%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : SWX206-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n027.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 : Tue May 5 07:01:14 PM UTC 2026
% Result : Unsatisfiable 0.29s 0.50s
% Output : Refutation 0.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX206-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.16/0.34 % Computer : n027.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 11:34:49 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.29/0.50 GeoParameters:
% 0.29/0.50
% 0.29/0.50 tptp_input = 1
% 0.29/0.50 tptp_output = 0
% 0.29/0.50 nonempty = 1
% 0.29/0.50 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.29/0.50 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 0.29/0.50
% 0.29/0.50
% 0.29/0.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.29/0.50 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.29/0.50
% 0.29/0.50 RuleSystem INPUT:
% 0.29/0.50
% 0.29/0.50 Initial Rules:
% 0.29/0.50 #0: input, references = 4, size of lhs = 3:
% 0.29/0.50 P_btrue-{F}(V0), P_impl-{F}(V0,V1,V2), V2 == V1 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #1: input, references = 4, size of lhs = 4:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_impl-{F}(V1,V2,V3), V3 == V0 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #2: input, references = 4, size of lhs = 5:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_x2-{F}(V2,V3,V4), V4 == V3 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #3: input, references = 5, size of lhs = 8:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_s-{F}(V4,V5), P_x2-{F}(V5,V3,V6), P_x2-{F}(V4,V3,V7), P_s-{F}(V7,V8), V6 == V8 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #4: input, references = 6, size of lhs = 9:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eq2-{F}(V0,V1,V3), P_plus_not_idem-{F}(V4,V5), P_x2-{F}(V4,V4,V6), P_eq-{F}(V6,V4,V7), P_impl-{F}(V7,V3,V8), V5 == V8 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #5: input, references = 4, size of lhs = 6:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eq2-{F}(V0,V1,V3), P_eq2-{F}(V1,V0,V4), V4 == V1 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #6: input, references = 4, size of lhs = 6:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eq2-{F}(V0,V1,V3), P_eq2-{F}(V1,V0,V4), V3 == V1 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #7: input, references = 3, size of lhs = 10:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eq2-{F}(V0,V1,V3), P_eq2-{F}(V1,V0,V4), P_s-{F}(V6,V7), P_s-{F}(V5,V8), P_eq-{F}(V7,V8,V9), P_eq-{F}(V6,V5,V10), V9 == V10 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #8: input, references = 4, size of lhs = 8:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eq2-{F}(V0,V1,V3), P_eq2-{F}(V1,V0,V4), P_s-{F}(V5,V6), P_eq-{F}(V2,V6,V7), V7 == V1 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #9: input, references = 4, size of lhs = 8:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eq2-{F}(V0,V1,V3), P_eq2-{F}(V1,V0,V4), P_s-{F}(V5,V6), P_eq-{F}(V6,V2,V7), V7 == V1 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #10: input, references = 4, size of lhs = 7:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eq2-{F}(V0,V1,V3), P_eq2-{F}(V1,V0,V4), P_eq-{F}(V5,V5,V6), V6 == V0 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #11: input, references = 4, size of lhs = 7:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eq2-{F}(V0,V1,V3), P_eq2-{F}(V1,V0,V4), P_eq2-{F}(V5,V5,V6), V6 == V0 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #12: input, references = 4, size of lhs = 7:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eq2-{F}(V0,V1,V3), P_eq2-{F}(V1,V0,V4), P_plus_not_idem-{F}(V5,V6), P_eq2-{F}(V6,V1,V0) | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #13: input, references = 6, size of lhs = 2:
% 0.29/0.50 #-{F} V0, #-{F} V1 | EXISTS V2: P_impl-{T}(V0,V1,V2)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #14: input, references = 4, size of lhs = 0:
