TSTP Solution File: GRP074-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP074-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 : Sat Jul 16 11:17:03 EDT 2022
% Result : Unsatisfiable 1.06s 1.30s
% Output : Refutation 1.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP074-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 03:35:09 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.06/1.30 ============================== Prover9 ===============================
% 1.06/1.30 Prover9 (32) version 2009-11A, November 2009.
% 1.06/1.30 Process 25601 was started by sandbox on n004.cluster.edu,
% 1.06/1.30 Tue Jun 14 03:35:09 2022
% 1.06/1.30 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25220_n004.cluster.edu".
% 1.06/1.30 ============================== end of head ===========================
% 1.06/1.30
% 1.06/1.30 ============================== INPUT =================================
% 1.06/1.30
% 1.06/1.30 % Reading from file /tmp/Prover9_25220_n004.cluster.edu
% 1.06/1.30
% 1.06/1.30 set(prolog_style_variables).
% 1.06/1.30 set(auto2).
% 1.06/1.30 % set(auto2) -> set(auto).
% 1.06/1.30 % set(auto) -> set(auto_inference).
% 1.06/1.30 % set(auto) -> set(auto_setup).
% 1.06/1.30 % set(auto_setup) -> set(predicate_elim).
% 1.06/1.30 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.06/1.30 % set(auto) -> set(auto_limits).
% 1.06/1.30 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.06/1.30 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.06/1.30 % set(auto) -> set(auto_denials).
% 1.06/1.30 % set(auto) -> set(auto_process).
% 1.06/1.30 % set(auto2) -> assign(new_constants, 1).
% 1.06/1.30 % set(auto2) -> assign(fold_denial_max, 3).
% 1.06/1.30 % set(auto2) -> assign(max_weight, "200.000").
% 1.06/1.30 % set(auto2) -> assign(max_hours, 1).
% 1.06/1.30 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.06/1.30 % set(auto2) -> assign(max_seconds, 0).
% 1.06/1.30 % set(auto2) -> assign(max_minutes, 5).
% 1.06/1.30 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.06/1.30 % set(auto2) -> set(sort_initial_sos).
% 1.06/1.30 % set(auto2) -> assign(sos_limit, -1).
% 1.06/1.30 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.06/1.30 % set(auto2) -> assign(max_megs, 400).
% 1.06/1.30 % set(auto2) -> assign(stats, some).
% 1.06/1.30 % set(auto2) -> clear(echo_input).
% 1.06/1.30 % set(auto2) -> set(quiet).
% 1.06/1.30 % set(auto2) -> clear(print_initial_clauses).
% 1.06/1.30 % set(auto2) -> clear(print_given).
% 1.06/1.30 assign(lrs_ticks,-1).
% 1.06/1.30 assign(sos_limit,10000).
% 1.06/1.30 assign(order,kbo).
% 1.06/1.30 set(lex_order_vars).
% 1.06/1.30 clear(print_given).
% 1.06/1.30
% 1.06/1.30 % formulas(sos). % not echoed (3 formulas)
% 1.06/1.30
% 1.06/1.30 ============================== end of input ==========================
% 1.06/1.30
% 1.06/1.30 % From the command line: assign(max_seconds, 300).
% 1.06/1.30
% 1.06/1.30 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.06/1.30
% 1.06/1.30 % Formulas that are not ordinary clauses:
% 1.06/1.30
% 1.06/1.30 ============================== end of process non-clausal formulas ===
% 1.06/1.30
% 1.06/1.30 ============================== PROCESS INITIAL CLAUSES ===============
% 1.06/1.30
% 1.06/1.30 ============================== PREDICATE ELIMINATION =================
% 1.06/1.30
% 1.06/1.30 ============================== end predicate elimination =============
% 1.06/1.30
% 1.06/1.30 Auto_denials:
% 1.06/1.30 % copying label prove_these_axioms to answer in negative clause
% 1.06/1.30
% 1.06/1.30 Term ordering decisions:
% 1.06/1.30
% 1.06/1.30 % Assigning unary symbol inverse kb_weight 0 and highest precedence (11).
