TSTP Solution File: BOO014-1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : BOO014-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %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 : 300s
% DateTime : Sat Jul 23 05:58:38 EDT 2022
% Result : Unsatisfiable 37.87s 38.07s
% Output : Refutation 37.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : BOO014-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jul 22 08:39:18 EDT 2022
% 0.13/0.33 % CPUTime :
% 37.87/38.07 GeoParameters:
% 37.87/38.07
% 37.87/38.07 tptp_input = 1
% 37.87/38.07 tptp_output = 0
% 37.87/38.07 nonempty = 1
% 37.87/38.07 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.87/38.07 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 37.87/38.07
% 37.87/38.07
% 37.87/38.07 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.87/38.07 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.87/38.07
% 37.87/38.07 RuleSystem INPUT:
% 37.87/38.07
% 37.87/38.07 Initial Rules:
% 37.87/38.07 #0: input, references = 35, size of lhs = 1:
% 37.87/38.07 P_add-{F}(V0,V1,V2) | sum-{T}(V0,V1,V2)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1: input, references = 54, size of lhs = 1:
% 37.87/38.07 P_multiply-{F}(V0,V1,V2) | product-{T}(V0,V1,V2)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #2: input, references = 24, size of lhs = 1:
% 37.87/38.07 sum-{F}(V0,V1,V2) | sum-{T}(V1,V0,V2)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #3: input, references = 79, size of lhs = 1:
% 37.87/38.07 product-{F}(V0,V1,V2) | product-{T}(V1,V0,V2)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #4: input, references = 8, size of lhs = 2:
% 37.87/38.07 P_additive_identity-{F}(V0), #-{F} V1 | sum-{T}(V0,V1,V1)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #5: input, references = 30, size of lhs = 2:
% 37.87/38.07 P_additive_identity-{F}(V0), #-{F} V1 | sum-{T}(V1,V0,V1)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #6: input, references = 45, size of lhs = 3:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), #-{F} V2 | product-{T}(V1,V2,V2)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #7: input, references = 3, size of lhs = 3:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), #-{F} V2 | product-{T}(V2,V1,V2)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #8: input, references = 22, size of lhs = 6:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), product-{F}(V6,V5,V4), product-{F}(V6,V7,V3), product-{F}(V6,V8,V2), sum-{F}(V8,V7,V5) | sum-{T}(V2,V3,V4)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #9: input, references = 12, size of lhs = 6:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), sum-{F}(V2,V3,V4), product-{F}(V6,V7,V3), product-{F}(V6,V8,V2), sum-{F}(V8,V7,V5) | product-{T}(V6,V5,V4)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #10: input, references = 5, size of lhs = 6:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), product-{F}(V5,V6,V4), product-{F}(V7,V6,V3), product-{F}(V8,V6,V2), sum-{F}(V8,V7,V5) | sum-{T}(V2,V3,V4)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #11: input, references = 3, size of lhs = 6:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), sum-{F}(V2,V3,V4), product-{F}(V7,V6,V3), product-{F}(V8,V6,V2), sum-{F}(V8,V7,V5) | product-{T}(V5,V6,V4)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #12: input, references = 17, size of lhs = 6:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), sum-{F}(V6,V5,V4), sum-{F}(V6,V7,V3), sum-{F}(V6,V8,V2), product-{F}(V8,V7,V5) | product-{T}(V2,V3,V4)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #13: input, references = 5, size of lhs = 6:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), product-{F}(V2,V3,V4), sum-{F}(V6,V7,V3), sum-{F}(V6,V8,V2), product-{F}(V8,V7,V5) | sum-{T}(V6,V5,V4)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #14: input, references = 3, size of lhs = 6:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), sum-{F}(V5,V6,V4), sum-{F}(V7,V6,V3), sum-{F}(V8,V6,V2), product-{F}(V8,V7,V5) | product-{T}(V2,V3,V4)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #15: input, references = 6, size of lhs = 6:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), product-{F}(V2,V3,V4), sum-{F}(V7,V6,V3), sum-{F}(V8,V6,V2), product-{F}(V8,V7,V5) | sum-{T}(V5,V6,V4)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #16: input, references = 20, size of lhs = 3:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_inverse-{F}(V2,V3) | sum-{T}(V3,V2,V1)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #17: input, references = 3, size of lhs = 3:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_inverse-{F}(V2,V3) | sum-{T}(V2,V3,V1)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #18: input, references = 32, size of lhs = 3:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_inverse-{F}(V2,V3) | product-{T}(V3,V2,V0)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #19: input, references = 3, size of lhs = 3:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_inverse-{F}(V2,V3) | product-{T}(V2,V3,V0)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #20: input, references = 9, size of lhs = 5:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), sum-{F}(V5,V4,V2), sum-{F}(V5,V4,V3), V2 == V3 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #21: input, references = 