TSTP Solution File: GRP776+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP776+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 11:21:01 EDT 2022
% Result : Theorem 7.54s 7.86s
% Output : Refutation 7.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP776+1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n021.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 : Mon Jun 13 06:40:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/0.99 ============================== Prover9 ===============================
% 0.43/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.99 Process 18422 was started by sandbox2 on n021.cluster.edu,
% 0.43/0.99 Mon Jun 13 06:40:42 2022
% 0.43/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_18269_n021.cluster.edu".
% 0.43/0.99 ============================== end of head ===========================
% 0.43/0.99
% 0.43/0.99 ============================== INPUT =================================
% 0.43/0.99
% 0.43/0.99 % Reading from file /tmp/Prover9_18269_n021.cluster.edu
% 0.43/0.99
% 0.43/0.99 set(prolog_style_variables).
% 0.43/0.99 set(auto2).
% 0.43/0.99 % set(auto2) -> set(auto).
% 0.43/0.99 % set(auto) -> set(auto_inference).
% 0.43/0.99 % set(auto) -> set(auto_setup).
% 0.43/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.99 % set(auto) -> set(auto_limits).
% 0.43/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.99 % set(auto) -> set(auto_denials).
% 0.43/0.99 % set(auto) -> set(auto_process).
% 0.43/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.99 % set(auto2) -> assign(stats, some).
% 0.43/0.99 % set(auto2) -> clear(echo_input).
% 0.43/0.99 % set(auto2) -> set(quiet).
% 0.43/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.99 % set(auto2) -> clear(print_given).
% 0.43/0.99 assign(lrs_ticks,-1).
% 0.43/0.99 assign(sos_limit,10000).
% 0.43/0.99 assign(order,kbo).
% 0.43/0.99 set(lex_order_vars).
% 0.43/0.99 clear(print_given).
% 0.43/0.99
% 0.43/0.99 % formulas(sos). % not echoed (19 formulas)
% 0.43/0.99
% 0.43/0.99 ============================== end of input ==========================
% 0.43/0.99
% 0.43/0.99 % From the command line: assign(max_seconds, 300).
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.99
% 0.43/0.99 % Formulas that are not ordinary clauses:
% 0.43/0.99 1 (all B all A (g(A) & g(B) -> g(product(A,B)))) # label(sos01) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 2 (all A (g(A) -> g(inv(A)))) # label(sos02) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 3 (all C all B all A (g(A) & g(B) & g(C) -> product(product(A,B),C) = product(A,product(B,C)))) # label(sos04) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 4 (all A (g(A) -> product(eh,A) = A)) # label(sos05) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 5 (all A (g(A) -> product(A,eh) = A)) # label(sos06) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 6 (all A (g(A) -> product(A,inv(A)) = eh)) # label(sos07) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 7 (all A (g(A) -> product(inv(A),A) = eh)) # label(sos08) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 8 (all B all A (h(A) & h(B) -> h(sum(A,B)))) # label(sos09) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 9 (all B all A (h(A) -> h(opp(B)))) # label(sos10) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 10 (all C all B all A (h(A) & h(B) & h(C) -> sum(sum(A,B),C) = sum(A,sum(B,C)))) # label(sos12) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 11 (all A (h(A) -> sum(eg,A) = A)) # label(sos13) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 12 (all A (h(A) -> sum(A,eg) = A)) # label(sos14) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 13 (all A (h(A) -> sum(A,opp(A)) = eg)) # label(sos15) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 14 (all A (h(A) -> sum(opp(A),A) = eg)) # label(sos16) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 15 (all A (g(A) -> h(f(A)))) # label(sos17) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 16 (all B all A f(product(A,B)) = sum(f(A),f(B))) # label(sos18) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 17 -(all X0 (f(eh) = eg & (-g(X0) | f(inv(X0)) = opp(f(X0))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/0.99
% 0.43/0.99 ============================== end of process non-clausal formulas ===
% 7.54/7.86
% 7.54/7.86 ============================== PROCESS INITIAL CLAUSES ===============
% 7.54/7.86
% 7.54/7.86 ============================== PREDICATE ELIMINATION =================
% 7.54/7.86
% 7.54/7.86 ============================== end predicate elimination =============
% 7.54/7.86
% 7.54/7.86 Auto_denials:
% 7.54/7.86 % copying label goals to answer in negative clause
% 7.54/7.86
% 7.54/7.86 Term ordering decisions:
% 7.54/7.86 Function symbol KB weights: eg=1. eh=1. c1=1. product=1. sum=1. f=1. inv=1. opp=1.
