TSTP Solution File: GRP781-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP781-1 : TPTP v8.1.0. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 11:21:03 EDT 2022
% Result : Unsatisfiable 5.26s 5.58s
% Output : Refutation 5.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP781-1 : TPTP v8.1.0. Released v5.4.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n008.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 : Tue Jun 14 04:06:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 5.26/5.58 ============================== Prover9 ===============================
% 5.26/5.58 Prover9 (32) version 2009-11A, November 2009.
% 5.26/5.58 Process 7997 was started by sandbox2 on n008.cluster.edu,
% 5.26/5.58 Tue Jun 14 04:06:38 2022
% 5.26/5.58 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7844_n008.cluster.edu".
% 5.26/5.58 ============================== end of head ===========================
% 5.26/5.58
% 5.26/5.58 ============================== INPUT =================================
% 5.26/5.58
% 5.26/5.58 % Reading from file /tmp/Prover9_7844_n008.cluster.edu
% 5.26/5.58
% 5.26/5.58 set(prolog_style_variables).
% 5.26/5.58 set(auto2).
% 5.26/5.58 % set(auto2) -> set(auto).
% 5.26/5.58 % set(auto) -> set(auto_inference).
% 5.26/5.58 % set(auto) -> set(auto_setup).
% 5.26/5.58 % set(auto_setup) -> set(predicate_elim).
% 5.26/5.58 % set(auto_setup) -> assign(eq_defs, unfold).
% 5.26/5.58 % set(auto) -> set(auto_limits).
% 5.26/5.58 % set(auto_limits) -> assign(max_weight, "100.000").
% 5.26/5.58 % set(auto_limits) -> assign(sos_limit, 20000).
% 5.26/5.58 % set(auto) -> set(auto_denials).
% 5.26/5.58 % set(auto) -> set(auto_process).
% 5.26/5.58 % set(auto2) -> assign(new_constants, 1).
% 5.26/5.58 % set(auto2) -> assign(fold_denial_max, 3).
% 5.26/5.58 % set(auto2) -> assign(max_weight, "200.000").
% 5.26/5.58 % set(auto2) -> assign(max_hours, 1).
% 5.26/5.58 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 5.26/5.58 % set(auto2) -> assign(max_seconds, 0).
% 5.26/5.58 % set(auto2) -> assign(max_minutes, 5).
% 5.26/5.58 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 5.26/5.58 % set(auto2) -> set(sort_initial_sos).
% 5.26/5.58 % set(auto2) -> assign(sos_limit, -1).
% 5.26/5.58 % set(auto2) -> assign(lrs_ticks, 3000).
% 5.26/5.58 % set(auto2) -> assign(max_megs, 400).
% 5.26/5.58 % set(auto2) -> assign(stats, some).
% 5.26/5.58 % set(auto2) -> clear(echo_input).
% 5.26/5.58 % set(auto2) -> set(quiet).
% 5.26/5.58 % set(auto2) -> clear(print_initial_clauses).
% 5.26/5.58 % set(auto2) -> clear(print_given).
% 5.26/5.58 assign(lrs_ticks,-1).
% 5.26/5.58 assign(sos_limit,10000).
% 5.26/5.58 assign(order,kbo).
% 5.26/5.58 set(lex_order_vars).
% 5.26/5.58 clear(print_given).
% 5.26/5.58
% 5.26/5.58 % formulas(sos). % not echoed (6 formulas)
% 5.26/5.58
% 5.26/5.58 ============================== end of input ==========================
% 5.26/5.58
% 5.26/5.58 % From the command line: assign(max_seconds, 300).