% 1.06/1.30 Function symbol KB weights: a1=1. a2=1. a3=1. b1=1. b2=1. b3=1. c3=1. divide=1. multiply=1. inverse=0.
% 1.06/1.30
% 1.06/1.30 ============================== end of process initial clauses ========
% 1.06/1.30
% 1.06/1.30 ============================== CLAUSES FOR SEARCH ====================
% 1.06/1.30
% 1.06/1.30 ============================== end of clauses for search =============
% 1.06/1.30
% 1.06/1.30 ============================== SEARCH ================================
% 1.06/1.30
% 1.06/1.30 % Starting search at 0.01 seconds.
% 1.06/1.30
% 1.06/1.30 ============================== PROOF =================================
% 1.06/1.30 % SZS status Unsatisfiable
% 1.06/1.30 % SZS output start Refutation
% 1.06/1.30
% 1.06/1.30 % Proof 1 at 0.32 (+ 0.01) seconds: prove_these_axioms.
% 1.06/1.30 % Length of proof is 52.
% 1.06/1.30 % Level of proof is 19.
% 1.06/1.30 % Maximum clause weight is 56.000.
% 1.06/1.30 % Given clauses 30.
% 1.06/1.30
% 1.06/1.30 1 multiply(A,B) = divide(A,inverse(B)) # label(multiply) # label(axiom). [assumption].
% 1.06/1.30 2 divide(inverse(divide(divide(divide(A,A),B),divide(C,divide(B,D)))),D) = C # label(single_axiom) # label(axiom). [assumption].
% 1.06/1.30 3 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) | multiply(multiply(inverse(b2),b2),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms) # label(negated_conjecture) # answer(prove_these_axioms). [assumption].
% 1.06/1.30 4 divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) | divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2 | divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) # answer(prove_these_axioms). [copy(3),rewrite([1(4),1(9),1(15),1(18),1(24),1(27),1(32),1(34)]),flip(a)].
% 1.06/1.30 5 divide(inverse(divide(divide(divide(A,A),inverse(divide(divide(divide(B,B),C),divide(D,divide(C,E))))),divide(F,D))),E) = F. [para(2(a,1),2(a,1,1,1,2,2))].
% 1.06/1.30 6 inverse(divide(divide(divide(A,A),B),divide(C,divide(B,divide(D,E))))) = divide(inverse(divide(divide(divide(F,F),D),C)),E). [para(2(a,1),2(a,1,1,1,2)),flip(a)].
% 1.06/1.30 11 divide(inverse(divide(divide(divide(A,A),inverse(divide(divide(divide(B,B),inverse(divide(divide(divide(C,C),inverse(divide(divide(divide(D,D),E),divide(F,divide(E,V6))))),divide(V7,F)))),divide(V8,V7)))),divide(V9,V8))),V6) = V9. [para(5(a,1),5(a,1,1,1,1,2,1,2,2))].
% 1.06/1.30 15 divide(divide(inverse(divide(divide(divide(A,A),B),C)),D),divide(B,D)) = C. [para(6(a,1),2(a,1,1))].
% 1.06/1.30 25 inverse(divide(divide(divide(A,A),B),divide(divide(C,D),divide(B,D)))) = C. [para(6(a,2),5(a,1)),rewrite([2(10)])].
% 1.06/1.30 49 divide(divide(divide(inverse(divide(divide(divide(A,A),B),C)),D),E),divide(F,E)) = divide(C,divide(F,divide(B,D))). [para(6(a,1),15(a,1,1,1))].
% 1.06/1.30 52 divide(divide(inverse(divide(A,B)),C),divide(divide(D,inverse(divide(divide(divide(E,E),D),A))),C)) = B. [para(15(a,1),15(a,1,1,1,1,1))].
% 1.06/1.30 62 divide(divide(A,B),divide(C,B)) = divide(divide(A,D),divide(C,D)). [para(25(a,1),15(a,1,1,1))].
