TSTP Solution File: SYO680-1 by SOS---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SOS---2.0
% Problem : SYO680-1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : sos-script %s
% Computer : n019.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 : Thu Jul 21 19:50:19 EDT 2022
% Result : Unsatisfiable 77.51s 77.79s
% Output : Refutation 77.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYO680-1 : TPTP v8.1.0. Released v7.3.0.
% 0.10/0.13 % Command : sos-script %s
% 0.13/0.34 % Computer : n019.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 : Sat Jul 9 09:25:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.37 ----- Otter 3.2, August 2001 -----
% 0.13/0.37 The process was started by sandbox on n019.cluster.edu,
% 0.13/0.37 Sat Jul 9 09:25:23 2022
% 0.13/0.37 The command was "./sos". The process ID is 3225.
% 0.13/0.37
% 0.13/0.37 set(prolog_style_variables).
% 0.13/0.37 set(auto).
% 0.13/0.37 dependent: set(auto1).
% 0.13/0.37 dependent: set(process_input).
% 0.13/0.37 dependent: clear(print_kept).
% 0.13/0.37 dependent: clear(print_new_demod).
% 0.13/0.37 dependent: clear(print_back_demod).
% 0.13/0.37 dependent: clear(print_back_sub).
% 0.13/0.37 dependent: set(control_memory).
% 0.13/0.37 dependent: assign(max_mem, 12000).
% 0.13/0.37 dependent: assign(pick_given_ratio, 4).
% 0.13/0.37 dependent: assign(stats_level, 1).
% 0.13/0.37 dependent: assign(pick_semantic_ratio, 3).
% 0.13/0.37 dependent: assign(sos_limit, 5000).
% 0.13/0.37 dependent: assign(max_weight, 60).
% 0.13/0.37 clear(print_given).
% 0.13/0.37
% 0.13/0.37 list(usable).
% 0.13/0.37
% 0.13/0.37 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=8.
% 0.13/0.37
% 0.13/0.37 This is a non-Horn set without equality. The strategy
% 0.13/0.37 will be ordered hyper_res, ur_res, unit deletion, and
% 0.13/0.37 factoring, with satellites in sos and nuclei in usable.
% 0.13/0.37
% 0.13/0.37 dependent: set(hyper_res).
% 0.13/0.37 dependent: set(factor).
% 0.13/0.37 dependent: set(unit_deletion).
% 0.13/0.37
% 0.13/0.37 ------------> process usable:
% 0.13/0.37
% 0.13/0.37 ------------> process sos:
% 0.13/0.37
% 0.13/0.37 ======= end of input processing =======
% 0.13/0.41
% 0.13/0.41 Model 1 (0.00 seconds, 0 Inserts)
% 0.13/0.41
% 0.13/0.41 Stopped by limit on number of solutions
% 0.13/0.41
% 0.13/0.41
% 0.13/0.41 -------------- Softie stats --------------
% 0.13/0.41
% 0.13/0.41 UPDATE_STOP: 300
% 0.13/0.41 SFINDER_TIME_LIMIT: 2
% 0.13/0.41 SHORT_CLAUSE_CUTOFF: 4
% 0.13/0.41 number of clauses in intial UL: 77
% 0.13/0.41 number of clauses initially in problem: 78
% 0.13/0.41 percentage of clauses intially in UL: 98
% 0.13/0.41 percentage of distinct symbols occuring in initial UL: 100
% 0.13/0.41 percent of all initial clauses that are short: 100
% 0.13/0.41 absolute distinct symbol count: 8
% 0.13/0.41 distinct predicate count: 3
% 0.13/0.41 distinct function count: 3
% 0.13/0.41 distinct constant count: 2
% 0.13/0.41
% 0.13/0.41 ---------- no more Softie stats ----------
% 0.13/0.41
% 0.13/0.41
% 0.13/0.41
% 0.13/0.41 =========== start of search ===========
% 77.51/77.79
% 77.51/77.79 -- HEY sandbox, WE HAVE A PROOF!! --
% 77.51/77.79
% 77.51/77.79 -----> EMPTY CLAUSE at 76.95 sec ----> 425 [hyper,424,38,423,424,423,408,408] {-} $F.
% 77.51/77.79
% 77.51/77.79 Length of proof is 107. Level of proof is 33.