% 7.54/7.86
% 7.54/7.86 ============================== end of process initial clauses ========
% 7.54/7.86
% 7.54/7.86 ============================== CLAUSES FOR SEARCH ====================
% 7.54/7.86
% 7.54/7.86 ============================== end of clauses for search =============
% 7.54/7.86
% 7.54/7.86 ============================== SEARCH ================================
% 7.54/7.86
% 7.54/7.86 % Starting search at 0.01 seconds.
% 7.54/7.86
% 7.54/7.86 Low Water (keep): wt=57.000, iters=3359
% 7.54/7.86
% 7.54/7.86 Low Water (keep): wt=54.000, iters=3397
% 7.54/7.86
% 7.54/7.86 Low Water (keep): wt=53.000, iters=3386
% 7.54/7.86
% 7.54/7.86 Low Water (keep): wt=50.000, iters=3391
% 7.54/7.86
% 7.54/7.86 Low Water (keep): wt=48.000, iters=3353
% 7.54/7.86
% 7.54/7.86 Low Water (keep): wt=47.000, iters=3368
% 7.54/7.86
% 7.54/7.86 Low Water (keep): wt=46.000, iters=3368
% 7.54/7.86
% 7.54/7.86 Low Water (keep): wt=45.000, iters=3352
% 7.54/7.86
% 7.54/7.86 Low Water (keep): wt=44.000, iters=3453
% 7.54/7.86
% 7.54/7.86 Low Water (keep): wt=43.000, iters=3367
% 7.54/7.86
% 7.54/7.86 Low Water (keep): wt=42.000, iters=3350
% 7.54/7.86
% 7.54/7.86 Low Water (keep): wt=41.000, iters=3405
% 7.54/7.86
% 7.54/7.86 Low Water (keep): wt=40.000, iters=3342
% 7.54/7.86
% 7.54/7.86 Low Water (keep): wt=39.000, iters=3373
% 7.54/7.86
% 7.54/7.86 Low Water (keep): wt=38.000, iters=3373
% 7.54/7.86
% 7.54/7.86 Low Water (displace): id=20743, wt=20.000
% 7.54/7.86
% 7.54/7.86 Low Water (displace): id=20757, wt=19.000
% 7.54/7.86
% 7.54/7.86 ============================== PROOF =================================
% 7.54/7.86 % SZS status Theorem
% 7.54/7.86 % SZS output start Refutation
% 7.54/7.86
% 7.54/7.86 % Proof 1 at 6.79 (+ 0.09) seconds: goals.
% 7.54/7.86 % Length of proof is 56.
% 7.54/7.86 % Level of proof is 11.
% 7.54/7.86 % Maximum clause weight is 17.000.
% 7.54/7.86 % Given clauses 168.
% 7.54/7.86
% 7.54/7.86 2 (all A (g(A) -> g(inv(A)))) # label(sos02) # label(axiom) # label(non_clause). [assumption].
% 7.54/7.86 3 (all C all B all A (g(A) & g(B) & g(C) -> product(product(A,B),C) = product(A,product(B,C)))) # label(sos04) # label(axiom) # label(non_clause). [assumption].
% 7.54/7.86 4 (all A (g(A) -> product(eh,A) = A)) # label(sos05) # label(axiom) # label(non_clause). [assumption].
% 7.54/7.86 5 (all A (g(A) -> product(A,eh) = A)) # label(sos06) # label(axiom) # label(non_clause). [assumption].
% 7.54/7.86 6 (all A (g(A) -> product(A,inv(A)) = eh)) # label(sos07) # label(axiom) # label(non_clause). [assumption].
% 7.54/7.86 7 (all A (g(A) -> product(inv(A),A) = eh)) # label(sos08) # label(axiom) # label(non_clause). [assumption].
