TSTP Solution File: NUM374+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM374+4 : TPTP v8.1.0. Released v3.2.0.
% 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 : Mon Jul 18 13:27:01 EDT 2022
% Result : Timeout 300.05s 300.30s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM374+4 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 14:38:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/1.00 ============================== Prover9 ===============================
% 0.43/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.00 Process 27987 was started by sandbox2 on n004.cluster.edu,
% 0.43/1.00 Wed Jul 6 14:38:38 2022
% 0.43/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27834_n004.cluster.edu".
% 0.43/1.00 ============================== end of head ===========================
% 0.43/1.00
% 0.43/1.00 ============================== INPUT =================================
% 0.43/1.00
% 0.43/1.00 % Reading from file /tmp/Prover9_27834_n004.cluster.edu
% 0.43/1.00
% 0.43/1.00 set(prolog_style_variables).
% 0.43/1.00 set(auto2).
% 0.43/1.00 % set(auto2) -> set(auto).
% 0.43/1.00 % set(auto) -> set(auto_inference).
% 0.43/1.00 % set(auto) -> set(auto_setup).
% 0.43/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.00 % set(auto) -> set(auto_limits).
% 0.43/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.00 % set(auto) -> set(auto_denials).
% 0.43/1.00 % set(auto) -> set(auto_process).
% 0.43/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.00 % set(auto2) -> assign(stats, some).
% 0.43/1.00 % set(auto2) -> clear(echo_input).
% 0.43/1.00 % set(auto2) -> set(quiet).
% 0.43/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.00 % set(auto2) -> clear(print_given).
% 0.43/1.00 assign(lrs_ticks,-1).
% 0.43/1.00 assign(sos_limit,10000).
% 0.43/1.00 assign(order,kbo).
% 0.43/1.00 set(lex_order_vars).
% 0.43/1.00 clear(print_given).
% 0.43/1.00
% 0.43/1.00 % formulas(sos). % not echoed (16 formulas)
% 0.43/1.00
% 0.43/1.00 ============================== end of input ==========================
% 0.43/1.00
% 0.43/1.00 % From the command line: assign(max_seconds, 300).
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.00
% 0.43/1.00 % Formulas that are not ordinary clauses:
% 0.43/1.00 1 (all X all Y sum(X,Y) = sum(Y,X)) # label(sum_symmetry) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 2 (all X all Y all Z sum(X,sum(Y,Z)) = sum(sum(X,Y),Z)) # label(sum_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 3 (all X product(X,n1) = X) # label(product_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 4 (all X all Y product(X,Y) = product(Y,X)) # label(product_symmetry) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 5 (all X all Y all Z product(X,product(Y,Z)) = product(product(X,Y),Z)) # label(product_associativity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 6 (all X all Y all Z product(X,sum(Y,Z)) = sum(product(X,Y),product(X,Z))) # label(sum_product_distribution) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 7 (all X exponent(n1,X) = n1) # label(exponent_n1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 8 (all X exponent(X,n1) = X) # label(exponent_identity) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 9 (all X all Y all Z exponent(X,sum(Y,Z)) = product(exponent(X,Y),exponent(X,Z))) # label(exponent_sum_product) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 10 (all X all Y all Z exponent(product(X,Y),Z) = product(exponent(X,Z),exponent(Y,Z))) # label(exponent_product_distribution) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 11 (all X all Y all Z exponent(exponent(X,Y),Z) = exponent(X,product(Y,Z))) # label(exponent_exponent) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 12 (all C all P all Q all R all S all B (lemmas(C,P,Q,R,S,B) <-> n2 = sum(n1,n1) & B != n0 & B != n1 & B != n2 & (all X B != product(n0,X)) & (all X P != product(Q,X)) & (all X Q != product(P,X)) & (all X R != product(S,X)) & (all X S != product(R,X)) & sum(n1,n0) != n1 & sum(n2,n0) != n1 & sum(n0,n0) != n1 & C != n1 & sum(n1,C) != n1 & product(C,n0) != n1 & sum(n1,n0) != n0 & sum(n2,n0) != n0 & sum(n0,n0) != n0 & C != n0 & sum(n1,C) != n0 & sum(n2,n0) != sum(n1,n0) & C != sum(n1,n0) & product(C,n0) != sum(n1,n0) & C != sum(n2,n0) & C != sum(n0,n0) & sum(n1,C) != C)) # label(lemmas) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 13 -(all C all P all Q all R all S all B (C = product(n0,n0) & P = sum(n1,n0) & Q = sum(P,C) & R = sum(n1,product(n0,C)) & S = sum(sum(n1,C),product(C,C)) & lemmas(C,P,Q,R,S,B) -> product(exponent(sum(exponent(P,n0),exponent(Q,n0)),B),exponent(sum(exponent(R,B),exponent(S,B)),n0)) = product(exponent(sum(exponent(P,B),exponent(Q,B)),n0),exponent(sum(exponent(R,n0),exponent(S,n0)),B)))) # label(wilkie) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.00
% 0.43/1.00 ============================== end of process non-clausal formulas ===
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.00
% 0.43/1.00 ============================== PREDICATE ELIMINATION =================
% 0.43/1.00 14 -lemmas(A,B,C,D,E,F) | n0 != F # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 15 lemmas(c1,c2,c3,c4,c5,c6) # label(wilkie) # label(negated_conjecture). [clausify(13)].