% 77.51/77.79
% 77.51/77.79 ---------------- PROOF ----------------
% 77.51/77.79 % SZS status Unsatisfiable
% 77.51/77.79 % SZS output start Refutation
% 77.51/77.79
% 77.51/77.79 1 [] {+} -'E'('0',f(A))| -'E'('0',f(suc(A)))|iLEQ(suc(A),suc(A)).
% 77.51/77.79 2 [] {+} -'E'(s('0'),f(A))| -'E'(s('0'),f(suc(A)))|iLEQ(suc(A),suc(A)).
% 77.51/77.79 3 [] {+} -'LE'(f(suc(A)),s('0'))|'E'('0',f(suc(A)))|'LE'(f(A),'0').
% 77.51/77.79 4 [] {+} -'E'(s(s('0')),f(A))| -'E'(s(s('0')),f(suc(A)))|iLEQ(suc(A),suc(A)).
% 77.51/77.79 5 [] {+} -'E'(s(s('0')),f(suc(A)))| -'E'(s(s('0')),f(A))| -iLEQ(suc(A),suc(B))| -'E'(s(s('0')),f(suc(C)))| -'E'(s(s('0')),f(suc(B)))| -iLEQ(suc(C),suc(A))| -'E'(s(s('0')),f(B))| -'E'(s(s('0')),f(C)).
% 77.51/77.79 6 [] {+} -iLEQ(suc(A),suc(B))| -'E'(s(s(s('0'))),f(B))| -'E'(s(s(s('0'))),f(A))| -iLEQ(suc(C),suc(A))| -'E'(s(s(s('0'))),f(C))| -'E'(s(s(s('0'))),f(suc(A)))| -'E'(s(s(s('0'))),f(suc(B)))| -'E'(s(s(s('0'))),f(suc(C))).
% 77.51/77.79 7 [] {+} -'LE'(f(A),s(s('0')))|'E'(s('0'),f(A))|'LE'(f(A),s('0')).
% 77.51/77.79 8 [] {+} -'LE'(f(z),'0').
% 77.51/77.79 9 [] {+} -'LE'(f(suc(A)),s(s(s('0'))))|'E'(s(s('0')),f(suc(A)))|'LE'(f(A),s(s('0'))).
% 77.51/77.79 10 [] {+} -'E'('0',f(suc(A)))| -iLEQ(suc(A),suc(B))| -iLEQ(suc(C),suc(A))| -'E'('0',f(suc(B)))| -'E'('0',f(A))| -'E'('0',f(suc(C)))| -'E'('0',f(B))| -'E'('0',f(C)).
% 77.51/77.79 11 [] {+} -'LE'(f(A),s(s(s(s('0')))))|'E'(s(s(s('0'))),f(A))|'LE'(f(A),s(s(s('0')))).
% 77.51/77.79 12 [] {+} -'LE'(f(A),s(s(s('0'))))|'E'(s(s('0')),f(A))|'LE'(f(A),s(s('0'))).
% 77.51/77.79 13 [] {+} -iLEQ(suc(A),suc(B))| -'E'(s('0'),f(suc(C)))| -iLEQ(suc(C),suc(A))| -'E'(s('0'),f(suc(B)))| -'E'(s('0'),f(C))| -'E'(s('0'),f(B))| -'E'(s('0'),f(suc(A)))| -'E'(s('0'),f(A)).
% 77.51/77.79 14 [] {+} -'LE'(f(suc(A)),s(s(s(s('0')))))|'E'(s(s(s('0'))),f(suc(A)))|'LE'(f(A),s(s(s('0')))).
% 77.51/77.79 15 [] {+} -'E'(s(s(s('0'))),f(A))| -'E'(s(s(s('0'))),f(suc(A)))|iLEQ(suc(A),suc(A)).
% 77.51/77.79 16 [] {+} -'LE'(f(A),s('0'))|'E'('0',f(A))|'LE'(f(A),'0').
% 77.51/77.79 17 [] {+} -'LE'(f(suc(A)),s(s('0')))|'E'(s('0'),f(suc(A)))|'LE'(f(A),s('0')).
% 77.51/77.79 23 [factor,5.4.5,factor_simp] {+} -'E'(s(s('0')),f(suc(A)))| -'E'(s(s('0')),f(A))| -iLEQ(suc(A),suc(B))| -'E'(s(s('0')),f(suc(B)))| -iLEQ(suc(B),suc(A))| -'E'(s(s('0')),f(B)).