% 7.54/7.86 9 (all B all A (h(A) -> h(opp(B)))) # label(sos10) # label(axiom) # label(non_clause). [assumption].
% 7.54/7.86 10 (all C all B all A (h(A) & h(B) & h(C) -> sum(sum(A,B),C) = sum(A,sum(B,C)))) # label(sos12) # label(axiom) # label(non_clause). [assumption].
% 7.54/7.86 11 (all A (h(A) -> sum(eg,A) = A)) # label(sos13) # label(axiom) # label(non_clause). [assumption].
% 7.54/7.86 12 (all A (h(A) -> sum(A,eg) = A)) # label(sos14) # label(axiom) # label(non_clause). [assumption].
% 7.54/7.86 14 (all A (h(A) -> sum(opp(A),A) = eg)) # label(sos16) # label(axiom) # label(non_clause). [assumption].
% 7.54/7.86 15 (all A (g(A) -> h(f(A)))) # label(sos17) # label(axiom) # label(non_clause). [assumption].
% 7.54/7.86 16 (all B all A f(product(A,B)) = sum(f(A),f(B))) # label(sos18) # label(axiom) # label(non_clause). [assumption].
% 7.54/7.86 17 -(all X0 (f(eh) = eg & (-g(X0) | f(inv(X0)) = opp(f(X0))))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 7.54/7.86 18 g(eh) # label(sos03) # label(axiom). [assumption].
% 7.54/7.86 19 h(eg) # label(sos11) # label(axiom). [assumption].
% 7.54/7.86 20 f(product(A,B)) = sum(f(A),f(B)) # label(sos18) # label(axiom). [clausify(16)].
% 7.54/7.86 21 sum(f(A),f(B)) = f(product(A,B)). [copy(20),flip(a)].
% 7.54/7.86 22 f(eh) != eg | f(inv(c1)) != opp(f(c1)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(17)].
% 7.54/7.86 23 f(eh) != eg | opp(f(c1)) != f(inv(c1)) # answer(goals). [copy(22),flip(b)].
% 7.54/7.86 24 -g(A) | g(inv(A)) # label(sos02) # label(axiom). [clausify(2)].
% 7.54/7.86 25 -h(A) | h(opp(B)) # label(sos10) # label(axiom). [clausify(9)].
% 7.54/7.86 26 -g(A) | h(f(A)) # label(sos17) # label(axiom). [clausify(15)].
% 7.54/7.86 27 f(eh) != eg | g(c1) # label(goals) # label(negated_conjecture). [clausify(17)].
% 7.54/7.86 28 -g(A) | product(eh,A) = A # label(sos05) # label(axiom). [clausify(4)].
% 7.54/7.86 29 -g(A) | product(A,eh) = A # label(sos06) # label(axiom). [clausify(5)].
% 7.54/7.86 30 -h(A) | sum(eg,A) = A # label(sos13) # label(axiom). [clausify(11)].
% 7.54/7.86 31 -h(A) | sum(A,eg) = A # label(sos14) # label(axiom). [clausify(12)].
% 7.54/7.86 33 -g(A) | product(A,inv(A)) = eh # label(sos07) # label(axiom). [clausify(6)].
% 7.54/7.86 34 -g(A) | product(inv(A),A) = eh # label(sos08) # label(axiom). [clausify(7)].
% 7.54/7.86 37 -h(A) | sum(opp(A),A) = eg # label(sos16) # label(axiom). [clausify(14)].
% 7.54/7.86 38 -g(A) | -g(B) | -g(C) | product(product(A,B),C) = product(A,product(B,C)) # label(sos04) # label(axiom). [clausify(3)].
% 7.54/7.86 39 -h(A) | -h(B) | -h(C) | sum(sum(A,B),C) = sum(A,sum(B,C)) # label(sos12) # label(axiom). [clausify(10)].
% 7.54/7.86 41 h(opp(A)). [hyper(25,a,19,a)].
% 7.54/7.86 42 h(f(eh)). [hyper(26,a,18,a)].
% 7.54/7.86 43 product(eh,eh) = eh. [hyper(28,a,18,a)].
% 7.54/7.86 68 sum(opp(A),eg) = opp(A). [hyper(31,a,41,a)].