% 5.26/5.58
% 5.26/5.58 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 5.26/5.58
% 5.26/5.58 % Formulas that are not ordinary clauses:
% 5.26/5.58
% 5.26/5.58 ============================== end of process non-clausal formulas ===
% 5.26/5.58
% 5.26/5.58 ============================== PROCESS INITIAL CLAUSES ===============
% 5.26/5.58
% 5.26/5.58 ============================== PREDICATE ELIMINATION =================
% 5.26/5.58
% 5.26/5.58 ============================== end predicate elimination =============
% 5.26/5.58
% 5.26/5.58 Auto_denials:
% 5.26/5.58 % copying label distributivity to answer in negative clause
% 5.26/5.58
% 5.26/5.58 Term ordering decisions:
% 5.26/5.58 Function symbol KB weights: x=1. y=1. z=1. m=1. c=1.
% 5.26/5.58
% 5.26/5.58 ============================== end of process initial clauses ========
% 5.26/5.58
% 5.26/5.58 ============================== CLAUSES FOR SEARCH ====================
% 5.26/5.58
% 5.26/5.58 ============================== end of clauses for search =============
% 5.26/5.58
% 5.26/5.58 ============================== SEARCH ================================
% 5.26/5.58
% 5.26/5.58 % Starting search at 0.01 seconds.
% 5.26/5.58
% 5.26/5.58 Low Water (keep): wt=147.000, iters=3366
% 5.26/5.58
% 5.26/5.58 Low Water (keep): wt=135.000, iters=3351
% 5.26/5.58
% 5.26/5.58 Low Water (keep): wt=127.000, iters=3342
% 5.26/5.58
% 5.26/5.58 Low Water (keep): wt=87.000, iters=3337
% 5.26/5.58
% 5.26/5.58 Low Water (keep): wt=83.000, iters=3361
% 5.26/5.58
% 5.26/5.58 Low Water (keep): wt=79.000, iters=3528
% 5.26/5.58
% 5.26/5.58 Low Water (keep): wt=75.000, iters=3475
% 5.26/5.58
% 5.26/5.58 Low Water (keep): wt=67.000, iters=3355
% 5.26/5.58
% 5.26/5.58 Low Water (keep): wt=65.000, iters=3380
% 5.26/5.58
% 5.26/5.58 Low Water (keep): wt=62.000, iters=3395
% 5.26/5.58
% 5.26/5.58 Low Water (keep): wt=58.000, iters=3345
% 5.26/5.58
% 5.26/5.58 Low Water (keep): wt=54.000, iters=3375
% 5.26/5.58
% 5.26/5.58 Low Water (keep): wt=53.000, iters=3353
% 5.26/5.58
% 5.26/5.58 ============================== PROOF =================================
% 5.26/5.58 % SZS status Unsatisfiable
% 5.26/5.58 % SZS output start Refutation
% 5.26/5.58
% 5.26/5.58 % Proof 1 at 4.62 (+ 0.02) seconds: distributivity.
% 5.26/5.58 % Length of proof is 71.
% 5.26/5.58 % Level of proof is 16.
% 5.26/5.58 % Maximum clause weight is 33.000.
% 5.26/5.58 % Given clauses 243.
% 5.26/5.58
% 5.26/5.58 1 m(A,m(B,C)) = m(m(A,B),C) # label(associativity) # label(axiom). [assumption].
% 5.26/5.58 2 m(m(A,B),C) = m(A,m(B,C)). [copy(1),flip(a)].
% 5.26/5.58 3 m(A,m(B,c(B,A))) = m(B,A) # label(commutator) # label(axiom). [assumption].
% 5.26/5.58 4 m(A,m(B,m(C,m(B,A)))) = m(B,m(A,m(C,m(A,B)))) # label(assumption) # label(axiom). [assumption].
% 5.26/5.58 5 c(m(x,y),z) != m(c(x,z),c(y,z)) # label(distributivity) # label(negated_conjecture) # answer(distributivity). [assumption].
% 5.26/5.58 6 m(c(x,z),c(y,z)) != c(m(x,y),z) # answer(distributivity). [copy(5),flip(a)].
% 5.26/5.58 7 m(A,B) != m(C,B) | A = C # label(cancellation) # label(axiom). [assumption].
% 5.26/5.58 8 m(A,B) != m(A,C) | B = C # label(cancellation_001) # label(axiom). [assumption].