% 0.29/0.50 FALSE | EXISTS V0: P_btrue-{T}(V0)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #15: input, references = 4, size of lhs = 0:
% 0.29/0.50 FALSE | EXISTS V0: P_bfalse-{T}(V0)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #16: input, references = 5, size of lhs = 2:
% 0.29/0.50 #-{F} V0, #-{F} V1 | EXISTS V2: P_x2-{T}(V0,V1,V2)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #17: input, references = 4, size of lhs = 0:
% 0.29/0.50 FALSE | EXISTS V0: P_z-{T}(V0)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #18: input, references = 4, size of lhs = 1:
% 0.29/0.50 #-{F} V0 | EXISTS V1: P_s-{T}(V0,V1)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #19: input, references = 5, size of lhs = 1:
% 0.29/0.50 #-{F} V0 | EXISTS V1: P_plus_not_idem-{T}(V0,V1)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #20: input, references = 5, size of lhs = 2:
% 0.29/0.50 #-{F} V0, #-{F} V1 | EXISTS V2: P_eq-{T}(V0,V1,V2)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #21: input, references = 8, size of lhs = 2:
% 0.29/0.50 #-{F} V0, #-{F} V1 | EXISTS V2: P_eq2-{T}(V0,V1,V2)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 number of initial rules = 22
% 0.29/0.50
% 0.29/0.50 Simplifiers:
% 0.29/0.50 #22: unsound, references = 3, size of lhs = 3:
% 0.29/0.50 P_impl-{F}(V0,V1,V2), P_impl-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #23: unsound, references = 3, size of lhs = 3:
% 0.29/0.50 P_btrue-{F}(V0), P_btrue-{F}(V1), V0 == V1 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #24: unsound, references = 3, size of lhs = 3:
% 0.29/0.50 P_bfalse-{F}(V0), P_bfalse-{F}(V1), V0 == V1 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #25: unsound, references = 3, size of lhs = 3:
% 0.29/0.50 P_x2-{F}(V0,V1,V2), P_x2-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #26: unsound, references = 3, size of lhs = 3:
% 0.29/0.50 P_z-{F}(V0), P_z-{F}(V1), V0 == V1 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #27: unsound, references = 3, size of lhs = 3:
% 0.29/0.50 P_s-{F}(V0,V1), P_s-{F}(V0,V3), V1 == V3 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #28: unsound, references = 3, size of lhs = 3:
% 0.29/0.50 P_plus_not_idem-{F}(V0,V1), P_plus_not_idem-{F}(V0,V3), V1 == V3 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #29: unsound, references = 3, size of lhs = 3:
% 0.29/0.50 P_eq-{F}(V0,V1,V2), P_eq-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #30: unsound, references = 3, size of lhs = 3:
% 0.29/0.50 P_eq2-{F}(V0,V1,V2), P_eq2-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 number of simplifiers = 9
% 0.29/0.50
% 0.29/0.50 Learnt:
% 0.29/0.50 #32: exists( #13, #0 ), references = 2, size of lhs = 2:
% 0.29/0.50 P_btrue-{F}(V0), #-{F} V1 | P_impl-{T}(V0,V1,V1)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #34: exists( #16, #2 ), references = 2, size of lhs = 4:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), #-{F} V3 | P_x2-{T}(V2,V3,V3)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #36: exists( #18, #3 ), references = 1, size of lhs = 6:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_s-{F}(V3,V4), P_x2-{F}(V4,V5,V6), P_x2-{F}(V3,V5,V7) | P_s-{T}(V7,V6)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #38: exists( #13, #1 ), references = 1, size of lhs = 3:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), #-{F} V2 | P_impl-{T}(V1,V2,V0)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #42: mergings( V3 == V0; #40 ), references = 3, size of lhs = 6:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_plus_not_idem-{F}(V3,V4), P_x2-{F}(V3,V3,V5), P_eq-{F}(V5,V3,V0) | P_eq2-{T}(V0,V1,V4)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #44: exists( #13, #4 ), references = 1, size of lhs = 7:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eq2-{F}(V0,V1,V3), P_plus_not_idem-{F}(V4,V5), P_x2-{F}(V4,V4,V6), P_eq-{F}(V6,V4,V7) | P_impl-{T}(V7,V3,V5)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #48: exists( #21, #8 ), references = 2, size of lhs = 7:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eq2-{F}(V0,V1,V3), P_s-{F}(V4,V5), P_eq-{F}(V2,V5,V6), V6 == V1 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #49: exists( #21, #10 ), references = 2, size of lhs = 6:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eq2-{F}(V0,V1,V3), P_eq-{F}(V4,V4,V5), V5 == V0 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #50: exists( #21, #11 ), references = 2, size of lhs = 6:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eq2-{F}(V0,V1,V3), P_eq2-{F}(V4,V4,V5), V5 == V0 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #57: exists( #21, #49 ), references = 1, size of lhs = 5:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eq-{F}(V3,V3,V4), V4 == V0 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #58: exists( #21, #50 ), references = 2, size of lhs = 5:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eq2-{F}(V3,V3,V4), V4 == V0 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #59: exists( #21, #48 ), references = 2, size of lhs = 6:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_s-{F}(V3,V4), P_eq-{F}(V2,V4,V5), V5 == V1 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #61: exists( #20, #54 ), references = 2, size of lhs = 4:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), #-{F} V3 | P_eq-{T}(V3,V3,V0)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #63: exists( #21, #58 ), references = 2, size of lhs = 4:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), #-{F} V3 | P_eq2-{T}(V3,V3,V0)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #66: exists( #16, #3 ), references = 1, size of lhs = 6:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_s-{F}(V3,V4), P_x2-{F}(V3,V5,V6), P_s-{F}(V6,V7) | P_x2-{T}(V4,V5,V7)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #68: exists( #19, #4 ), references = 1, size of lhs = 7:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eq2-{F}(V0,V1,V3), P_x2-{F}(V4,V4,V5), P_eq-{F}(V5,V4,V6), P_impl-{F}(V6,V3,V7) | P_plus_not_idem-{T}(V4,V7)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #72: exists( #20, #59 ), references = 1, size of lhs = 4:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_s-{F}(V3,V4) | P_eq-{T}(V2,V4,V1)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #76: exists( #21, #6 ), references = 2, size of lhs = 5:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_eq2-{F}(V0,V1,V3), V3 == V1 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #78: mergings( V4 == V0; #75 ), references = 1, size of lhs = 7:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_eq2-{F}(V0,V1,V1), P_z-{F}(V2), P_s-{F}(V3,V4), P_eq-{F}(V4,V2,V5), V5 == V1 | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #80: mergings( V4 == V0; #73 ), references = 2, size of lhs = 4:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_eq2-{F}(V0,V1,V1), P_z-{F}(V2) | P_eq2-{T}(V1,V0,V1)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #89: mergings( V2 == V5; #87 ), references = 1, size of lhs = 5:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1), P_z-{F}(V2), P_x2-{F}(V3,V3,V4), P_eq-{F}(V4,V3,V0) | P_plus_not_idem-{T}(V3,V1)
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #101: mergings( V1 == V5, V2 == V3, V3 == V4, V4 == V6; #96 ), references = 1, size of lhs = 2:
% 0.29/0.50 P_btrue-{F}(V0), P_bfalse-{F}(V1) | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #104: mergings( V1 == V2; #102 ), references = 1, size of lhs = 1:
% 0.29/0.50 P_btrue-{F}(V0) | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 #106: exists( #14, #102 ), references = 1, size of lhs = 0:
% 0.29/0.50 FALSE | FALSE
% 0.29/0.50 (used 0 times, uses = {})
% 0.29/0.50
% 0.29/0.50 number of learnt formulas = 24
% 0.29/0.50
% 0.29/0.50
% 0.29/0.50 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.29/0.50
% 0.29/0.50 randbase = 1
%------------------------------------------------------------------------------