% 1.06/1.30 65 divide(inverse(divide(divide(divide(A,B),divide(C,B)),divide(D,divide(divide(C,A),E)))),E) = D. [para(62(a,1),2(a,1,1,1,1))].
% 1.06/1.30 81 divide(divide(inverse(divide(divide(divide(A,B),divide(C,B)),D)),E),divide(divide(C,A),E)) = D. [para(62(a,1),15(a,1,1,1,1,1))].
% 1.06/1.30 82 divide(divide(inverse(divide(divide(divide(A,A),B),divide(C,B))),D),divide(E,D)) = divide(C,E). [para(62(a,1),15(a,1,1,1,1))].
% 1.06/1.30 84 divide(divide(A,B),divide(divide(inverse(divide(divide(divide(C,C),D),E)),F),B)) = divide(divide(A,divide(D,F)),E). [para(15(a,1),62(a,1,2)),flip(a)].
% 1.06/1.30 169 divide(divide(inverse(divide(divide(divide(A,B),C),D)),divide(E,A)),divide(C,divide(E,B))) = D. [para(2(a,1),81(a,1,1,1,1,1,2)),rewrite([84(14)])].
% 1.06/1.30 240 divide(divide(inverse(divide(divide(divide(A,A),B),divide(C,B))),divide(D,E)),F) = divide(C,divide(inverse(divide(divide(divide(V6,V6),D),F)),E)). [para(15(a,1),82(a,1,2))].
% 1.06/1.30 244 divide(divide(A,B),divide(C,divide(B,D))) = divide(divide(A,E),divide(C,divide(E,D))). [para(82(a,1),62(a,1,1)),rewrite([49(13)])].
% 1.06/1.30 245 divide(divide(A,divide(B,C)),divide(D,B)) = divide(divide(A,divide(E,C)),divide(D,E)). [para(82(a,1),62(a,1,2)),rewrite([84(13)])].
% 1.06/1.30 607 divide(A,divide(divide(B,C),divide(D,C))) = divide(A,divide(divide(B,E),divide(D,E))). [para(65(a,1),169(a,1,1))].
% 1.06/1.30 792 divide(divide(inverse(divide(divide(divide(A,A),B),divide(C,B))),divide(divide(D,E),divide(F,E))),divide(V6,divide(divide(D,V7),divide(F,V7)))) = divide(C,V6). [para(607(a,1),82(a,1,1))].
% 1.06/1.30 1339 divide(A,divide(B,inverse(divide(divide(divide(C,C),B),divide(divide(D,D),E))))) = divide(A,E). [para(52(a,1),82(a,1)),flip(a)].
% 1.06/1.30 1415 divide(A,inverse(divide(divide(divide(B,B),A),divide(divide(C,C),D)))) = D. [para(1339(a,1),15(a,1,1,1,1)),rewrite([15(7)]),flip(a)].
% 1.06/1.30 1444 divide(divide(A,B),divide(C,divide(B,inverse(divide(divide(divide(D,D),E),divide(divide(F,F),V6)))))) = divide(divide(A,E),divide(C,V6)). [para(1339(a,1),244(a,1,2)),flip(a)].
% 1.06/1.30 1493 inverse(divide(divide(divide(A,A),B),divide(C,C))) = B. [para(1415(a,1),25(a,1,1,2,1)),rewrite([1444(11)])].
% 1.06/1.30 1557 divide(inverse(divide(divide(divide(A,A),divide(B,B)),divide(divide(C,C),D))),inverse(divide(D,divide(divide(E,E),F)))) = F. [para(1415(a,1),1415(a,1,2,1,1))].
% 1.06/1.30 1576 divide(divide(A,B),divide(inverse(divide(divide(divide(C,C),inverse(divide(divide(divide(D,D),inverse(divide(divide(divide(E,E),inverse(divide(divide(divide(F,F),V6),divide(V7,divide(V6,V8))))),divide(V9,V7)))),divide(V10,V9)))),divide(V11,V10))),B)) = divide(divide(A,V8),V11). [para(11(a,1),62(a,1,2)),flip(a)].