% 77.51/77.79 27 [factor,6.2.5,factor_simp] {+} -iLEQ(suc(A),suc(B))| -'E'(s(s(s('0'))),f(B))| -'E'(s(s(s('0'))),f(A))| -iLEQ(suc(B),suc(A))| -'E'(s(s(s('0'))),f(suc(A)))| -'E'(s(s(s('0'))),f(suc(B))).
% 77.51/77.79 38 [factor,10.4.6,factor_simp] {+} -'E'('0',f(suc(A)))| -iLEQ(suc(A),suc(B))| -iLEQ(suc(B),suc(A))| -'E'('0',f(suc(B)))| -'E'('0',f(A))| -'E'('0',f(B)).
% 77.51/77.79 43 [factor,13.2.4,factor_simp] {+} -iLEQ(suc(A),suc(B))| -'E'(s('0'),f(suc(B)))| -iLEQ(suc(B),suc(A))| -'E'(s('0'),f(B))| -'E'(s('0'),f(suc(A)))| -'E'(s('0'),f(A)).
% 77.51/77.79 78 [] {-} 'LE'(f(A),s(s(s(s('0'))))).
% 77.51/77.79 79 [hyper,78,14] {-} 'E'(s(s(s('0'))),f(suc(A)))|'LE'(f(A),s(s(s('0')))).
% 77.51/77.79 80 [hyper,78,11] {-} 'E'(s(s(s('0'))),f(A))|'LE'(f(A),s(s(s('0')))).
% 77.51/77.79 81 [hyper,80,12] {-} 'E'(s(s(s('0'))),f(A))|'E'(s(s('0')),f(A))|'LE'(f(A),s(s('0'))).
% 77.51/77.79 82 [hyper,80,9] {-} 'E'(s(s(s('0'))),f(suc(A)))|'E'(s(s('0')),f(suc(A)))|'LE'(f(A),s(s('0'))).
% 77.51/77.79 83 [hyper,79,12] {-} 'E'(s(s(s('0'))),f(suc(A)))|'E'(s(s('0')),f(A))|'LE'(f(A),s(s('0'))).
% 77.51/77.79 84 [hyper,79,9] {-} 'E'(s(s(s('0'))),f(suc(suc(A))))|'E'(s(s('0')),f(suc(A)))|'LE'(f(A),s(s('0'))).
% 77.51/77.79 85 [hyper,81,17] {-} 'E'(s(s(s('0'))),f(suc(A)))|'E'(s(s('0')),f(suc(A)))|'E'(s('0'),f(suc(A)))|'LE'(f(A),s('0')).
% 77.51/77.79 86 [hyper,81,7] {-} 'E'(s(s(s('0'))),f(A))|'E'(s(s('0')),f(A))|'E'(s('0'),f(A))|'LE'(f(A),s('0')).
% 77.51/77.79 87 [hyper,83,17] {-} 'E'(s(s(s('0'))),f(suc(suc(A))))|'E'(s(s('0')),f(suc(A)))|'E'(s('0'),f(suc(A)))|'LE'(f(A),s('0')).
% 77.51/77.79 88 [hyper,83,7] {-} 'E'(s(s(s('0'))),f(suc(A)))|'E'(s(s('0')),f(A))|'E'(s('0'),f(A))|'LE'(f(A),s('0')).
% 77.51/77.79 89 [hyper,82,17] {-} 'E'(s(s(s('0'))),f(suc(suc(A))))|'E'(s(s('0')),f(suc(suc(A))))|'E'(s('0'),f(suc(A)))|'LE'(f(A),s('0')).
% 77.51/77.79 90 [hyper,82,7] {-} 'E'(s(s(s('0'))),f(suc(A)))|'E'(s(s('0')),f(suc(A)))|'E'(s('0'),f(A))|'LE'(f(A),s('0')).
% 77.51/77.79 91 [hyper,84,17] {-} 'E'(s(s(s('0'))),f(suc(suc(suc(A)))))|'E'(s(s('0')),f(suc(suc(A))))|'E'(s('0'),f(suc(A)))|'LE'(f(A),s('0')).
% 77.51/77.79 92 [hyper,84,7] {-} 'E'(s(s(s('0'))),f(suc(suc(A))))|'E'(s(s('0')),f(suc(A)))|'E'(s('0'),f(A))|'LE'(f(A),s('0')).
% 77.51/77.79 93 [hyper,86,16] {-} 'E'(s(s(s('0'))),f(A))|'E'(s(s('0')),f(A))|'E'(s('0'),f(A))|'E'('0',f(A))|'LE'(f(A),'0').