% 5.26/5.58 9 m(A,m(B,m(c(B,A),C))) = m(B,m(A,C)). [para(3(a,1),2(a,1,1)),rewrite([2(2),2(5)]),flip(a)].
% 5.26/5.58 10 m(A,m(B,m(C,c(C,m(A,B))))) = m(C,m(A,B)). [para(3(a,1),2(a,1)),flip(a)].
% 5.26/5.58 11 m(A,m(B,m(C,c(m(B,C),A)))) = m(B,m(C,A)). [para(2(a,1),3(a,1,2)),rewrite([2(7)])].
% 5.26/5.58 13 m(A,m(B,m(C,m(D,m(C,m(A,B)))))) = m(C,m(A,m(B,m(D,m(A,m(B,C)))))). [para(4(a,1),2(a,1)),rewrite([2(3),2(5)]),flip(a)].
% 5.26/5.58 27 m(A,c(A,A)) = A. [hyper(8,a,3,a)].
% 5.26/5.58 28 m(A,m(c(x,z),c(y,z))) != m(A,c(m(x,y),z)) # answer(distributivity). [ur(8,b,6,a)].
% 5.26/5.58 30 m(A,B) != m(C,A) | m(C,c(C,A)) = B. [para(3(a,1),8(a,1)),flip(a)].
% 5.26/5.58 31 m(A,m(B,m(C,m(B,A)))) != m(B,D) | m(A,m(C,m(A,B))) = D. [para(4(a,1),8(a,1))].
% 5.26/5.58 32 m(A,m(c(A,A),B)) = m(A,B). [hyper(8,a,9,a)].
% 5.26/5.58 35 m(A,m(B,m(C,c(C,c(A,B))))) = m(B,m(A,m(C,c(A,B)))). [para(3(a,1),9(a,1,2,2)),flip(a)].
% 5.26/5.58 45 m(A,m(B,m(C,m(c(C,c(A,B)),D)))) = m(B,m(A,m(C,m(c(A,B),D)))). [para(9(a,1),9(a,1,2,2)),flip(a)].
% 5.26/5.58 57 m(A,m(B,m(c(x,z),c(y,z)))) != m(A,m(B,c(m(x,y),z))) # answer(distributivity). [ur(8,b,28,a)].
% 5.26/5.58 76 m(A,B) != A | c(A,A) = B. [para(27(a,1),8(a,1)),flip(a)].
% 5.26/5.58 96 m(A,m(B,c(B,m(B,A)))) = m(B,A). [hyper(8,a,10,a)].
% 5.26/5.58 110 m(A,m(B,c(c(A,B),m(B,A)))) = m(c(A,B),m(B,A)). [para(10(a,1),9(a,1)),flip(a)].
% 5.26/5.58 123 m(z,m(x,m(y,m(c(x,z),c(y,z))))) != m(x,m(y,z)) # answer(distributivity). [para(3(a,1),57(a,2)),rewrite([2(12),2(18)])].
% 5.26/5.58 132 m(z,m(x,m(y,m(c(x,z),m(c(y,z),A))))) != m(x,m(y,m(z,A))) # answer(distributivity). [ur(7,b,123,a),rewrite([2(14),2(13),2(12),2(11),2(20),2(19)])].
% 5.26/5.58 136 m(c(A,A),B) = B. [hyper(8,a,32,a)].
% 5.26/5.58 147 m(A,c(c(B,B),A)) = A. [para(136(a,1),3(a,1,2)),rewrite([136(5)])].
% 5.26/5.58 150 m(A,B) != B | c(C,C) = A. [para(136(a,1),7(a,1)),flip(a)].
% 5.26/5.58 156 c(c(A,A),B) = c(B,B). [hyper(76,a,147,a),flip(a)].
% 5.26/5.58 160 m(A,B) != A | c(c(C,C),A) = B. [para(147(a,1),8(a,1)),flip(a)].