% 1.06/1.30 1580 divide(inverse(divide(divide(divide(A,A),inverse(divide(divide(divide(B,B),inverse(divide(divide(divide(C,C),inverse(divide(divide(divide(D,D),E),divide(F,divide(E,V6))))),divide(V7,F)))),divide(divide(V8,V9),V7)))),divide(divide(V10,V11),divide(V8,V11)))),V6) = divide(V10,V9). [para(62(a,1),11(a,1,1,1,2))].
% 1.06/1.30 1591 inverse(divide(divide(divide(A,A),inverse(divide(divide(divide(B,B),inverse(divide(divide(divide(C,C),inverse(divide(divide(divide(D,D),E),divide(F,divide(E,divide(divide(V6,V7),V8)))))),divide(V9,F)))),divide(V10,V9)))),divide(V11,V10))) = divide(inverse(divide(divide(divide(V7,V12),divide(V6,V12)),V11)),V8). [para(11(a,1),65(a,1,1,1,2)),flip(a)].
% 1.06/1.30 1596 inverse(divide(divide(divide(A,B),divide(C,B)),divide(D,divide(divide(C,A),E)))) = divide(inverse(divide(divide(divide(F,F),inverse(divide(divide(divide(V6,V6),inverse(divide(divide(divide(V7,V7),inverse(divide(divide(divide(V8,V8),V9),divide(V10,divide(V9,V11))))),divide(V12,V10)))),divide(E,V12)))),D)),V11). [para(65(a,1),11(a,1,1,1,2)),flip(a)].
% 1.06/1.30 1730 inverse(divide(divide(divide(A,B),divide(C,B)),divide(D,D))) = divide(C,A). [para(62(a,1),1493(a,1,1,1))].
% 1.06/1.30 1733 divide(divide(A,B),divide(C,B)) = divide(A,C). [para(1493(a,1),82(a,1,1,1))].
% 1.06/1.30 1736 inverse(divide(divide(divide(A,A),B),divide(C,inverse(divide(divide(D,D),C))))) = B. [para(82(a,1),1493(a,1,1,2)),rewrite([1733(6)])].
% 1.06/1.30 1741 inverse(divide(divide(A,A),B)) = B. [para(244(a,1),1493(a,1,1)),rewrite([1733(5),1733(4)])].
% 1.06/1.30 1742 inverse(divide(divide(A,B),divide(C,C))) = divide(B,A). [para(245(a,1),1493(a,1,1,1)),rewrite([1733(3),1733(3)])].
% 1.06/1.30 1744 divide(A,A) = divide(B,B). [para(1493(a,1),169(a,1,1,1)),rewrite([1733(5)])].
% 1.06/1.30 1745 divide(A,divide(B,B)) = A. [para(607(a,1),1493(a,1,1,1,1)),rewrite([1733(3),1733(4),1733(3),1742(5)])].
% 1.06/1.30 1751 divide(divide(A,A),B) = inverse(B). [para(1415(a,1),1493(a,1,1,1)),rewrite([1745(2),1745(4),1741(6)]),flip(a)].
% 1.06/1.30 1804 divide(inverse(divide(inverse(A),divide(B,A))),C) = divide(B,C). [back_rewrite(792),rewrite([1751(2),1733(7),1733(9),1733(9)])].
% 1.06/1.30 1858 divide(divide(A,divide(B,C)),D) = divide(A,divide(inverse(divide(inverse(B),D)),C)). [back_rewrite(240),rewrite([1751(2),1804(6),1751(5)])].
% 1.06/1.30 1877 inverse(divide(A,B)) = divide(B,A). [back_rewrite(1730),rewrite([1733(3),1745(3)])].
% 1.06/1.30 1887 divide(A,divide(divide(B,inverse(inverse(B))),C)) = divide(A,inverse(C)). [back_rewrite(1596),rewrite([1733(3),1877(6),1858(5),1877(2),1733(3),1877(2),1751(2),1751(7),1877(10),1858(9),1877(9),1751(9),1751(8),1877(7),1733(8),1877(7),1751(7),1877(6),1733(7),1877(6),1751(6),1877(5),1877(6),1858(6),1877(6)]),flip(a)].