% 0.43/1.00 Derived: n0 != c6. [resolve(14,a,15,a)].
% 0.43/1.00 16 -lemmas(A,B,C,D,E,F) | F != n1 # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: c6 != n1. [resolve(16,a,15,a)].
% 0.43/1.00 17 -lemmas(A,B,C,D,E,F) | n2 != F # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: n2 != c6. [resolve(17,a,15,a)].
% 0.43/1.00 18 -lemmas(A,B,C,D,E,F) | A != n1 # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: c1 != n1. [resolve(18,a,15,a)].
% 0.43/1.00 19 -lemmas(A,B,C,D,E,F) | n0 != A # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: n0 != c1. [resolve(19,a,15,a)].
% 0.43/1.00 20 -lemmas(A,B,C,D,E,F) | product(n0,V6) != F # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: product(n0,A) != c6. [resolve(20,a,15,a)].
% 0.43/1.00 21 -lemmas(A,B,C,D,E,F) | product(C,V6) != B # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: product(c3,A) != c2. [resolve(21,a,15,a)].
% 0.43/1.00 22 -lemmas(A,B,C,D,E,F) | product(B,V6) != C # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: product(c2,A) != c3. [resolve(22,a,15,a)].
% 0.43/1.00 23 -lemmas(A,B,C,D,E,F) | product(E,V6) != D # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: product(c5,A) != c4. [resolve(23,a,15,a)].
% 0.43/1.00 24 -lemmas(A,B,C,D,E,F) | product(D,V6) != E # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: product(c4,A) != c5. [resolve(24,a,15,a)].
% 0.43/1.00 25 -lemmas(A,B,C,D,E,F) | sum(n1,n0) != n1 # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: sum(n1,n0) != n1. [resolve(25,a,15,a)].
% 0.43/1.00 26 -lemmas(A,B,C,D,E,F) | sum(n2,n0) != n1 # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: sum(n2,n0) != n1. [resolve(26,a,15,a)].
% 0.43/1.00 27 -lemmas(A,B,C,D,E,F) | sum(n0,n0) != n1 # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: sum(n0,n0) != n1. [resolve(27,a,15,a)].
% 0.43/1.00 28 -lemmas(A,B,C,D,E,F) | sum(n1,A) != n1 # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: sum(n1,c1) != n1. [resolve(28,a,15,a)].
% 0.43/1.00 29 -lemmas(A,B,C,D,E,F) | product(A,n0) != n1 # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: product(c1,n0) != n1. [resolve(29,a,15,a)].
% 0.43/1.00 30 -lemmas(A,B,C,D,E,F) | sum(n1,n0) != n0 # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: sum(n1,n0) != n0. [resolve(30,a,15,a)].
% 0.43/1.00 31 -lemmas(A,B,C,D,E,F) | sum(n2,n0) != n0 # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: sum(n2,n0) != n0. [resolve(31,a,15,a)].
% 0.43/1.00 32 -lemmas(A,B,C,D,E,F) | sum(n0,n0) != n0 # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: sum(n0,n0) != n0. [resolve(32,a,15,a)].