% 5.26/5.58 167 m(c(c(A,A),B),C) = C. [para(156(a,2),136(a,1,1))].
% 5.26/5.58 168 m(A,c(c(c(B,B),C),A)) = A. [para(156(a,2),147(a,1,2,1))].
% 5.26/5.58 171 m(A,m(B,c(m(A,B),A))) = m(B,A). [hyper(8,a,11,a)].
% 5.26/5.58 235 m(A,c(A,c(c(B,B),C))) = m(A,c(c(B,B),C)). [para(167(a,1),3(a,1))].
% 5.26/5.58 244 m(c(c(c(A,A),B),C),D) = D. [para(156(a,2),167(a,1,1,1))].
% 5.26/5.58 247 c(c(A,A),B) = c(C,C). [hyper(150,a,167,a),flip(a)].
% 5.26/5.58 248 c(A,A) = c(B,B). [hyper(150,a,136,a)].
% 5.26/5.58 249 m(A,m(B,C)) != C | c(D,D) = m(A,B). [para(2(a,1),150(a,1))].
% 5.26/5.58 256 c(A,A) = c_0. [new_symbol(248)].
% 5.26/5.58 263 m(A,m(B,C)) != C | m(A,B) = c_0. [back_rewrite(249),rewrite([256(4)]),flip(b)].
% 5.26/5.58 264 c(c_0,A) = c_0. [back_rewrite(247),rewrite([256(1),256(3)])].
% 5.26/5.58 267 m(c_0,A) = A. [back_rewrite(244),rewrite([256(1),264(2),264(2)])].
% 5.26/5.58 272 m(A,c(A,c_0)) = m(A,c_0). [back_rewrite(235),rewrite([256(1),264(2),256(4),264(5)])].
% 5.26/5.58 275 m(A,c_0) = A. [back_rewrite(168),rewrite([256(1),264(2),264(2)])].
% 5.26/5.58 276 m(A,B) != A | c_0 = B. [back_rewrite(160),rewrite([256(3),264(4)])].
% 5.26/5.58 284 m(A,c(A,c_0)) = A. [back_rewrite(272),rewrite([275(5)])].
% 5.26/5.58 349 m(z,m(x,m(y,m(c(x,z),m(c(y,z),m(c(z,y),A)))))) != m(x,m(z,m(y,A))) # answer(distributivity). [para(9(a,1),132(a,2,2))].
% 5.26/5.58 509 c(A,c_0) = c_0. [hyper(276,a,284,a),flip(a)].
% 5.26/5.58 1654 m(A,c(m(B,A),B)) = m(A,c(A,B)). [hyper(30,a,171,a),flip(a)].
% 5.26/5.58 1655 m(A,c(A,m(A,B))) = m(A,c(A,B)). [hyper(30,a,96,a),flip(a)].
% 5.26/5.58 1689 c(m(A,B),A) = c(B,A). [hyper(8,a,1654,a)].
% 5.26/5.58 1701 m(A,c(A,B)) != A | c(A,B) = c_0. [para(1654(a,1),276(a,1)),rewrite([1689(6)]),flip(b)].
% 5.26/5.58 1723 c(m(A,m(B,C)),m(A,B)) = c(C,m(A,B)). [para(2(a,1),1689(a,1,1))].
% 5.26/5.58 2075 c(A,m(A,B)) = c(A,B). [hyper(8,a,1655,a)].
% 5.26/5.58 2117 c(m(A,B),m(A,m(B,C))) = c(m(A,B),C). [para(2(a,1),2075(a,1,2))].
% 5.26/5.58 3087 c(c(A,B),m(B,A)) = c(m(A,B),m(B,A)). [para(3(a,1),1723(a,1,1)),flip(a)].
% 5.26/5.58 3150 m(A,m(B,c(m(A,B),m(B,A)))) = m(c(A,B),m(B,A)). [back_rewrite(110),rewrite([3087(3)])].