% 1.06/1.30 1889 divide(divide(divide(A,inverse(B)),C),D) = divide(A,divide(divide(D,inverse(C)),B)). [back_rewrite(1591),rewrite([1751(5),1877(10),1858(9),1877(7),1751(9),1877(6),1751(7),1877(6),1858(5),1877(5),1858(8),1877(5),1733(6),1877(5),1877(7),1751(7),1877(6),1858(7),1877(4),1733(5),1877(4),1877(6),1751(6),1877(5),1858(6),1877(3),1733(4),1877(3),1877(5),1733(7),1877(7),1858(7),1877(7)])].
% 1.06/1.30 1890 divide(A,inverse(inverse(B))) = divide(A,B). [back_rewrite(1580),rewrite([1751(5),1877(8),1858(7),1877(7),1751(7),1751(6),1877(5),1733(6),1877(5),1751(5),1877(4),1733(6),1877(5),1751(5),1877(4),1733(6),1858(5),1877(5),1877(7),1889(6),1733(6),1858(5),1877(4),1887(6)])].
% 1.06/1.30 1891 divide(divide(A,B),C) = divide(A,divide(C,inverse(B))). [back_rewrite(1576),rewrite([1751(6),1877(9),1858(8),1877(8),1751(8),1751(7),1877(6),1733(7),1877(6),1751(6),1877(5),1733(6),1877(5),1751(5),1877(4),1733(5),1877(4),1733(5)]),flip(a)].
% 1.06/1.30 1930 inverse(inverse(A)) = A. [back_rewrite(1736),rewrite([1751(2),1751(3),1890(4),1745(3)])].
% 1.06/1.30 1931 divide(A,A) = c_0. [new_symbol(1744)].
% 1.06/1.30 1932 divide(c_0,inverse(a2)) != a2 # answer(prove_these_axioms). [back_unit_del(4),rewrite([1931(5),1931(6),1931(8),1891(16),1930(15),1877(21)]),xx(a),xx(c)].
% 1.06/1.30 1933 divide(c_0,divide(A,B)) = divide(B,A). [back_rewrite(1742),rewrite([1931(2),1891(3),1877(5),1891(4),1930(3)])].
% 1.06/1.30 1936 divide(c_0,inverse(A)) = A. [back_rewrite(1557),rewrite([1931(1),1931(2),1931(3),1931(2),1933(4),1877(3),1931(3),1877(6),1891(5),1933(6),1891(5),1891(5),1931(5),1933(5)])].
% 1.06/1.30 1937 $F # answer(prove_these_axioms). [resolve(1936,a,1932,a)].
% 1.06/1.30
% 1.06/1.30 % SZS output end Refutation
% 1.06/1.30 ============================== end of proof ==========================
% 1.06/1.30
% 1.06/1.30 ============================== STATISTICS ============================
% 1.06/1.30
% 1.06/1.30 Given=30. Generated=4042. Kept=1935. proofs=1.
% 1.06/1.30 Usable=18. Sos=929. Demods=758. Limbo=191, Disabled=799. Hints=0.
% 1.06/1.30 Megabytes=4.02.
% 1.06/1.30 User_CPU=0.33, System_CPU=0.01, Wall_clock=1.
% 1.06/1.30
% 1.06/1.30 ============================== end of statistics =====================
% 1.06/1.30
% 1.06/1.30 ============================== end of search =========================
% 1.06/1.30
% 1.06/1.30 THEOREM PROVED
% 1.06/1.30 % SZS status Unsatisfiable
% 1.06/1.30
% 1.06/1.30 Exiting with 1 proof.
% 1.06/1.30
% 1.06/1.30 Process 25601 exit (max_proofs) Tue Jun 14 03:35:10 2022
% 1.06/1.30 Prover9 interrupted
%------------------------------------------------------------------------------