% 7.54/7.86 75 sum(sum(opp(A),f(eh)),f(eh)) = sum(opp(A),f(eh)). [hyper(39,a,41,a,b,42,a,c,42,a),rewrite([21(13),43(11)])].
% 7.54/7.86 91 sum(opp(f(eh)),f(eh)) = eg. [hyper(37,a,42,a)].
% 7.54/7.86 98 sum(eg,f(eh)) = f(eh). [hyper(30,a,42,a)].
% 7.54/7.86 7022 f(eh) = eg. [para(91(a,1),75(a,1,1)),rewrite([98(4),91(8)])].
% 7.54/7.86 7023 g(c1). [back_rewrite(27),rewrite([7022(2)]),xx(a)].
% 7.54/7.86 7024 opp(f(c1)) != f(inv(c1)) # answer(goals). [back_rewrite(23),rewrite([7022(2)]),xx(a)].
% 7.54/7.86 7032 product(inv(c1),c1) = eh. [hyper(34,a,7023,a)].
% 7.54/7.86 7033 product(c1,inv(c1)) = eh. [hyper(33,a,7023,a)].
% 7.54/7.86 7039 h(f(c1)). [hyper(26,a,7023,a)].
% 7.54/7.86 7040 g(inv(c1)). [hyper(24,a,7023,a)].
% 7.54/7.86 7136 sum(opp(f(c1)),f(c1)) = eg. [hyper(37,a,7039,a)].
% 7.54/7.86 7199 product(inv(c1),eh) = product(eh,inv(c1)). [hyper(38,a,7040,a,b,7023,a,c,7040,a),rewrite([7032(4),7033(10)]),flip(a)].
% 7.54/7.86 7201 product(c1,product(inv(c1),inv(c1))) = product(eh,inv(c1)). [hyper(38,a,7023,a,b,7040,a,c,7040,a),rewrite([7033(4)]),flip(a)].
% 7.54/7.86 7215 product(eh,inv(c1)) = inv(c1). [hyper(29,a,7040,a),rewrite([7199(4)])].
% 7.54/7.86 7216 h(f(inv(c1))). [hyper(26,a,7040,a)].
% 7.54/7.86 7220 product(c1,product(inv(c1),inv(c1))) = inv(c1). [back_rewrite(7201),rewrite([7215(11)])].
% 7.54/7.86 7258 sum(eg,f(inv(c1))) = f(inv(c1)). [hyper(39,a,7039,a,b,7216,a,c,7216,a),rewrite([21(6),7033(4),7022(2),21(14),21(14),7220(12)])].
% 7.54/7.86 7282 sum(sum(opp(A),f(c1)),f(inv(c1))) = opp(A). [hyper(39,a,41,a,b,7039,a,c,7216,a),rewrite([21(15),7033(13),7022(11),68(11)])].
% 7.54/7.86 21156 $F # answer(goals). [para(7136(a,1),7282(a,1,1)),rewrite([7258(5)]),flip(a),unit_del(a,7024)].
% 7.54/7.86
% 7.54/7.86 % SZS output end Refutation
% 7.54/7.86 ============================== end of proof ==========================
% 7.54/7.86
% 7.54/7.86 ============================== STATISTICS ============================
% 7.54/7.86
% 7.54/7.86 Given=168. Generated=106608. Kept=21136. proofs=1.
% 7.54/7.86 Usable=140. Sos=9998. Demods=9270. Limbo=0, Disabled=11018. Hints=0.
% 7.54/7.86 Megabytes=31.50.
% 7.54/7.86 User_CPU=6.79, System_CPU=0.09, Wall_clock=7.
% 7.54/7.86
% 7.54/7.86 ============================== end of statistics =====================
% 7.54/7.86
% 7.54/7.86 ============================== end of search =========================
% 7.54/7.86
% 7.54/7.86 THEOREM PROVED
% 7.54/7.86 % SZS status Theorem
% 7.54/7.86
% 7.54/7.86 Exiting with 1 proof.
% 7.54/7.86
% 7.54/7.86 Process 18422 exit (max_proofs) Mon Jun 13 06:40:49 2022
% 7.54/7.86 Prover9 interrupted
%------------------------------------------------------------------------------