% 77.51/77.79 94 [hyper,86,3] {-} 'E'(s(s(s('0'))),f(suc(A)))|'E'(s(s('0')),f(suc(A)))|'E'(s('0'),f(suc(A)))|'E'('0',f(suc(A)))|'LE'(f(A),'0').
% 77.51/77.79 95 [hyper,88,16] {-} 'E'(s(s(s('0'))),f(suc(A)))|'E'(s(s('0')),f(A))|'E'(s('0'),f(A))|'E'('0',f(A))|'LE'(f(A),'0').
% 77.51/77.79 96 [hyper,88,3] {-} 'E'(s(s(s('0'))),f(suc(suc(A))))|'E'(s(s('0')),f(suc(A)))|'E'(s('0'),f(suc(A)))|'E'('0',f(suc(A)))|'LE'(f(A),'0').
% 77.51/77.79 97 [hyper,90,16] {-} 'E'(s(s(s('0'))),f(suc(A)))|'E'(s(s('0')),f(suc(A)))|'E'(s('0'),f(A))|'E'('0',f(A))|'LE'(f(A),'0').
% 77.51/77.79 98 [hyper,90,3] {-} 'E'(s(s(s('0'))),f(suc(suc(A))))|'E'(s(s('0')),f(suc(suc(A))))|'E'(s('0'),f(suc(A)))|'E'('0',f(suc(A)))|'LE'(f(A),'0').
% 77.51/77.79 99 [hyper,85,16] {-} 'E'(s(s(s('0'))),f(suc(A)))|'E'(s(s('0')),f(suc(A)))|'E'(s('0'),f(suc(A)))|'E'('0',f(A))|'LE'(f(A),'0').
% 77.51/77.79 100 [hyper,85,3] {-} 'E'(s(s(s('0'))),f(suc(suc(A))))|'E'(s(s('0')),f(suc(suc(A))))|'E'(s('0'),f(suc(suc(A))))|'E'('0',f(suc(A)))|'LE'(f(A),'0').
% 77.51/77.79 101 [hyper,92,16] {-} 'E'(s(s(s('0'))),f(suc(suc(A))))|'E'(s(s('0')),f(suc(A)))|'E'(s('0'),f(A))|'E'('0',f(A))|'LE'(f(A),'0').
% 77.51/77.79 102 [hyper,92,3] {-} 'E'(s(s(s('0'))),f(suc(suc(suc(A)))))|'E'(s(s('0')),f(suc(suc(A))))|'E'(s('0'),f(suc(A)))|'E'('0',f(suc(A)))|'LE'(f(A),'0').
% 77.51/77.79 103 [hyper,93,8] {+} 'E'(s(s(s('0'))),f(z))|'E'(s(s('0')),f(z))|'E'(s('0'),f(z))|'E'('0',f(z)).
% 77.51/77.79 104 [hyper,87,16] {-} 'E'(s(s(s('0'))),f(suc(suc(A))))|'E'(s(s('0')),f(suc(A)))|'E'(s('0'),f(suc(A)))|'E'('0',f(A))|'LE'(f(A),'0').
% 77.51/77.79 105 [hyper,87,3] {-} 'E'(s(s(s('0'))),f(suc(suc(suc(A)))))|'E'(s(s('0')),f(suc(suc(A))))|'E'(s('0'),f(suc(suc(A))))|'E'('0',f(suc(A)))|'LE'(f(A),'0').
% 77.51/77.79 106 [hyper,95,8] {+} 'E'(s(s(s('0'))),f(suc(z)))|'E'(s(s('0')),f(z))|'E'(s('0'),f(z))|'E'('0',f(z)).
% 77.51/77.79 107 [hyper,89,16] {-} 'E'(s(s(s('0'))),f(suc(suc(A))))|'E'(s(s('0')),f(suc(suc(A))))|'E'(s('0'),f(suc(A)))|'E'('0',f(A))|'LE'(f(A),'0').
% 77.51/77.79 108 [hyper,89,3] {-} 'E'(s(s(s('0'))),f(suc(suc(suc(A)))))|'E'(s(s('0')),f(suc(suc(suc(A)))))|'E'(s('0'),f(suc(suc(A))))|'E'('0',f(suc(A)))|'LE'(f(A),'0').
% 77.51/77.79 109 [hyper,97,8] {+} 'E'(s(s(s('0'))),f(suc(z)))|'E'(s(s('0')),f(suc(z)))|'E'(s('0'),f(z))|'E'('0',f(z)).
