little_set(f20(A)) | -little_set(B) | little_set(image(B,A)). [resolve(27,a,22,b)].
% 0.74/1.01 Derived: -relation(A) | little_set(f20(A)) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(27,a,24,b)].
% 0.74/1.01 Derived: -relation(A) | little_set(f20(A)) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(27,a,25,a)].
% 0.74/1.01 28 function(A) | -relation(A) | little_set(f21(A)). [resolve(12,c,7,a)].
% 0.74/1.01 Derived: -relation(A) | little_set(f21(A)) | -little_set(B) | little_set(image(B,A)). [resolve(28,a,22,b)].
% 0.74/1.01 Derived: -relation(A) | little_set(f21(A)) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(28,a,24,b)].
% 0.74/1.01 Derived: -relation(A) | little_set(f21(A)) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(28,a,25,a)].
% 0.74/1.01 29 function(A) | -relation(A) | member(ordered_pair(f19(A),f20(A)),A). [resolve(12,c,8,a)].
% 0.74/1.01 Derived: -relation(A) | member(ordered_pair(f19(A),f20(A)),A) | -little_set(B) | little_set(image(B,A)). [resolve(29,a,22,b)].
% 0.74/1.01 Derived: -relation(A) | member(ordered_pair(f19(A),f20(A)),A) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(29,a,24,b)].
% 0.74/1.01 Derived: -relation(A) | member(ordered_pair(f19(A),f20(A)),A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(29,a,25,a)].
% 0.74/1.01 30 function(A) | -relation(A) | member(ordered_pair(f19(A),f21(A)),A). [resolve(12,c,9,a)].
% 0.74/1.01 Derived: -relation(A) | member(ordered_pair(f19(A),f21(A)),A) | -little_set(B) | little_set(image(B,A)). [resolve(30,a,22,b)].
% 0.74/1.01 Derived: -relation(A) | member(ordered_pair(f19(A),f21(A)),A) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(30,a,24,b)].
% 0.74/1.01 Derived: -relation(A) | member(ordered_pair(f19(A),f21(A)),A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(30,a,25,a)].
% 0.74/1.01 31 function(A) | -relation(A) | f20(A) != f21(A). [resolve(12,c,10,a)].
% 0.74/1.01 Derived: -relation(A) | f20(A) != f21(A) | -little_set(B) | little_set(image(B,A)). [resolve(31,a,22,b)].
% 0.74/1.01 Derived: -relation(A) | f20(A) != f21(A) | maps(A,B,C) | domain_of(A) != B | -subset(range_of(A),C). [resolve(31,a,24,b)].
% 0.74/1.01 Derived: -relation(A) | f20(A) != f21(A) | -little_set(B) | -little_set(C) | -little_set(D) | -member(ordered_pair(B,C),A) | -member(ordered_pair(B,D),A) | C = D. [resolve(31,a,25,a)].
% 0.74/1.01 32 homomorphism(A,B,C,D,E) | -closed(B,C) | -closed(D,E) | -maps(A,B,D) | member(f32(A,B,C,D,E),B) # label(homomorphism5) # label(axiom). [assumption].
% 0.74/1.01 33 -homomorphism(A,B,C,D,E) | closed(B,C) # label(homomorphism1) # label(axiom). [assumption].
% 0.74/1.01 34 -homomorphism(A,B,C,D,E) | closed(D,E) # label(homomorphism2) # label(axiom). [assumption].
% 0.74/1.01 35 -homomorphism(A,B,C,D,E) | maps(A,B,D) # label(homomorphism3) # label(axiom). [assumption].
% 0.74/1.01 36 -homomorphism(A,B,C,D,E) | -member(F,B) | -member(V6,B) | apply(A,apply_to_two_arguments(C,F,V6)) = apply_to_two_arguments(E,apply(A,F),apply(A,V6)) # label(homomorphism4) # label(axiom). [assumption].
% 0.74/1.01 Derived: -closed(A,B) | -closed(C,D) | -maps(E,A,C) | member(f32(E,A,B,C,D),A) | -member(F,A) | -member(V6,A) | apply(E,apply_to_two_arguments(B,F,V6)) = apply_to_two_arguments(D,apply(E,F),apply(E,V6)). [resolve(32,a,36,a)].
% 0.74/1.01 37 homomorphism(A,B,C,D,E) | -closed(B,C) | -closed(D,E) | -maps(A,B,D) | member(f33(A,B,C,D,E),B) # label(homomorphism6) # label(axiom). [assumption].
% 0.74/1.01 Derived: -closed(A,B) | -closed(C,D) | -maps(E,A,C) | member(f33(E,A,B,C,D),A) | -member(F,A) | -member(V6,A) | apply(E,apply_to_two_arguments(B,F,V6)) = apply_to_two_arguments(D,apply(E,F),apply(E,V6)). [resolve(37,a,36,a)].
% 0.74/1.01 38 homomorphism(A,B,C,D,E) | -closed(B,C) | -closed(D,E) | -maps(A,B,D) | apply(A,apply_to_two_arguments(C,f32(Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------