% 5.26/5.58 3153 c(m(A,B),c(B,A)) = c(m(A,B),m(B,A)). [para(3(a,1),2117(a,1,2)),flip(a)].
% 5.26/5.58 3531 m(c(A,B),m(c(B,A),m(A,B))) = m(A,B). [para(3153(a,1),3(a,1,2,2)),rewrite([2(6),3150(6),2(8),3(8)])].
% 5.26/5.58 3570 m(c(A,B),m(B,A)) != m(A,B) | c(m(A,B),m(B,A)) = c_0. [para(3153(a,1),1701(a,1,2)),rewrite([2(5),3150(5),3153(8)])].
% 5.26/5.58 3601 m(c(A,B),c(B,A)) = c_0. [hyper(263,a,3531,a)].
% 5.26/5.58 3712 m(c(A,B),m(c(B,A),C)) = C. [para(3601(a,1),2(a,1,1)),rewrite([267(2)]),flip(a)].
% 5.26/5.58 3764 m(z,m(x,m(y,m(c(x,z),A)))) != m(x,m(z,m(y,A))) # answer(distributivity). [back_rewrite(349),rewrite([3712(14)])].
% 5.26/5.58 3768 m(A,m(c(B,A),m(A,B))) = m(A,m(B,A)). [hyper(31,a,9,a)].
% 5.26/5.58 4714 m(c(A,B),m(B,m(A,m(C,c(m(B,A),m(A,B)))))) = m(A,m(B,m(C,c(C,c(m(B,A),m(A,B)))))). [para(3153(a,1),35(a,1,2,2,2,2)),rewrite([2(9),9(9),3153(12),2(14)]),flip(a)].
% 5.26/5.58 5498 m(c(A,B),m(B,A)) = m(A,B). [hyper(8,a,3768,a)].
% 5.26/5.58 5611 c(m(A,B),m(B,A)) = c_0. [back_rewrite(3570),rewrite([5498(3)]),xx(a)].
% 5.26/5.58 5650 m(c(A,B),m(B,m(A,C))) = m(A,m(B,C)). [back_rewrite(4714),rewrite([5611(4),275(3),5611(7),509(6),275(6)])].
% 5.26/5.58 8776 m(A,m(B,m(C,m(c(B,A),m(B,m(C,A)))))) = m(B,m(C,m(A,m(B,m(A,C))))). [para(13(a,2),45(a,2)),rewrite([45(8),5650(11)])].
% 5.26/5.58 9013 m(z,m(x,m(y,m(c(x,z),m(A,m(y,z)))))) != m(x,m(y,m(z,m(A,m(z,y))))) # answer(distributivity). [para(4(a,1),3764(a,2,2))].
% 5.26/5.58 9014 $F # answer(distributivity). [resolve(9013,a,8776,a)].
% 5.26/5.58
% 5.26/5.58 % SZS output end Refutation
% 5.26/5.58 ============================== end of proof ==========================
% 5.26/5.58
% 5.26/5.58 ============================== STATISTICS ============================
% 5.26/5.58
% 5.26/5.58 Given=243. Generated=22100. Kept=9011. proofs=1.
% 5.26/5.58 Usable=199. Sos=6785. Demods=1775. Limbo=15, Disabled=2017. Hints=0.
% 5.26/5.58 Megabytes=16.79.
% 5.26/5.58 User_CPU=4.62, System_CPU=0.02, Wall_clock=4.
% 5.26/5.58
% 5.26/5.58 ============================== end of statistics =====================
% 5.26/5.58
% 5.26/5.58 ============================== end of search =========================
% 5.26/5.58
% 5.26/5.58 THEOREM PROVED
% 5.26/5.58 % SZS status Unsatisfiable
% 5.26/5.58
% 5.26/5.58 Exiting with 1 proof.
% 5.26/5.58
% 5.26/5.58 Process 7997 exit (max_proofs) Tue Jun 14 04:06:42 2022
% 5.26/5.58 Prover9 interrupted
%------------------------------------------------------------------------------