% 77.51/77.79 110 [hyper,91,16] {-} 'E'(s(s(s('0'))),f(suc(suc(suc(A)))))|'E'(s(s('0')),f(suc(suc(A))))|'E'(s('0'),f(suc(A)))|'E'('0',f(A))|'LE'(f(A),'0').
% 77.51/77.79 111 [hyper,91,3] {-} 'E'(s(s(s('0'))),f(suc(suc(suc(suc(A))))))|'E'(s(s('0')),f(suc(suc(suc(A)))))|'E'(s('0'),f(suc(suc(A))))|'E'('0',f(suc(A)))|'LE'(f(A),'0').
% 77.51/77.79 112 [hyper,99,8] {+} 'E'(s(s(s('0'))),f(suc(z)))|'E'(s(s('0')),f(suc(z)))|'E'(s('0'),f(suc(z)))|'E'('0',f(z)).
% 77.51/77.79 113 [hyper,94,8] {-} 'E'(s(s(s('0'))),f(suc(z)))|'E'(s(s('0')),f(suc(z)))|'E'(s('0'),f(suc(z)))|'E'('0',f(suc(z))).
% 77.51/77.79 118 [hyper,101,8] {+} 'E'(s(s(s('0'))),f(suc(suc(z))))|'E'(s(s('0')),f(suc(z)))|'E'(s('0'),f(z))|'E'('0',f(z)).
% 77.51/77.79 119 [hyper,104,8] {+} 'E'(s(s(s('0'))),f(suc(suc(z))))|'E'(s(s('0')),f(suc(z)))|'E'(s('0'),f(suc(z)))|'E'('0',f(z)).
% 77.51/77.79 120 [hyper,106,15,103,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s('0')),f(z))|'E'(s('0'),f(z))|'E'('0',f(z))|iLEQ(suc(z),suc(z)).
% 77.51/77.79 124 [hyper,96,8] {-} 'E'(s(s(s('0'))),f(suc(suc(z))))|'E'(s(s('0')),f(suc(z)))|'E'(s('0'),f(suc(z)))|'E'('0',f(suc(z))).
% 77.51/77.79 125 [hyper,124,15,113,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s('0')),f(suc(z)))|'E'(s('0'),f(suc(z)))|'E'('0',f(suc(z)))|iLEQ(suc(suc(z)),suc(suc(z))).
% 77.51/77.79 129 [hyper,107,8] {+} 'E'(s(s(s('0'))),f(suc(suc(z))))|'E'(s(s('0')),f(suc(suc(z))))|'E'(s('0'),f(suc(z)))|'E'('0',f(z)).
% 77.51/77.79 131 [hyper,120,27,120,103,103,106,106,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s('0')),f(z))|'E'(s('0'),f(z))|'E'('0',f(z)).
% 77.51/77.79 132 [hyper,98,8] {-} 'E'(s(s(s('0'))),f(suc(suc(z))))|'E'(s(s('0')),f(suc(suc(z))))|'E'(s('0'),f(suc(z)))|'E'('0',f(suc(z))).
% 77.51/77.79 133 [hyper,100,8] {-} 'E'(s(s(s('0'))),f(suc(suc(z))))|'E'(s(s('0')),f(suc(suc(z))))|'E'(s('0'),f(suc(suc(z))))|'E'('0',f(suc(z))).
% 77.51/77.79 134 [hyper,132,4,124,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s(s('0'))),f(suc(suc(z))))|'E'(s('0'),f(suc(z)))|'E'('0',f(suc(z)))|iLEQ(suc(suc(z)),suc(suc(z))).
% 77.51/77.79 140 [hyper,133,2,132,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s(s('0'))),f(suc(suc(z))))|'E'(s(s('0')),f(suc(suc(z))))|'E'('0',f(suc(z)))|iLEQ(suc(suc(z)),suc(suc(z))).
% 77.51/77.79 142 [hyper,110,8] {+} 'E'(s(s(s('0'))),f(suc(suc(suc(z)))))|'E'(s(s('0')),f(suc(suc(z))))|'E'(s('0'),f(suc(z)))|'E'('0',f(z)).
% 77.51/77.79 143 [hyper,102,8] {-} 'E'(s(s(s('0'))),f(suc(suc(suc(z)))))|'E'(s(s('0')),f(suc(suc(z))))|'E'(s('0'),f(suc(z)))|'E'('0',f(suc(z))).