% 0.43/1.00 33 -lemmas(A,B,C,D,E,F) | sum(n1,A) != n0 # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: sum(n1,c1) != n0. [resolve(33,a,15,a)].
% 0.43/1.00 34 -lemmas(A,B,C,D,E,F) | sum(n1,n0) != A # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: sum(n1,n0) != c1. [resolve(34,a,15,a)].
% 0.43/1.00 35 -lemmas(A,B,C,D,E,F) | sum(n2,n0) != A # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: sum(n2,n0) != c1. [resolve(35,a,15,a)].
% 0.43/1.00 36 -lemmas(A,B,C,D,E,F) | sum(n0,n0) != A # label(lemmas) # label(axiom). [clausify(12)].
% 0.43/1.00 Derived: sum(n0,n0) != c1. [resolve(36,a,15,a)].
% 0.43/1.00 37 -lemmas(A,B,C,D,E,F) | sum(n1,A) != A # label(lemmas) # label(axiom). [clausify(12)].
% 0.74/1.02 Derived: sum(n1,c1) != c1. [resolve(37,a,15,a)].
% 0.74/1.02 38 -lemmas(A,B,C,D,E,F) | sum(n2,n0) != sum(n1,n0) # label(lemmas) # label(axiom). [clausify(12)].
% 0.74/1.02 Derived: sum(n2,n0) != sum(n1,n0). [resolve(38,a,15,a)].
% 0.74/1.02 39 -lemmas(A,B,C,D,E,F) | product(A,n0) != sum(n1,n0) # label(lemmas) # label(axiom). [clausify(12)].
% 0.74/1.02 Derived: product(c1,n0) != sum(n1,n0). [resolve(39,a,15,a)].
% 0.74/1.02 40 -lemmas(A,B,C,D,E,F) | sum(n1,n1) = n2 # label(lemmas) # label(axiom). [clausify(12)].
% 0.74/1.02 Derived: sum(n1,n1) = n2. [resolve(40,a,15,a)].
% 0.74/1.02 41 lemmas(A,B,C,D,E,F) | sum(n1,n1) != n2 | n0 = F | F = n1 | n2 = F | product(n0,f1(A,B,C,D,E,F)) = F | product(C,f2(A,B,C,D,E,F)) = B | product(B,f3(A,B,C,D,E,F)) = C | product(E,f4(A,B,C,D,E,F)) = D | product(D,f5(A,B,C,D,E,F)) = E | sum(n1,n0) = n1 | sum(n2,n0) = n1 | sum(n0,n0) = n1 | A = n1 | sum(n1,A) = n1 | product(A,n0) = n1 | sum(n1,n0) = n0 | sum(n2,n0) = n0 | sum(n0,n0) = n0 | n0 = A | sum(n1,A) = n0 | sum(n2,n0) = sum(n1,n0) | sum(n1,n0) = A | product(A,n0) = sum(n1,n0) | sum(n2,n0) = A | sum(n0,n0) = A | sum(n1,A) = A # label(lemmas) # label(axiom). [clausify(12)].
% 0.74/1.02 Derived: sum(n1,n1) != n2 | n0 = A | A = n1 | n2 = A | product(n0,f1(B,C,D,E,F,A)) = A | product(D,f2(B,C,D,E,F,A)) = C | product(C,f3(B,C,D,E,F,A)) = D | product(F,f4(B,C,D,E,F,A)) = E | product(E,f5(B,C,D,E,F,A)) = F | sum(n1,n0) = n1 | sum(n2,n0) = n1 | sum(n0,n0) = n1 | B = n1 | sum(n1,B) = n1 | product(B,n0) = n1 | sum(n1,n0) = n0 | sum(n2,n0) = n0 | sum(n0,n0) = n0 | n0 = B | sum(n1,B) = n0 | sum(n2,n0) = sum(n1,n0) | sum(n1,n0) = B | product(B,n0) = sum(n1,n0) | sum(n2,n0) = B | sum(n0,n0) = B | sum(n1,B) = B | product(n0,V6) != A. [resolve(41,a,20,a)].