12, size of lhs = 5:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), product-{F}(V5,V4,V2), product-{F}(V5,V4,V3), V2 == V3 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #22: input, references = 11, size of lhs = 5:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), P_x_plus_y-{F}(V4) | sum-{T}(V2,V3,V4)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #23: input, references = 18, size of lhs = 8:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), P_x_plus_y-{F}(V4), P_inverse-{F}(V2,V5), P_inverse-{F}(V3,V6), P_x_inverse_times_y_inverse-{F}(V7) | product-{T}(V5,V6,V7)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #24: input, references = 9, size of lhs = 9:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), P_x_plus_y-{F}(V4), P_inverse-{F}(V2,V5), P_inverse-{F}(V3,V6), P_x_inverse_times_y_inverse-{F}(V7), P_inverse-{F}(V4,V7) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #25: input, references = 4, size of lhs = 2:
% 37.87/38.07 #-{F} V0, #-{F} V1 | EXISTS V2: P_add-{T}(V0,V1,V2)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #26: input, references = 5, size of lhs = 2:
% 37.87/38.07 #-{F} V0, #-{F} V1 | EXISTS V2: P_multiply-{T}(V0,V1,V2)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #27: input, references = 4, size of lhs = 0:
% 37.87/38.07 FALSE | EXISTS V0: P_additive_identity-{T}(V0)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #28: input, references = 4, size of lhs = 0:
% 37.87/38.07 FALSE | EXISTS V0: P_multiplicative_identity-{T}(V0)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #29: input, references = 27, size of lhs = 1:
% 37.87/38.07 #-{F} V0 | EXISTS V1: P_inverse-{T}(V0,V1)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #30: input, references = 4, size of lhs = 0:
% 37.87/38.07 FALSE | EXISTS V0: P_x-{T}(V0)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #31: input, references = 6, size of lhs = 0:
% 37.87/38.07 FALSE | EXISTS V0: P_y-{T}(V0)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #32: input, references = 7, size of lhs = 0:
% 37.87/38.07 FALSE | EXISTS V0: P_x_plus_y-{T}(V0)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #33: input, references = 9, size of lhs = 0:
% 37.87/38.07 FALSE | EXISTS V0: P_x_inverse_times_y_inverse-{T}(V0)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 number of initial rules = 34
% 37.87/38.07
% 37.87/38.07 Simplifiers:
% 37.87/38.07 #34: unsound, references = 3, size of lhs = 3:
% 37.87/38.07 P_add-{F}(V0,V1,V2), P_add-{F}(V0,V1,V5), V2 == V5 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #35: unsound, references = 3, size of lhs = 3:
% 37.87/38.07 P_multiply-{F}(V0,V1,V2), P_multiply-{F}(V0,V1,V5), V2 == V5 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #36: unsound, references = 3, size of lhs = 3:
% 37.87/38.07 P_additive_identity-{F}(V0), P_additive_identity-{F}(V1), V0 == V1 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #37: unsound, references = 3, size of lhs = 3:
% 37.87/38.07 P_multiplicative_identity-{F}(V0), P_multiplicative_identity-{F}(V1), V0 == V1 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #38: unsound, references = 3, size of lhs = 3:
% 37.87/38.07 P_inverse-{F}(V0,V1), P_inverse-{F}(V0,V3), V1 == V3 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #39: unsound, references = 3, size of lhs = 3:
% 37.87/38.07 P_x-{F}(V0), P_x-{F}(V1), V0 == V1 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #40: unsound, references = 3, size of lhs = 3:
% 37.87/38.07 P_y-{F}(V0), P_y-{F}(V1), V0 == V1 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #41: unsound, references = 3, size of lhs = 3:
% 37.87/38.07 P_x_plus_y-{F}(V0), P_x_plus_y-{F}(V1), V0 == V1 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #42: unsound, references = 3, size of lhs = 3:
% 37.87/38.07 P_x_inverse_times_y_inverse-{F}(V0), P_x_inverse_times_y_inverse-{F}(V1), V0 == V1 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 number of simplifiers = 9
% 37.87/38.07
% 37.87/38.07 Learnt:
% 37.87/38.07 #57: mergings( V2 == V3, V3 == V5, V5 == V7, V4 == V6, V6 == V8; #50 ), references = 2, size of lhs = 5:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), product-{F}(V0,V2,V3), sum-{F}(V0,V3,V4), V4 == V0 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #63: mergings( V2 == V3, V3 == V5, V5 == V7, V4 == V6, V6 == V8; #51 ), references = 2, size of lhs = 5:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), product-{F}(V2,V0,V3), sum-{F}(V0,V3,V4), V0 == V4 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #81: mergings( V3 == V4, V4 == V6, V5 == V7; #77 ), references = 47, size of lhs = 5:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), product-{F}(V2,V3,V0), sum-{F}(V3,V4,V5), product-{F}(V2,V5,V6) | P_multiply-{T}(V2,V4,V6)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #86: mergings( V1 == V5, V2 == V6; #83 ), references = 2, size of lhs = 5:
% 37.87/38.07 P_x-{F}(V0), P_y-{F}(V1), P_additive_identity-{F}(V2), P_multiplicative_identity-{F}(V3), sum-{F}(V0,V1,V4) | P_x_plus_y-{T}(V4)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #110: mergings( V3 == V5, V5 == V7, V4 == V6, V6 == V8; #104 ), references = 31, size of lhs = 7:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), product-{F}(V2,V3,V3), product-{F}(V2,V4,V4), sum-{F}(V4,V5,V2), product-{F}(V3,V5,V6), sum-{F}(V4,V6,V7) | P_add-{T}(V4,V3,V7)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #115: mergings( V3 == V5, V5 == V7, V4 == V6, V6 == V8; #105 ), references = 1, size of lhs = 7:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), product-{F}(V2,V3,V3), product-{F}(V2,V4,V4), sum-{F}(V4,V5,V2), product-{F}(V3,V5,V6), sum-{F}(V4,V6,V7) | P_add-{T}(V4,V3,V7)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #127: mergings( V0 == V2, V2 == V4, V3 == V5; #123 ), references = 1, size of lhs = 2:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1) | P_inverse-{T}(V0,V1)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #146: mergings( V2 == V3, V3 == V6, V6 == V8, V8 == V12, V4 == V5, V5 == V7, V7 == V9, V9 == V13; #137 ), references = 1, size of lhs = 6:
% 37.87/38.07 P_x-{F}(V0), P_y-{F}(V0), P_x_plus_y-{F}(V1), P_x_inverse_times_y_inverse-{F}(V2), P_additive_identity-{F}(V3), P_multiplicative_identity-{F}(V4) | P_inverse-{T}(V0,V2)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #160: mergings( V1 == V2, V2 == V5, V5 == V7, V7 == V10, V10 == V12, V3 == V4, V4 == V6, V6 == V8, V8 == V11, V11 == V13, V9 == V14; #148 ), references = 1, size of lhs = 5:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V2), P_x_plus_y-{F}(V2) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #173: mergings( V2 == V3, V3 == V5, V0 == V4, V4 == V6; #168 ), references = 1, size of lhs = 2:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1) | P_inverse-{T}(V1,V0)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #180: mergings( V1 == V8, V2 == V9; #177 ), references = 9, size of lhs = 8:
% 37.87/38.07 P_x-{F}(V0), P_y-{F}(V1), P_x_plus_y-{F}(V2), P_inverse-{F}(V0,V3), P_inverse-{F}(V1,V4), P_additive_identity-{F}(V5), P_multiplicative_identity-{F}(V6), product-{F}(V3,V4,V7) | P_x_inverse_times_y_inverse-{T}(V7)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #213: mergings( V2 == V5, V5 == V7, V7 == V9, V3 == V4, V4 == V6, V6 == V8, V8 == V10; #204 ), references = 4, size of lhs = 8:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), sum-{F}(V2,V3,V2), sum-{F}(V4,V3,V5), sum-{F}(V4,V0,V6), product-{F}(V6,V5,V7), sum-{F}(V4,V0,V8), V8 == V7 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #221: mergings( V2 == V5, V5 == V7, V7 == V9, V3 == V4, V4 == V6, V6 == V8, V8 == V10; #205 ), references = 4, size of lhs = 8:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), sum-{F}(V2,V3,V2), sum-{F}(V4,V0,V5), sum-{F}(V4,V3,V6), sum-{F}(V4,V0,V7), product-{F}(V6,V5,V8), V8 == V7 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #236: exists( #29, #24 ), references = 7, size of lhs = 8:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), P_x_plus_y-{F}(V4), P_inverse-{F}(V2,V5), P_x_inverse_times_y_inverse-{F}(V6), P_inverse-{F}(V4,V6) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #249: mergings( V2 == V6, V3 == V8; #246 ), references = 2, size of lhs = 9:
% 37.87/38.07 P_x-{F}(V0), P_y-{F}(V1), P_x_plus_y-{F}(V2), P_inverse-{F}(V0,V3), P_additive_identity-{F}(V3), P_x_inverse_times_y_inverse-{F}(V4), P_multiplicative_identity-{F}(V5), sum-{F}(V3,V4,V6), V6 == V3 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #252: exists( #33, #250 ), references = 2, size of lhs = 6:
% 37.87/38.07 P_x-{F}(V0), P_y-{F}(V1), P_x_plus_y-{F}(V2), P_inverse-{F}(V0,V3), P_additive_identity-{F}(V3), P_multiplicative_identity-{F}(V4) | P_x_inverse_times_y_inverse-{T}(V3)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #265: mergings( V1 == V3, V3 == V7, V2 == V4, V4 == V8; #259 ), references = 1, size of lhs = 7:
% 37.87/38.07 P_x-{F}(V0), P_y-{F}(V1), P_additive_identity-{F}(V2), sum-{F}(V0,V2,V3), P_multiplicative_identity-{F}(V3), sum-{F}(V4,V1,V4), sum-{F}(V0,V2,V5) | P_x_plus_y-{T}(V5)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #270: mergings( V1 == V3, V3 == V7, V2 == V4, V4 == V8; #260 ), references = 1, size of lhs = 7:
% 37.87/38.07 P_x-{F}(V0), P_y-{F}(V1), P_additive_identity-{F}(V2), sum-{F}(V0,V2,V3), P_multiplicative_identity-{F}(V3), sum-{F}(V4,V1,V4), sum-{F}(V0,V2,V5) | P_x_plus_y-{T}(V5)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #292: mergings( V1 == V3, V3 == V5, V5 == V7, V7 == V10, V10 == V14, V14 == V16, V2 == V4, V4 == V6, V6 == V8, V8 == V11, V11 == V15, V15 == V17, V9 == V13, V13 == V18, V16 == V19; #276 ), references = 1, size of lhs = 8:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), sum-{F}(V1,V1,V1), P_x-{F}(V2), sum-{F}(V2,V0,V1), P_inverse-{F}(V2,V0), sum-{F}(V2,V0,V3), P_inverse-{F}(V3,V0) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #310: mergings( V2 == V6, V6 == V8, V3 == V7, V7 == V9, V4 == V10, V9 == V11, V5 == V0; #302 ), references = 2, size of lhs = 6:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_x-{F}(V2), P_inverse-{F}(V2,V1), P_y-{F}(V3), P_x_plus_y-{F}(V3) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #320: mergings( V1 == V2, V2 == V4, V3 == V5, V4 == V6; #315 ), references = 1, size of lhs = 4:
% 37.87/38.07 P_additive_identity-{F}(V0), P_x-{F}(V0), P_multiplicative_identity-{F}(V1), P_inverse-{F}(V0,V1) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #345: mergings( V1 == V3, V3 == V7, V2 == V4, V4 == V8; #339 ), references = 1, size of lhs = 7:
% 37.87/38.07 P_x-{F}(V0), P_y-{F}(V1), P_additive_identity-{F}(V2), sum-{F}(V1,V2,V3), P_multiplicative_identity-{F}(V3), sum-{F}(V4,V0,V4), sum-{F}(V1,V2,V5) | P_x_plus_y-{T}(V5)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #350: mergings( V1 == V3, V3 == V7, V2 == V4, V4 == V8; #340 ), references = 1, size of lhs = 7:
% 37.87/38.07 P_x-{F}(V0), P_y-{F}(V1), P_additive_identity-{F}(V2), sum-{F}(V1,V2,V3), P_multiplicative_identity-{F}(V3), sum-{F}(V4,V0,V4), sum-{F}(V1,V2,V5) | P_x_plus_y-{T}(V5)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #356: exists( #29, #236 ), references = 4, size of lhs = 7:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), P_x_plus_y-{F}(V4), P_x_inverse_times_y_inverse-{F}(V5), P_inverse-{F}(V4,V5) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #366: mergings( V2 == V6, V3 == V8; #363 ), references = 2, size of lhs = 9:
% 37.87/38.07 P_x-{F}(V0), P_y-{F}(V1), P_x_plus_y-{F}(V2), P_inverse-{F}(V1,V3), P_additive_identity-{F}(V3), P_x_inverse_times_y_inverse-{F}(V4), P_multiplicative_identity-{F}(V5), sum-{F}(V3,V4,V6), V3 == V6 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #369: exists( #33, #367 ), references = 1, size of lhs = 6:
% 37.87/38.07 P_x-{F}(V0), P_y-{F}(V1), P_x_plus_y-{F}(V2), P_inverse-{F}(V1,V3), P_additive_identity-{F}(V3), P_multiplicative_identity-{F}(V4) | P_x_inverse_times_y_inverse-{T}(V3)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #393: mergings( V2 == V6, V6 == V8, V3 == V7, V7 == V9, V4 == V10, V5 == V0; #385 ), references = 1, size of lhs = 6:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_x-{F}(V2), P_x_plus_y-{F}(V2), P_y-{F}(V3), P_inverse-{F}(V3,V1) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #412: mergings( V3 == V5, V5 == V11, V2 == V4, V4 == V6, V6 == V12; #406 ), references = 2, size of lhs = 9:
% 37.87/38.07 P_x-{F}(V0), P_y-{F}(V1), P_x_plus_y-{F}(V2), P_inverse-{F}(V0,V3), sum-{F}(V1,V3,V1), P_x_inverse_times_y_inverse-{F}(V4), P_additive_identity-{F}(V5), V5 == V4, P_multiplicative_identity-{F}(V6) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #435: mergings( V2 == V3, V3 == V6, V6 == V8, V8 == V10, V10 == V15, V4 == V5, V5 == V7, V7 == V9, V9 == V11, V11 == V16; #424 ), references = 1, size of lhs = 12:
% 37.87/38.07 P_x-{F}(V0), P_y-{F}(V1), P_x_plus_y-{F}(V2), P_x_inverse_times_y_inverse-{F}(V3), P_additive_identity-{F}(V4), V4 == V3, P_multiplicative_identity-{F}(V5), product-{F}(V5,V6,V6), product-{F}(V6,V0,V0), product-{F}(V7,V6,V1), product-{F}(V7,V5,V1), sum-{F}(V0,V7,V5) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #447: mergings( V1 == V2, V2 == V5, V5 == V7, V7 == V9, V9 == V14, V3 == V4, V4 == V6, V6 == V8, V8 == V10, V10 == V15; #436 ), references = 1, size of lhs = 10:
% 37.87/38.07 P_x-{F}(V0), P_y-{F}(V1), P_x_plus_y-{F}(V2), P_additive_identity-{F}(V3), P_multiplicative_identity-{F}(V4), product-{F}(V4,V5,V5), product-{F}(V5,V0,V0), product-{F}(V6,V5,V1), product-{F}(V6,V4,V1), sum-{F}(V0,V6,V4) | P_x_inverse_times_y_inverse-{T}(V3)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #484: mergings( V2 == V4, V4 == V7, V7 == V9, V9 == V11, V3 == V5, V5 == V6, V6 == V8, V8 == V10, V10 == V12; #473 ), references = 4, size of lhs = 5:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), product-{F}(V2,V3,V0), sum-{F}(V3,V2,V1), product-{F}(V2,V1,V4) | P_inverse-{T}(V3,V4)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #497: mergings( V2 == V3, V3 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V14, V4 == V5, V5 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V15; #474 ), references = 1, size of lhs = 10:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), product-{F}(V1,V2,V2), product-{F}(V2,V3,V3), sum-{F}(V3,V4,V1), product-{F}(V1,V4,V5), product-{F}(V5,V3,V0), product-{F}(V5,V1,V6), product-{F}(V2,V4,V7), sum-{F}(V8,V7,V8) | P_inverse-{T}(V3,V6)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #561: mergings( V2 == V6, V6 == V11, V11 == V13, V3 == V4, V4 == V5, V5 == V7, V7 == V12, V12 == V14, V8 == V15, V0 == V16, V16 == V9; #547 ), references = 2, size of lhs = 8:
% 37.87/38.07 P_x_plus_y-{F}(V0), P_y-{F}(V0), P_additive_identity-{F}(V1), P_multiplicative_identity-{F}(V2), P_x-{F}(V3), P_inverse-{F}(V3,V4), sum-{F}(V5,V4,V2), sum-{F}(V0,V5,V0) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #573: mergings( V2 == V6, V6 == V11, V11 == V13, V3 == V4, V4 == V5, V5 == V7, V7 == V12, V12 == V14, V8 == V15, V10 == V16, V9 == V0; #549 ), references = 1, size of lhs = 8:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), P_x_plus_y-{F}(V3), P_inverse-{F}(V2,V4), sum-{F}(V5,V4,V1), sum-{F}(V3,V5,V3) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #586: mergings( V2 == V6, V6 == V11, V11 == V13, V3 == V4, V4 == V5, V5 == V7, V7 == V12, V12 == V14, V8 == V15, V10 == V17, V0 == V16, V16 == V9; #548 ), references = 1, size of lhs = 8:
% 37.87/38.07 P_x_plus_y-{F}(V0), P_y-{F}(V0), P_additive_identity-{F}(V1), P_multiplicative_identity-{F}(V2), P_x-{F}(V3), P_inverse-{F}(V3,V4), sum-{F}(V5,V4,V2), sum-{F}(V0,V5,V0) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #612: mergings( V2 == V4; #608 ), references = 1, size of lhs = 6:
% 37.87/38.07 P_x_plus_y-{F}(V0), P_y-{F}(V0), P_additive_identity-{F}(V1), P_multiplicative_identity-{F}(V2), P_x-{F}(V3), sum-{F}(V0,V3,V0) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #645: mergings( V2 == V4, V4 == V6, V3 == V5, V5 == V7; #640 ), references = 1, size of lhs = 7:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), sum-{F}(V2,V3,V2), sum-{F}(V4,V3,V0), sum-{F}(V4,V0,V5), sum-{F}(V4,V0,V6), V6 == V0 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #703: mergings( V2 == V6, V6 == V11, V11 == V13, V3 == V4, V4 == V5, V5 == V7, V7 == V12, V12 == V14, V8 == V15, V9 == V0; #691 ), references = 2, size of lhs = 8:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_x-{F}(V2), P_x_plus_y-{F}(V2), P_y-{F}(V3), P_inverse-{F}(V3,V4), sum-{F}(V5,V4,V1), sum-{F}(V2,V5,V2) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #715: mergings( V2 == V6, V6 == V11, V11 == V13, V3 == V4, V4 == V5, V5 == V7, V7 == V12, V12 == V14, V0 == V15, V8 == V16, V15 == V9; #690 ), references = 1, size of lhs = 8:
% 37.87/38.07 P_x_plus_y-{F}(V0), P_x-{F}(V0), P_additive_identity-{F}(V1), P_multiplicative_identity-{F}(V2), P_y-{F}(V3), P_inverse-{F}(V3,V4), sum-{F}(V5,V4,V2), sum-{F}(V0,V5,V0) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #727: mergings( V2 == V6, V6 == V11, V11 == V13, V3 == V4, V4 == V5, V5 == V7, V7 == V12, V12 == V14, V8 == V15, V10 == V16, V9 == V0; #692 ), references = 1, size of lhs = 8:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_x-{F}(V2), P_x_plus_y-{F}(V2), P_y-{F}(V3), P_inverse-{F}(V3,V4), sum-{F}(V5,V4,V1), sum-{F}(V2,V5,V2) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #756: mergings( V2 == V3; #752 ), references = 1, size of lhs = 6:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_x-{F}(V2), P_x_plus_y-{F}(V2), P_y-{F}(V3), sum-{F}(V2,V3,V2) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #858: mergings( V2 == V3, V3 == V7, V7 == V9, V9 == V11, V11 == V17, V17 == V19, V19 == V21, V21 == V23, V23 == V25, V4 == V5, V5 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V18, V18 == V20, V20 == V22, V22 == V24, V24 == V26, V13 == V27, V14 == V28, V16 == V29; #834 ), references = 3, size of lhs = 19:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), P_inverse-{F}(V3,V4), sum-{F}(V1,V4,V1), P_x_plus_y-{F}(V5), P_x_inverse_times_y_inverse-{F}(V6), product-{F}(V6,V1,V6), sum-{F}(V7,V2,V5), sum-{F}(V7,V0,V8), sum-{F}(V6,V8,V1), sum-{F}(V7,V0,V9), sum-{F}(V6,V9,V10), product-{F}(V10,V5,V5), product-{F}(V10,V6,V6), sum-{F}(V2,V11,V5), product-{F}(V6,V11,V12), sum-{F}(V0,V12,V0) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #882: mergings( V2 == V3, V3 == V7, V7 == V9, V9 == V11, V11 == V17, V17 == V19, V19 == V21, V21 == V23, V23 == V25, V4 == V5, V5 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V18, V18 == V20, V20 == V22, V22 == V24, V24 == V26, V0 == V27, V13 == V28, V14 == V29, V16 == V30; #833 ), references = 3, size of lhs = 19:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), P_inverse-{F}(V3,V4), sum-{F}(V1,V4,V1), P_x_plus_y-{F}(V5), P_x_inverse_times_y_inverse-{F}(V6), product-{F}(V6,V1,V6), sum-{F}(V7,V2,V5), sum-{F}(V7,V0,V8), sum-{F}(V6,V8,V1), sum-{F}(V7,V0,V9), sum-{F}(V6,V9,V10), product-{F}(V10,V5,V5), product-{F}(V10,V6,V6), sum-{F}(V2,V11,V5), product-{F}(V6,V11,V12), sum-{F}(V0,V12,V0) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #906: mergings( V2 == V3, V3 == V7, V7 == V9, V9 == V11, V11 == V17, V17 == V19, V19 == V21, V21 == V23, V23 == V25, V4 == V5, V5 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V18, V18 == V20, V20 == V22, V22 == V24, V24 == V26, V13 == V27, V15 == V30, V14 == V28, V16 == V29; #835 ), references = 3, size of lhs = 19:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), P_x_plus_y-{F}(V4), P_x_inverse_times_y_inverse-{F}(V5), product-{F}(V5,V1,V5), P_inverse-{F}(V3,V6), sum-{F}(V1,V6,V1), sum-{F}(V7,V2,V4), sum-{F}(V7,V0,V8), sum-{F}(V5,V8,V1), sum-{F}(V7,V0,V9), sum-{F}(V5,V9,V10), product-{F}(V10,V4,V4), product-{F}(V10,V5,V5), sum-{F}(V2,V11,V4), product-{F}(V5,V11,V12), sum-{F}(V0,V12,V0) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1044: mergings( V2 == V3, V3 == V4, V4 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V15, V15 == V20, V20 == V22, V22 == V24, V5 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V14, V14 == V16, V16 == V21, V21 == V23, V23 == V25, V17 == V26, V18 == V27; #1020 ), references = 1, size of lhs = 26:
% 37.87/38.07 P_additive_identity-{F}(V0), sum-{F}(V0,V0,V0), P_multiplicative_identity-{F}(V1), product-{F}(V1,V1,V1), P_x-{F}(V2), P_inverse-{F}(V2,V3), sum-{F}(V1,V3,V1), P_y-{F}(V4), product-{F}(V1,V4,V4), P_x_plus_y-{F}(V5), product-{F}(V1,V5,V5), sum-{F}(V2,V4,V5), P_x_inverse_times_y_inverse-{F}(V6), product-{F}(V6,V1,V6), product-{F}(V1,V6,V6), sum-{F}(V6,V2,V1), sum-{F}(V7,V0,V2), sum-{F}(V7,V4,V8), sum-{F}(V7,V0,V9), sum-{F}(V6,V9,V10), product-{F}(V10,V6,V6), product-{F}(V10,V8,V8), sum-{F}(V11,V0,V8), product-{F}(V8,V12,V11), sum-{F}(V12,V9,V13), product-{F}(V8,V13,V5) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1066: mergings( V2 == V3, V3 == V4, V4 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V15, V15 == V20, V20 == V22, V22 == V24, V5 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V14, V14 == V16, V16 == V21, V21 == V23, V23 == V25, V17 == V26, V18 == V27; #1021 ), references = 1, size of lhs = 26:
% 37.87/38.07 P_additive_identity-{F}(V0), sum-{F}(V0,V0,V0), P_multiplicative_identity-{F}(V1), product-{F}(V1,V1,V1), P_x-{F}(V2), P_inverse-{F}(V2,V3), sum-{F}(V1,V3,V1), P_y-{F}(V4), product-{F}(V1,V4,V4), P_x_plus_y-{F}(V5), product-{F}(V1,V5,V5), sum-{F}(V2,V4,V5), P_x_inverse_times_y_inverse-{F}(V6), product-{F}(V6,V1,V6), product-{F}(V1,V6,V6), sum-{F}(V6,V2,V1), sum-{F}(V7,V0,V2), sum-{F}(V7,V4,V8), sum-{F}(V7,V0,V9), sum-{F}(V6,V9,V10), product-{F}(V10,V6,V6), product-{F}(V10,V8,V8), sum-{F}(V11,V0,V8), product-{F}(V8,V12,V11), sum-{F}(V12,V9,V13), product-{F}(V8,V13,V5) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1088: mergings( V2 == V3, V3 == V4, V4 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V15, V15 == V20, V20 == V22, V22 == V24, V5 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V14, V14 == V16, V16 == V21, V21 == V23, V23 == V25, V17 == V26, V18 == V27; #1022 ), references = 1, size of lhs = 26:
% 37.87/38.07 P_additive_identity-{F}(V0), sum-{F}(V0,V0,V0), P_multiplicative_identity-{F}(V1), product-{F}(V1,V1,V1), P_x-{F}(V2), P_inverse-{F}(V2,V3), sum-{F}(V1,V3,V1), P_y-{F}(V4), product-{F}(V1,V4,V4), P_x_plus_y-{F}(V5), product-{F}(V1,V5,V5), sum-{F}(V2,V4,V5), P_x_inverse_times_y_inverse-{F}(V6), product-{F}(V6,V1,V6), product-{F}(V1,V6,V6), sum-{F}(V6,V2,V1), sum-{F}(V7,V0,V2), sum-{F}(V7,V4,V8), sum-{F}(V7,V0,V9), sum-{F}(V6,V9,V10), product-{F}(V10,V6,V6), product-{F}(V10,V8,V8), sum-{F}(V11,V0,V8), product-{F}(V8,V12,V11), sum-{F}(V12,V9,V13), product-{F}(V8,V13,V5) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1209: mergings( V2 == V3, V3 == V5, V5 == V7, V7 == V13, V13 == V15, V15 == V17, V4 == V6, V6 == V8, V8 == V14, V14 == V16, V16 == V18; #1197 ), references = 1, size of lhs = 15:
% 37.87/38.07 P_x-{F}(V0), P_y-{F}(V1), P_x_plus_y-{F}(V2), P_inverse-{F}(V0,V3), P_x_inverse_times_y_inverse-{F}(V4), P_additive_identity-{F}(V5), P_multiplicative_identity-{F}(V6), product-{F}(V6,V7,V7), product-{F}(V7,V1,V1), product-{F}(V3,V7,V8), product-{F}(V9,V8,V5), product-{F}(V3,V6,V10), product-{F}(V9,V10,V11), product-{F}(V9,V4,V12), V12 == V11 | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1224: mergings( V3 == V4, V4 == V6, V6 == V8, V8 == V14, V14 == V16, V16 == V18, V5 == V7, V7 == V9, V9 == V15, V15 == V17, V17 == V19; #1212 ), references = 1, size of lhs = 13:
% 37.87/38.07 P_x-{F}(V0), P_y-{F}(V1), P_x_plus_y-{F}(V2), P_inverse-{F}(V0,V3), P_x_inverse_times_y_inverse-{F}(V4), P_additive_identity-{F}(V5), P_multiplicative_identity-{F}(V6), product-{F}(V6,V7,V7), product-{F}(V7,V1,V1), product-{F}(V3,V7,V8), product-{F}(V9,V8,V5), product-{F}(V3,V6,V10), product-{F}(V9,V10,V11) | P_multiply-{T}(V4,V9,V11)
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1424: mergings( V2 == V3, V3 == V4, V4 == V8, V8 == V10, V10 == V12, V12 == V14, V14 == V16, V16 == V21, V21 == V23, V23 == V25, V25 == V27, V27 == V29, V29 == V31, V31 == V33, V5 == V6, V6 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V15, V15 == V17, V17 == V22, V22 == V24, V24 == V26, V26 == V28, V28 == V30, V30 == V32, V32 == V34, V18 == V35, V19 == V36; #1391 ), references = 1, size of lhs = 34:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), sum-{F}(V1,V0,V1), product-{F}(V1,V1,V1), P_x-{F}(V2), P_inverse-{F}(V2,V3), sum-{F}(V1,V3,V1), P_y-{F}(V4), P_x_plus_y-{F}(V5), product-{F}(V1,V5,V5), P_x_inverse_times_y_inverse-{F}(V6), product-{F}(V6,V1,V6), product-{F}(V1,V6,V6), sum-{F}(V3,V2,V7), product-{F}(V7,V1,V1), sum-{F}(V8,V0,V2), sum-{F}(V1,V0,V9), product-{F}(V9,V1,V1), product-{F}(V9,V4,V4), sum-{F}(V8,V0,V10), sum-{F}(V3,V10,V11), product-{F}(V11,V3,V3), sum-{F}(V8,V4,V12), product-{F}(V11,V12,V12), product-{F}(V1,V12,V12), product-{F}(V12,V4,V4), sum-{F}(V0,V13,V0), product-{F}(V12,V14,V5), sum-{F}(V15,V10,V14), product-{F}(V12,V15,V16), sum-{F}(V16,V0,V12), sum-{F}(V4,V17,V16), product-{F}(V6,V17,V18), sum-{F}(V0,V18,V13) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1455: mergings( V2 == V3, V3 == V4, V4 == V8, V8 == V10, V10 == V12, V12 == V14, V14 == V16, V16 == V21, V21 == V23, V23 == V25, V25 == V27, V27 == V29, V29 == V31, V31 == V33, V5 == V6, V6 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V15, V15 == V17, V17 == V22, V22 == V24, V24 == V26, V26 == V28, V28 == V30, V30 == V32, V32 == V34, V18 == V35, V19 == V36; #1392 ), references = 1, size of lhs = 34:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), sum-{F}(V1,V0,V1), product-{F}(V1,V1,V1), P_x-{F}(V2), P_inverse-{F}(V2,V3), sum-{F}(V1,V3,V1), P_y-{F}(V4), P_x_plus_y-{F}(V5), product-{F}(V1,V5,V5), P_x_inverse_times_y_inverse-{F}(V6), product-{F}(V6,V1,V6), product-{F}(V1,V6,V6), sum-{F}(V3,V2,V7), product-{F}(V7,V1,V1), sum-{F}(V8,V0,V2), sum-{F}(V1,V0,V9), product-{F}(V9,V1,V1), product-{F}(V9,V4,V4), sum-{F}(V8,V0,V10), sum-{F}(V3,V10,V11), product-{F}(V11,V3,V3), sum-{F}(V8,V4,V12), product-{F}(V11,V12,V12), product-{F}(V1,V12,V12), product-{F}(V12,V4,V4), sum-{F}(V0,V13,V0), product-{F}(V12,V14,V5), sum-{F}(V15,V10,V14), product-{F}(V12,V15,V16), sum-{F}(V16,V0,V12), sum-{F}(V4,V17,V16), product-{F}(V6,V17,V18), sum-{F}(V0,V18,V13) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1486: mergings( V2 == V3, V3 == V4, V4 == V8, V8 == V10, V10 == V12, V12 == V14, V14 == V16, V16 == V21, V21 == V23, V23 == V25, V25 == V27, V27 == V29, V29 == V31, V31 == V33, V5 == V6, V6 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V15, V15 == V17, V17 == V22, V22 == V24, V24 == V26, V26 == V28, V28 == V30, V30 == V32, V32 == V34, V18 == V35, V19 == V36; #1393 ), references = 1, size of lhs = 34:
% 37.87/38.07 P_additive_identity-{F}(V0), P_multiplicative_identity-{F}(V1), sum-{F}(V1,V0,V1), product-{F}(V1,V1,V1), P_x-{F}(V2), P_inverse-{F}(V2,V3), sum-{F}(V1,V3,V1), P_y-{F}(V4), P_x_plus_y-{F}(V5), product-{F}(V1,V5,V5), P_x_inverse_times_y_inverse-{F}(V6), product-{F}(V6,V1,V6), product-{F}(V1,V6,V6), sum-{F}(V3,V2,V7), product-{F}(V7,V1,V1), sum-{F}(V8,V0,V2), sum-{F}(V1,V0,V9), product-{F}(V9,V1,V1), product-{F}(V9,V4,V4), sum-{F}(V8,V0,V10), sum-{F}(V3,V10,V11), product-{F}(V11,V3,V3), sum-{F}(V8,V4,V12), product-{F}(V11,V12,V12), product-{F}(V1,V12,V12), product-{F}(V12,V4,V4), sum-{F}(V0,V13,V0), product-{F}(V12,V14,V5), sum-{F}(V15,V10,V14), product-{F}(V12,V15,V16), sum-{F}(V16,V0,V12), sum-{F}(V4,V17,V16), product-{F}(V6,V17,V18), sum-{F}(V0,V18,V13) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1591: mergings( V2 == V3, V3 == V4, V4 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V14, V14 == V16, V16 == V18, V18 == V22, V22 == V24, V24 == V26, V26 == V28, V28 == V29, V29 == V30, V30 == V34, V34 == V36, V36 == V38, V38 == V40, V40 == V42, V42 == V45, V45 == V47, V47 == V49, V49 == V51, V51 == V53, V53 == V55, V55 == V57, V5 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V15, V15 == V17, V17 == V19, V19 == V23, V23 == V25, V25 == V27, V27 == V31, V31 == V32, V32 == V33, V33 == V35, V35 == V37, V37 == V39, V39 == V41, V41 == V43, V43 == V46, V46 == V48, V48 == V50, V50 == V52, V52 == V54, V54 == V56, V56 == V58, V20 == V59, V21 == V44, V44 == V60, V66 == V57; #1532 ), references = 2, size of lhs = 28:
% 37.87/38.07 P_additive_identity-{F}(V0), sum-{F}(V0,V0,V0), P_multiplicative_identity-{F}(V1), sum-{F}(V1,V0,V1), product-{F}(V1,V1,V1), P_x-{F}(V2), P_y-{F}(V3), product-{F}(V1,V3,V3), P_x_plus_y-{F}(V4), product-{F}(V1,V4,V4), P_x_inverse_times_y_inverse-{F}(V5), product-{F}(V5,V1,V5), product-{F}(V1,V5,V5), sum-{F}(V6,V0,V2), sum-{F}(V1,V0,V7), product-{F}(V7,V1,V1), product-{F}(V7,V3,V3), sum-{F}(V6,V3,V8), product-{F}(V1,V8,V8), product-{F}(V8,V1,V4), sum-{F}(V3,V2,V9), sum-{F}(V9,V0,V8), product-{F}(V8,V1,V9), sum-{F}(V10,V2,V8), sum-{F}(V10,V0,V3), sum-{F}(V1,V0,V11), product-{F}(V11,V2,V2), product-{F}(V11,V1,V1) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1648: mergings( V2 == V3, V3 == V4, V4 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V14, V14 == V16, V16 == V18, V18 == V22, V22 == V24, V24 == V26, V26 == V28, V28 == V29, V29 == V30, V30 == V34, V34 == V36, V36 == V38, V38 == V40, V40 == V42, V42 == V45, V45 == V47, V47 == V49, V49 == V51, V51 == V53, V53 == V55, V55 == V57, V5 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V15, V15 == V17, V17 == V19, V19 == V23, V23 == V25, V25 == V27, V27 == V31, V31 == V32, V32 == V33, V33 == V35, V35 == V37, V37 == V39, V39 == V41, V41 == V43, V43 == V46, V46 == V48, V48 == V50, V50 == V52, V52 == V54, V54 == V56, V56 == V58, V20 == V59, V21 == V44, V44 == V60, V66 == V57; #1533 ), references = 2, size of lhs = 28:
% 37.87/38.07 P_additive_identity-{F}(V0), sum-{F}(V0,V0,V0), P_multiplicative_identity-{F}(V1), sum-{F}(V1,V0,V1), product-{F}(V1,V1,V1), P_x-{F}(V2), P_y-{F}(V3), product-{F}(V1,V3,V3), P_x_plus_y-{F}(V4), product-{F}(V1,V4,V4), P_x_inverse_times_y_inverse-{F}(V5), product-{F}(V5,V1,V5), product-{F}(V1,V5,V5), sum-{F}(V6,V0,V2), sum-{F}(V1,V0,V7), product-{F}(V7,V1,V1), product-{F}(V7,V3,V3), sum-{F}(V6,V3,V8), product-{F}(V1,V8,V8), product-{F}(V8,V1,V4), sum-{F}(V3,V2,V9), sum-{F}(V9,V0,V8), product-{F}(V8,V1,V9), sum-{F}(V10,V2,V8), sum-{F}(V10,V0,V3), sum-{F}(V1,V0,V11), product-{F}(V11,V2,V2), product-{F}(V11,V1,V1) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1705: mergings( V2 == V3, V3 == V4, V4 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V14, V14 == V16, V16 == V18, V18 == V22, V22 == V24, V24 == V26, V26 == V28, V28 == V29, V29 == V30, V30 == V34, V34 == V36, V36 == V38, V38 == V40, V40 == V42, V42 == V45, V45 == V47, V47 == V49, V49 == V51, V51 == V53, V53 == V55, V55 == V57, V5 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V15, V15 == V17, V17 == V19, V19 == V23, V23 == V25, V25 == V27, V27 == V31, V31 == V32, V32 == V33, V33 == V35, V35 == V37, V37 == V39, V39 == V41, V41 == V43, V43 == V46, V46 == V48, V48 == V50, V50 == V52, V52 == V54, V54 == V56, V56 == V58, V20 == V59, V21 == V44, V44 == V60, V66 == V57; #1534 ), references = 2, size of lhs = 28:
% 37.87/38.07 P_additive_identity-{F}(V0), sum-{F}(V0,V0,V0), P_multiplicative_identity-{F}(V1), sum-{F}(V1,V0,V1), product-{F}(V1,V1,V1), P_x-{F}(V2), P_y-{F}(V3), product-{F}(V1,V3,V3), P_x_plus_y-{F}(V4), product-{F}(V1,V4,V4), P_x_inverse_times_y_inverse-{F}(V5), product-{F}(V5,V1,V5), product-{F}(V1,V5,V5), sum-{F}(V6,V0,V2), sum-{F}(V1,V0,V7), product-{F}(V7,V1,V1), product-{F}(V7,V3,V3), sum-{F}(V6,V3,V8), product-{F}(V1,V8,V8), product-{F}(V8,V1,V4), sum-{F}(V3,V2,V9), sum-{F}(V9,V0,V8), product-{F}(V8,V1,V9), sum-{F}(V10,V2,V8), sum-{F}(V10,V0,V3), sum-{F}(V1,V0,V11), product-{F}(V11,V2,V2), product-{F}(V11,V1,V1) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1716: mergings( V1 == V2; #1712 ), references = 1, size of lhs = 25:
% 37.87/38.07 P_additive_identity-{F}(V0), sum-{F}(V0,V0,V0), P_multiplicative_identity-{F}(V1), sum-{F}(V1,V0,V1), product-{F}(V1,V1,V1), P_x-{F}(V2), P_y-{F}(V3), product-{F}(V1,V3,V3), P_x_plus_y-{F}(V4), product-{F}(V1,V4,V4), sum-{F}(V5,V0,V2), sum-{F}(V1,V0,V6), product-{F}(V6,V1,V1), product-{F}(V6,V3,V3), sum-{F}(V5,V3,V7), product-{F}(V1,V7,V7), product-{F}(V7,V1,V4), sum-{F}(V3,V2,V8), sum-{F}(V8,V0,V7), product-{F}(V7,V1,V8), sum-{F}(V9,V2,V7), sum-{F}(V9,V0,V3), sum-{F}(V1,V0,V10), product-{F}(V10,V2,V2), product-{F}(V10,V1,V1) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1718: mergings( V1 == V2; #1713 ), references = 1, size of lhs = 25:
% 37.87/38.07 P_additive_identity-{F}(V0), sum-{F}(V0,V0,V0), P_multiplicative_identity-{F}(V1), sum-{F}(V1,V0,V1), product-{F}(V1,V1,V1), P_x-{F}(V2), P_y-{F}(V3), product-{F}(V1,V3,V3), P_x_plus_y-{F}(V4), product-{F}(V1,V4,V4), sum-{F}(V5,V0,V2), sum-{F}(V1,V0,V6), product-{F}(V6,V1,V1), product-{F}(V6,V3,V3), sum-{F}(V5,V3,V7), product-{F}(V1,V7,V7), product-{F}(V7,V1,V4), sum-{F}(V3,V2,V8), sum-{F}(V8,V0,V7), product-{F}(V7,V1,V8), sum-{F}(V9,V2,V7), sum-{F}(V9,V0,V3), sum-{F}(V1,V0,V10), product-{F}(V10,V2,V2), product-{F}(V10,V1,V1) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1720: mergings( V1 == V2; #1714 ), references = 1, size of lhs = 25:
% 37.87/38.07 P_additive_identity-{F}(V0), sum-{F}(V0,V0,V0), P_multiplicative_identity-{F}(V1), sum-{F}(V1,V0,V1), product-{F}(V1,V1,V1), P_x-{F}(V2), P_y-{F}(V3), product-{F}(V1,V3,V3), P_x_plus_y-{F}(V4), product-{F}(V1,V4,V4), sum-{F}(V5,V0,V2), sum-{F}(V1,V0,V6), product-{F}(V6,V1,V1), product-{F}(V6,V3,V3), sum-{F}(V5,V3,V7), product-{F}(V1,V7,V7), product-{F}(V7,V1,V4), sum-{F}(V3,V2,V8), sum-{F}(V8,V0,V7), product-{F}(V7,V1,V8), sum-{F}(V9,V2,V7), sum-{F}(V9,V0,V3), sum-{F}(V1,V0,V10), product-{F}(V10,V2,V2), product-{F}(V10,V1,V1) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1743: mergings( V1 == V2, V2 == V4, V4 == V5, V3 == V6; #1736 ), references = 1, size of lhs = 16:
% 37.87/38.07 P_additive_identity-{F}(V0), sum-{F}(V0,V0,V0), P_multiplicative_identity-{F}(V1), sum-{F}(V1,V0,V1), product-{F}(V1,V1,V1), P_x-{F}(V2), sum-{F}(V2,V0,V2), P_y-{F}(V3), product-{F}(V1,V3,V3), sum-{F}(V3,V0,V3), sum-{F}(V1,V0,V4), product-{F}(V4,V1,V1), product-{F}(V4,V3,V3), sum-{F}(V1,V0,V5), product-{F}(V5,V2,V2), product-{F}(V5,V1,V1) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1748: mergings( V1 == V2, V2 == V4, V4 == V5, V3 == V6; #1737 ), references = 1, size of lhs = 16:
% 37.87/38.07 P_additive_identity-{F}(V0), sum-{F}(V0,V0,V0), P_multiplicative_identity-{F}(V1), sum-{F}(V1,V0,V1), product-{F}(V1,V1,V1), P_x-{F}(V2), sum-{F}(V2,V0,V2), P_y-{F}(V3), product-{F}(V1,V3,V3), sum-{F}(V3,V0,V3), sum-{F}(V1,V0,V4), product-{F}(V4,V1,V1), product-{F}(V4,V3,V3), sum-{F}(V1,V0,V5), product-{F}(V5,V2,V2), product-{F}(V5,V1,V1) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1753: mergings( V1 == V2, V2 == V4, V4 == V5, V3 == V6; #1738 ), references = 1, size of lhs = 16:
% 37.87/38.07 P_additive_identity-{F}(V0), sum-{F}(V0,V0,V0), P_multiplicative_identity-{F}(V1), sum-{F}(V1,V0,V1), product-{F}(V1,V1,V1), P_x-{F}(V2), sum-{F}(V2,V0,V2), P_y-{F}(V3), product-{F}(V1,V3,V3), sum-{F}(V3,V0,V3), sum-{F}(V1,V0,V4), product-{F}(V4,V1,V1), product-{F}(V4,V3,V3), sum-{F}(V1,V0,V5), product-{F}(V5,V2,V2), product-{F}(V5,V1,V1) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1768: mergings( V1 == V2, V2 == V3, V3 == V5, V5 == V6, V4 == V7; #1760 ), references = 1, size of lhs = 10:
% 37.87/38.07 P_additive_identity-{F}(V0), sum-{F}(V0,V0,V0), P_multiplicative_identity-{F}(V1), sum-{F}(V1,V0,V1), product-{F}(V1,V1,V1), P_x-{F}(V2), sum-{F}(V2,V0,V2), sum-{F}(V1,V0,V3), product-{F}(V3,V2,V2), product-{F}(V3,V1,V1) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1774: mergings( V1 == V2, V2 == V3, V3 == V5, V5 == V6, V4 == V7; #1761 ), references = 1, size of lhs = 10:
% 37.87/38.07 P_additive_identity-{F}(V0), sum-{F}(V0,V0,V0), P_multiplicative_identity-{F}(V1), sum-{F}(V1,V0,V1), product-{F}(V1,V1,V1), P_x-{F}(V2), sum-{F}(V2,V0,V2), sum-{F}(V1,V0,V3), product-{F}(V3,V2,V2), product-{F}(V3,V1,V1) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1780: mergings( V1 == V2, V2 == V3, V3 == V5, V5 == V6, V4 == V7; #1762 ), references = 1, size of lhs = 10:
% 37.87/38.07 P_additive_identity-{F}(V0), sum-{F}(V0,V0,V0), P_multiplicative_identity-{F}(V1), sum-{F}(V1,V0,V1), product-{F}(V1,V1,V1), P_x-{F}(V2), sum-{F}(V2,V0,V2), sum-{F}(V1,V0,V3), product-{F}(V3,V2,V2), product-{F}(V3,V1,V1) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1797: mergings( V1 == V3, V3 == V4, V4 == V5, V5 == V7, V7 == V8, V2 == V6, V6 == V9; #1787 ), references = 1, size of lhs = 5:
% 37.87/38.07 P_additive_identity-{F}(V0), sum-{F}(V0,V0,V0), P_multiplicative_identity-{F}(V1), sum-{F}(V1,V0,V1), product-{F}(V1,V1,V1) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1813: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7; #1804 ), references = 1, size of lhs = 2:
% 37.87/38.07 P_additive_identity-{F}(V0), sum-{F}(V0,V0,V0) | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 #1820: exists( #27, #1814 ), references = 1, size of lhs = 0:
% 37.87/38.07 FALSE | FALSE
% 37.87/38.07 (used 0 times, uses = {})
% 37.87/38.07
% 37.87/38.07 number of learnt formulas = 67
% 37.87/38.07
% 37.87/38.07
% 37.87/38.07 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.87/38.07
% 37.87/38.07 randbase = 1
%------------------------------------------------------------------------------