% 77.51/77.79 145 [hyper,109,4,131,factor_simp,factor_simp] {+} 'E'(s(s(s('0'))),f(suc(z)))|'E'(s('0'),f(z))|'E'('0',f(z))|iLEQ(suc(z),suc(z)).
% 77.51/77.79 155 [hyper,143,15,132,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s('0')),f(suc(suc(z))))|'E'(s('0'),f(suc(z)))|'E'('0',f(suc(z)))|iLEQ(suc(suc(suc(z))),suc(suc(suc(z)))).
% 77.51/77.79 159 [hyper,105,8] {-} 'E'(s(s(s('0'))),f(suc(suc(suc(z)))))|'E'(s(s('0')),f(suc(suc(z))))|'E'(s('0'),f(suc(suc(z))))|'E'('0',f(suc(z))).
% 77.51/77.79 160 [hyper,159,15,133,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s('0')),f(suc(suc(z))))|'E'(s('0'),f(suc(suc(z))))|'E'('0',f(suc(z)))|iLEQ(suc(suc(suc(z))),suc(suc(suc(z)))).
% 77.51/77.79 165 [hyper,108,8] {-} 'E'(s(s(s('0'))),f(suc(suc(suc(z)))))|'E'(s(s('0')),f(suc(suc(suc(z)))))|'E'(s('0'),f(suc(suc(z))))|'E'('0',f(suc(z))).
% 77.51/77.79 167 [hyper,165,4,159,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s(s('0'))),f(suc(suc(suc(z)))))|'E'(s('0'),f(suc(suc(z))))|'E'('0',f(suc(z)))|iLEQ(suc(suc(suc(z))),suc(suc(suc(z)))).
% 77.51/77.79 172 [hyper,111,8] {-} 'E'(s(s(s('0'))),f(suc(suc(suc(suc(z))))))|'E'(s(s('0')),f(suc(suc(suc(z)))))|'E'(s('0'),f(suc(suc(z))))|'E'('0',f(suc(z))).
% 77.51/77.79 173 [hyper,172,15,165,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s('0')),f(suc(suc(suc(z)))))|'E'(s('0'),f(suc(suc(z))))|'E'('0',f(suc(z)))|iLEQ(suc(suc(suc(suc(z)))),suc(suc(suc(suc(z))))).
% 77.51/77.79 181 [hyper,145,23,109,131,145,109,131,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s(s('0'))),f(suc(z)))|'E'(s('0'),f(z))|'E'('0',f(z)).
% 77.51/77.79 195 [hyper,181,2,112,factor_simp,factor_simp] {+} 'E'(s(s(s('0'))),f(suc(z)))|'E'('0',f(z))|iLEQ(suc(z),suc(z))|'E'(s(s('0')),f(suc(z))).
% 77.51/77.79 206 [hyper,195,43,195,112,181,112,181,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s(s('0'))),f(suc(z)))|'E'('0',f(z))|'E'(s(s('0')),f(suc(z))).
% 77.51/77.79 214 [hyper,118,15,206,factor_simp,factor_simp] {+} 'E'(s(s('0')),f(suc(z)))|'E'(s('0'),f(z))|'E'('0',f(z))|iLEQ(suc(suc(z)),suc(suc(z))).
% 77.51/77.79 229 [hyper,119,15,206,factor_simp,factor_simp] {+} 'E'(s(s('0')),f(suc(z)))|'E'(s('0'),f(suc(z)))|'E'('0',f(z))|iLEQ(suc(suc(z)),suc(suc(z))).
% 77.51/77.79 246 [hyper,214,27,214,206,206,118,118,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s('0')),f(suc(z)))|'E'(s('0'),f(z))|'E'('0',f(z)).
% 77.51/77.79 247 [hyper,246,4,131,factor_simp,factor_simp] {+} 'E'(s('0'),f(z))|'E'('0',f(z))|iLEQ(suc(z),suc(z)).
% 77.51/77.79 255 [hyper,247,23,246,131,247,246,131,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {+} 'E'(s('0'),f(z))|'E'('0',f(z)).
% 77.51/77.79 269 [hyper,125,27,125,113,113,124,124,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {-} 'E'(s(s('0')),f(suc(z)))|'E'(s('0'),f(suc(z)))|'E'('0',f(suc(z))).