% 0.74/1.02 Derived: sum(n1,n1) != n2 | n0 = A | A = n1 | n2 = A | product(n0,f1(B,C,D,E,F,A)) = A | product(D,f2(B,C,D,E,F,A)) = C | product(C,f3(B,C,D,E,F,A)) = D | product(F,f4(B,C,D,E,F,A)) = E | product(E,f5(B,C,D,E,F,A)) = F | sum(n1,n0) = n1 | sum(n2,n0) = n1 | sum(n0,n0) = n1 | B = n1 | sum(n1,B) = n1 | product(B,n0) = n1 | sum(n1,n0) = n0 | sum(n2,n0) = n0 | sum(n0,n0) = n0 | n0 = B | sum(n1,B) = n0 | sum(n2,n0) = sum(n1,n0) | sum(n1,n0) = B | product(B,n0) = sum(n1,n0) | sum(n2,n0) = B | sum(n0,n0) = B | sum(n1,B) = B | product(D,V6) != C. [resolve(41,a,21,a)].
% 0.74/1.02 Derived: sum(n1,n1) != n2 | n0 = A | A = n1 | n2 = A | product(n0,f1(B,C,D,E,F,A)) = A | product(D,f2(B,C,D,E,F,A)) = C | product(C,f3(B,C,D,E,F,A)) = D | product(F,f4(B,C,D,E,F,A)) = E | product(E,f5(B,C,D,E,F,A)) = F | sum(n1,n0) = n1 | sum(n2,n0) = n1 | sum(n0,n0) = n1 | B = n1 | sum(n1,B) = n1 | product(B,n0) = n1 | sum(n1,n0) = n0 | sum(n2,n0) = n0 | sum(n0,n0) = n0 | n0 = B | sum(n1,B) = n0 | sum(n2,n0) = sum(n1,n0) | sum(n1,n0) = B | product(B,n0) = sum(n1,n0) | sum(n2,n0) = B | sum(n0,n0) = B | sum(n1,B) = B | product(C,V6) != D. [resolve(41,a,22,a)].
% 0.74/1.02 Derived: sum(n1,n1) != n2 | n0 = A | A = n1 | n2 = A | product(n0,f1(B,C,D,E,F,A)) = A | product(D,f2(B,C,D,E,F,A)) = C | product(C,f3(B,C,D,E,F,A)) = D | product(F,f4(B,C,D,E,F,A)) = E | product(E,f5(B,C,D,E,F,A)) = F | sum(n1,n0) = n1 | sum(n2,n0) = n1 | sum(n0,n0) = n1 | B = n1 | sum(n1,B) = n1 | product(B,n0) = n1 | sum(n1,n0) = n0 | sum(n2,n0) = n0 | sum(n0,n0) = n0 | n0 = B | sum(n1,B) = n0 | sum(n2,n0) = sum(n1,n0) | sum(n1,n0) = B | product(B,n0) = sum(n1,n0) | sum(n2,n0) = B | sum(n0,n0) = B | sum(n1,B) = B | product(F,V6) != E. [resolve(41,a,23,a)].
% 0.74/1.02 Derived: sum(n1,n1) != n2 | n0 = A | A = n1 | n2 = A | product(n0,f1(B,C,D,E,F,A)) = A | product(D,f2(B,C,D,E,F,A)) = C | product(C,f3(B,C,D,E,F,A)) = D | product(F,f4(B,C,D,E,F,A)) = E | product(E,f5(B,C,D,E,F,A)) = F | sum(n1,n0) = n1 | sum(n2,n0) = n1 | sum(n0,n0) = n1 | B = n1 | sum(n1,B) = n1 | product(B,n0) = n1 | sum(n1,n0) = n0 | sum(n2,n0) = n0 | sum(n0,n0) = n0 | n0 = B | sum(n1,B) = n0 | sum(n2,n0) = sum(n1,n0) | sum(n1,n0) = B | product(B,n0) = sum(n1,n0) | sum(n2,n0) = B | sum(n0,n0) = B | sum(n1,B) = B | product(E,V6) != F. [resolve(41,a,24,a)].
% 0.74/1.02
% 0.74/1.02 ============================== end predicate elimination =============
% 0.74/1.02
% 0.74/1.02 Auto_denials: (non-Horn, no changes).
% 0.74/1.02
% 0.74/1.02 Term ordering decisions:
% 0.74/1.02 Function symbol KB Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------