% 77.51/77.79 281 [hyper,129,4,119,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s(s('0'))),f(suc(suc(z))))|'E'(s('0'),f(suc(z)))|'E'('0',f(z))|iLEQ(suc(suc(z)),suc(suc(z))).
% 77.51/77.79 290 [hyper,229,27,229,206,206,119,119,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s('0')),f(suc(z)))|'E'(s('0'),f(suc(z)))|'E'('0',f(z)).
% 77.51/77.79 291 [hyper,290,2,255,factor_simp] {+} 'E'(s(s('0')),f(suc(z)))|'E'('0',f(z))|iLEQ(suc(z),suc(z)).
% 77.51/77.79 292 [hyper,290,1,269,factor_simp,factor_simp] {+} 'E'(s(s('0')),f(suc(z)))|'E'(s('0'),f(suc(z)))|iLEQ(suc(z),suc(z)).
% 77.51/77.79 293 [hyper,291,43,291,290,255,290,255,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s('0')),f(suc(z)))|'E'('0',f(z)).
% 77.51/77.79 301 [hyper,134,23,132,269,134,132,269,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {-} 'E'(s(s(s('0'))),f(suc(suc(z))))|'E'(s('0'),f(suc(z)))|'E'('0',f(suc(z))).
% 77.51/77.79 312 [hyper,292,38,269,292,269,293,293,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {-} 'E'(s(s('0')),f(suc(z)))|'E'(s('0'),f(suc(z))).
% 77.51/77.79 320 [hyper,140,43,140,133,301,133,301,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {-} 'E'(s(s(s('0'))),f(suc(suc(z))))|'E'(s(s('0')),f(suc(suc(z))))|'E'('0',f(suc(z))).
% 77.51/77.79 328 [hyper,142,15,129,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s('0')),f(suc(suc(z))))|'E'(s('0'),f(suc(z)))|'E'('0',f(z))|iLEQ(suc(suc(suc(z))),suc(suc(suc(z)))).
% 77.51/77.79 336 [hyper,281,23,129,312,281,129,312,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s(s('0'))),f(suc(suc(z))))|'E'(s('0'),f(suc(z)))|'E'('0',f(z)).
% 77.51/77.79 337 [hyper,336,2,255,factor_simp] {+} 'E'(s(s(s('0'))),f(suc(suc(z))))|'E'('0',f(z))|iLEQ(suc(z),suc(z)).
% 77.51/77.79 338 [hyper,336,1,301,factor_simp,factor_simp] {+} 'E'(s(s(s('0'))),f(suc(suc(z))))|'E'(s('0'),f(suc(z)))|iLEQ(suc(z),suc(z)).
% 77.51/77.79 339 [hyper,337,43,337,336,255,336,255,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s(s('0'))),f(suc(suc(z))))|'E'('0',f(z)).
% 77.51/77.79 345 [hyper,155,27,155,320,320,143,143,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {-} 'E'(s(s('0')),f(suc(suc(z))))|'E'(s('0'),f(suc(z)))|'E'('0',f(suc(z))).
% 77.51/77.79 346 [hyper,345,4,312,factor_simp] {+} 'E'(s('0'),f(suc(z)))|'E'('0',f(suc(z)))|iLEQ(suc(suc(z)),suc(suc(z))).
% 77.51/77.79 354 [hyper,346,23,345,312,346,345,312,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {-} 'E'(s('0'),f(suc(z)))|'E'('0',f(suc(z))).
% 77.51/77.79 362 [hyper,160,27,160,320,320,159,159,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {-} 'E'(s(s('0')),f(suc(suc(z))))|'E'(s('0'),f(suc(suc(z))))|'E'('0',f(suc(z))).
% 77.51/77.79 365 [hyper,362,2,354,factor_simp] {+} 'E'(s(s('0')),f(suc(suc(z))))|'E'('0',f(suc(z)))|iLEQ(suc(suc(z)),suc(suc(z))).
% 77.51/77.79 372 [hyper,167,23,165,362,167,165,362,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {-} 'E'(s(s(s('0'))),f(suc(suc(suc(z)))))|'E'(s('0'),f(suc(suc(z))))|'E'('0',f(suc(z))).
% 77.51/77.79 379 [hyper,338,38,354,338,354,339,339,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {-} 'E'(s(s(s('0'))),f(suc(suc(z))))|'E'(s('0'),f(suc(z))).
% 77.51/77.79 380 [hyper,173,27,173,372,372,172,172,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {-} 'E'(s(s('0')),f(suc(suc(suc(z)))))|'E'(s('0'),f(suc(suc(z))))|'E'('0',f(suc(z))).
% 77.51/77.79 384 [hyper,365,43,365,362,354,362,354,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {-} 'E'(s(s('0')),f(suc(suc(z))))|'E'('0',f(suc(z))).
% 77.51/77.79 386 [hyper,384,1,255] {+} 'E'(s(s('0')),f(suc(suc(z))))|iLEQ(suc(z),suc(z))|'E'(s('0'),f(z)).
% 77.51/77.79 387 [hyper,380,4,384,factor_simp] {+} 'E'(s('0'),f(suc(suc(z))))|'E'('0',f(suc(z)))|iLEQ(suc(suc(suc(z))),suc(suc(suc(z)))).
% 77.51/77.79 396 [hyper,386,38,384,386,384,255,255,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s('0')),f(suc(suc(z))))|'E'(s('0'),f(z)).
% 77.51/77.79 397 [hyper,328,27,328,379,379,142,142,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {+} 'E'(s(s('0')),f(suc(suc(z))))|'E'(s('0'),f(suc(z)))|'E'('0',f(z)).
% 77.51/77.79 398 [hyper,397,4,312,factor_simp] {+} 'E'(s('0'),f(suc(z)))|'E'('0',f(z))|iLEQ(suc(suc(z)),suc(suc(z))).
% 77.51/77.79 401 [hyper,398,23,397,312,398,397,312,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {+} 'E'(s('0'),f(suc(z)))|'E'('0',f(z)).
% 77.51/77.79 402 [hyper,401,2,255,factor_simp] {+} 'E'('0',f(z))|iLEQ(suc(z),suc(z)).
% 77.51/77.79 405 [hyper,401,1,354,factor_simp] {+} 'E'(s('0'),f(suc(z)))|iLEQ(suc(z),suc(z)).
% 77.51/77.79 408 [hyper,402,43,402,401,255,401,255,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {+} 'E'('0',f(z)).
% 77.51/77.79 409 [hyper,408,1,384] {+} iLEQ(suc(z),suc(z))|'E'(s(s('0')),f(suc(suc(z)))).
% 77.51/77.79 415 [hyper,405,38,354,405,354,408,408,factor_simp,factor_simp,factor_simp] {-} 'E'(s('0'),f(suc(z))).
% 77.51/77.79 418 [hyper,409,43,409,415,396,415,396,factor_simp,factor_simp,factor_simp] {-} 'E'(s(s('0')),f(suc(suc(z)))).
% 77.51/77.79 420 [hyper,387,23,380,418,387,380,418,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp,factor_simp] {-} 'E'(s('0'),f(suc(suc(z))))|'E'('0',f(suc(z))).
% 77.51/77.79 421 [hyper,420,2,415] {+} 'E'('0',f(suc(z)))|iLEQ(suc(suc(z)),suc(suc(z))).
% 77.51/77.79 423 [hyper,421,43,421,420,415,420,415,factor_simp,factor_simp,factor_simp] {-} 'E'('0',f(suc(z))).
% 77.51/77.79 424 [hyper,423,1,408] {+} iLEQ(suc(z),suc(z)).
% 77.51/77.79 425 [hyper,424,38,423,424,423,408,408] {-} $F.
% 77.51/77.79
% 77.51/77.79 % SZS output end Refutation
% 77.51/77.79 ------------ end of proof -------------
% 77.51/77.79
% 77.51/77.79
% 77.51/77.79 Search stopped by max_proofs option.
% 77.51/77.79
% 77.51/77.79
% 77.51/77.79 Search stopped by max_proofs option.
% 77.51/77.79
% 77.51/77.79 ============ end of search ============
% 77.51/77.79
% 77.51/77.79 ----------- soft-scott stats ----------
% 77.51/77.79
% 77.51/77.79 true clauses given 64 (53.3%)
% 77.51/77.79 false clauses given 56
% 77.51/77.79
% 77.51/77.79 FALSE TRUE
% 77.51/77.79 tot: 0 0 (-nan% true)
% 77.51/77.79
% 77.51/77.79
% 77.51/77.79 Model 1 (0.01 seconds, 0 Inserts)
% 77.51/77.79
% 77.51/77.79 That finishes the proof of the theorem.
% 77.51/77.79
% 77.51/77.79 Process 3225 finished Sat Jul 9 09:26:40 2022
%------------------------------------------------------------------------------