%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:05:42 PM UTC 2026
% Result : Unsatisfiable 0.55s 0.83s
% Output : Refutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Fri Sep 4 19:50:27 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.55/0.83 GeoParameters:
% 0.55/0.83
% 0.55/0.83 tptp_input = 1
% 0.55/0.83 tptp_output = 0
% 0.55/0.83 nonempty = 1
% 0.55/0.83 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.83 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 0.55/0.83
% 0.55/0.83
% 0.55/0.83 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.83 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.83
% 0.55/0.83 RuleSystem INPUT:
% 0.55/0.83
% 0.55/0.83 Initial Rules:
% 0.55/0.83 #0: input, references = 4, size of lhs = 3:
% 0.55/0.83 P_truth-{F}(V0), P_implies-{F}(V0,V1,V2), V2 == V1 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #1: input, references = 7, size of lhs = 7:
% 0.55/0.83 P_truth-{F}(V0), P_implies-{F}(V1,V2,V4), P_implies-{F}(V2,V3,V5), P_implies-{F}(V1,V3,V6), P_implies-{F}(V5,V6,V7), P_implies-{F}(V4,V7,V8), V8 == V0 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #2: input, references = 4, size of lhs = 6:
% 0.55/0.83 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3), P_implies-{F}(V3,V2,V4), P_implies-{F}(V2,V1,V5), P_implies-{F}(V5,V1,V6), V4 == V6 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #3: input, references = 3, size of lhs = 7:
% 0.55/0.83 P_truth-{F}(V0), P_not-{F}(V1,V3), P_not-{F}(V2,V4), P_implies-{F}(V3,V4,V5), P_implies-{F}(V2,V1,V6), P_implies-{F}(V5,V6,V7), V7 == V0 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #4: input, references = 5, size of lhs = 5:
% 0.55/0.83 P_truth-{F}(V0), P_big_V-{F}(V1,V2,V3), P_implies-{F}(V1,V2,V4), P_implies-{F}(V4,V2,V5), V3 == V5 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #5: input, references = 5, size of lhs = 7:
% 0.55/0.83 P_truth-{F}(V0), P_big_hat-{F}(V1,V2,V3), P_not-{F}(V1,V4), P_not-{F}(V2,V5), P_big_V-{F}(V4,V5,V6), P_not-{F}(V6,V7), V3 == V7 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #6: input, references = 7, size of lhs = 4:
% 0.55/0.83 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3), ordered-{F}(V1,V2), V3 == V0 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #7: input, references = 6, size of lhs = 2:
% 0.55/0.83 P_truth-{F}(V0), P_implies-{F}(V1,V2,V0) | ordered-{T}(V1,V2)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #8: input, references = 6, size of lhs = 4:
% 0.55/0.83 P_truth-{F}(V0), ordered-{F}(V1,V2), P_implies-{F}(V1,V3,V4), P_implies-{F}(V2,V3,V5) | ordered-{T}(V4,V5)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #9: input, references = 3, size of lhs = 4:
% 0.55/0.83 P_truth-{F}(V0), ordered-{F}(V1,V2), P_implies-{F}(V3,V1,V4), P_implies-{F}(V3,V2,V5) | ordered-{T}(V4,V5)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #10: input, references = 3, size of lhs = 4:
% 0.55/0.83 P_truth-{F}(V0), P_implies-{F}(V2,V3,V4), P_implies-{F}(V1,V3,V5), ordered-{F}(V1,V4) | ordered-{T}(V2,V5)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #11: input, references = 3, size of lhs = 4:
% 0.55/0.83 P_truth-{F}(V0), P_implies-{F}(V1,V3,V4), P_implies-{F}(V2,V3,V5), ordered-{F}(V2,V4) | ordered-{T}(V1,V5)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #12: input, references = 5, size of lhs = 7:
% 0.55/0.83 P_truth-{F}(V0), P_big_V-{F}(V1,V2,V3), P_not-{F}(V3,V4), P_not-{F}(V1,V5), P_not-{F}(V2,V6), P_big_hat-{F}(V5,V6,V7), V4 == V7 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #13: input, references = 4, size of lhs = 7:
% 0.55/0.83 P_truth-{F}(V0), P_big_hat-{F}(V1,V2,V3), P_not-{F}(V3,V4), P_not-{F}(V1,V5), P_not-{F}(V2,V6), P_big_V-{F}(V5,V6,V7), V4 == V7 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #14: input, references = 4, size of lhs = 7:
% 0.55/0.83 P_truth-{F}(V0), P_big_V-{F}(V1,V2,V4), P_implies-{F}(V4,V3,V5), P_implies-{F}(V1,V3,V6), P_implies-{F}(V2,V3,V7), P_big_hat-{F}(V6,V7,V8), V5 == V8 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #15: input, references = 5, size of lhs = 7:
% 0.55/0.83 P_truth-{F}(V0), P_big_hat-{F}(V2,V3,V4), P_implies-{F}(V1,V4,V5), P_implies-{F}(V1,V2,V6), P_implies-{F}(V1,V3,V7), P_big_hat-{F}(V6,V7,V8), V5 == V8 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #16: input, references = 4, size of lhs = 6:
% 0.55/0.83 P_truth-{F}(V0), P_x-{F}(V1), P_y-{F}(V2), P_implies-{F}(V1,V2,V3), P_implies-{F}(V2,V1,V4), P_big_V-{F}(V3,V4,V0) | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #17: input, references = 9, size of lhs = 2:
% 0.55/0.83 #-{F} V0, #-{F} V1 | EXISTS V2: P_implies-{T}(V0,V1,V2)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #18: input, references = 4, size of lhs = 0:
% 0.55/0.83 FALSE | EXISTS V0: P_truth-{T}(V0)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #19: input, references = 4, size of lhs = 1:
% 0.55/0.83 #-{F} V0 | EXISTS V1: P_not-{T}(V0,V1)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #20: input, references = 4, size of lhs = 2:
% 0.55/0.83 #-{F} V0, #-{F} V1 | EXISTS V2: P_big_V-{T}(V0,V1,V2)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #21: input, references = 5, size of lhs = 2:
% 0.55/0.83 #-{F} V0, #-{F} V1 | EXISTS V2: P_big_hat-{T}(V0,V1,V2)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #22: input, references = 4, size of lhs = 0:
% 0.55/0.83 FALSE | EXISTS V0: P_x-{T}(V0)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #23: input, references = 4, size of lhs = 0:
% 0.55/0.83 FALSE | EXISTS V0: P_y-{T}(V0)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 number of initial rules = 24
% 0.55/0.83
% 0.55/0.83 Simplifiers:
% 0.55/0.83 #24: unsound, references = 3, size of lhs = 3:
% 0.55/0.83 P_implies-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #25: unsound, references = 3, size of lhs = 3:
% 0.55/0.83 P_truth-{F}(V0), P_truth-{F}(V1), V0 == V1 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #26: unsound, references = 3, size of lhs = 3:
% 0.55/0.83 P_not-{F}(V0,V1), P_not-{F}(V0,V3), V1 == V3 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #27: unsound, references = 3, size of lhs = 3:
% 0.55/0.83 P_big_V-{F}(V0,V1,V2), P_big_V-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #28: unsound, references = 3, size of lhs = 3:
% 0.55/0.83 P_big_hat-{F}(V0,V1,V2), P_big_hat-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #29: unsound, references = 3, size of lhs = 3:
% 0.55/0.83 P_x-{F}(V0), P_x-{F}(V1), V0 == V1 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #30: unsound, references = 3, size of lhs = 3:
% 0.55/0.83 P_y-{F}(V0), P_y-{F}(V1), V0 == V1 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 number of simplifiers = 7
% 0.55/0.83
% 0.55/0.83 Learnt:
% 0.55/0.83 #32: exists( #17, #0 ), references = 4, size of lhs = 2:
% 0.55/0.83 P_truth-{F}(V0), #-{F} V1 | P_implies-{T}(V0,V1,V1)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #35: exists( #20, #4 ), references = 3, size of lhs = 3:
% 0.55/0.83 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3), P_implies-{F}(V3,V2,V4) | P_big_V-{T}(V1,V2,V4)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #36: exists( #20, #13 ), references = 1, size of lhs = 5:
% 0.55/0.83 P_truth-{F}(V0), P_not-{F}(V1,V2), P_big_hat-{F}(V1,V3,V4), P_not-{F}(V4,V5), P_not-{F}(V3,V6) | P_big_V-{T}(V2,V6,V5)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #39: exists( #21, #14 ), references = 2, size of lhs = 5:
% 0.55/0.83 P_truth-{F}(V0), P_big_V-{F}(V1,V2,V3), P_implies-{F}(V3,V4,V5), P_implies-{F}(V1,V4,V6), P_implies-{F}(V2,V4,V7) | P_big_hat-{T}(V6,V7,V5)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #41: exists( #17, #6 ), references = 2, size of lhs = 2:
% 0.55/0.83 P_truth-{F}(V0), ordered-{F}(V1,V2) | P_implies-{T}(V1,V2,V0)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #48: exists( #21, #5 ), references = 1, size of lhs = 5:
% 0.55/0.83 P_truth-{F}(V0), P_not-{F}(V1,V2), P_not-{F}(V3,V4), P_big_V-{F}(V2,V4,V5), P_not-{F}(V5,V6) | P_big_hat-{T}(V1,V3,V6)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #49: exists( #21, #12 ), references = 1, size of lhs = 5:
% 0.55/0.83 P_truth-{F}(V0), P_not-{F}(V1,V2), P_big_V-{F}(V1,V3,V4), P_not-{F}(V4,V5), P_not-{F}(V3,V6) | P_big_hat-{T}(V2,V6,V5)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #56: exists( #19, #5 ), references = 1, size of lhs = 5:
% 0.55/0.83 P_truth-{F}(V0), P_not-{F}(V1,V2), P_big_hat-{F}(V1,V3,V4), P_not-{F}(V3,V5), P_big_V-{F}(V2,V5,V6) | P_not-{T}(V6,V4)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #57: exists( #19, #12 ), references = 1, size of lhs = 5:
% 0.55/0.83 P_truth-{F}(V0), P_not-{F}(V1,V2), P_big_V-{F}(V1,V3,V4), P_not-{F}(V3,V5), P_big_hat-{F}(V2,V5,V6) | P_not-{T}(V4,V6)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #59: exists( #17, #15 ), references = 1, size of lhs = 5:
% 0.55/0.83 P_truth-{F}(V0), P_big_hat-{F}(V1,V2,V3), P_implies-{F}(V4,V1,V5), P_implies-{F}(V4,V2,V6), P_big_hat-{F}(V5,V6,V7) | P_implies-{T}(V4,V3,V7)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #73: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7; #68 ), references = 1, size of lhs = 5:
% 0.55/0.83 P_truth-{F}(V0), ordered-{F}(V1,V1), P_implies-{F}(V1,V2,V0), P_big_hat-{F}(V3,V2,V4), P_implies-{F}(V1,V4,V5) | P_implies-{T}(V1,V3,V5)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #79: exists( #17, #2 ), references = 1, size of lhs = 4:
% 0.55/0.83 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3), P_implies-{F}(V3,V2,V4), P_implies-{F}(V2,V1,V5) | P_implies-{T}(V5,V1,V4)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #80: exists( #17, #4 ), references = 1, size of lhs = 3:
% 0.55/0.83 P_truth-{F}(V0), P_big_V-{F}(V1,V2,V3), P_implies-{F}(V1,V2,V4) | P_implies-{T}(V4,V2,V3)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #81: exists( #17, #1 ), references = 1, size of lhs = 5:
% 0.55/0.83 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3), P_implies-{F}(V2,V4,V5), P_implies-{F}(V1,V4,V6), P_implies-{F}(V5,V6,V7) | P_implies-{T}(V3,V7,V0)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #85: mergings( V3 == V4; #83 ), references = 1, size of lhs = 5:
% 0.55/0.83 P_truth-{F}(V0), P_implies-{F}(V1,V2,V2), P_implies-{F}(V1,V3,V3), P_implies-{F}(V3,V2,V4), P_implies-{F}(V4,V2,V3) | P_implies-{T}(V2,V3,V0)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #95: exists( #18, #93 ), references = 5, size of lhs = 1:
% 0.55/0.83 #-{F} V0 | P_truth-{T}(V0)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #100: exists( #22, #96 ), references = 1, size of lhs = 2:
% 0.55/0.83 ordered-{F}(V0,V1), P_implies-{F}(V0,V1,V2) | P_x-{T}(V2)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #101: exists( #22, #97 ), references = 1, size of lhs = 5:
% 0.55/0.83 P_implies-{F}(V0,V1,V2), P_implies-{F}(V1,V3,V4), P_implies-{F}(V0,V3,V5), P_implies-{F}(V4,V5,V6), P_implies-{F}(V2,V6,V7) | P_x-{T}(V7)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #106: exists( #23, #102 ), references = 1, size of lhs = 2:
% 0.55/0.83 ordered-{F}(V0,V1), P_implies-{F}(V0,V1,V2) | P_y-{T}(V2)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #107: exists( #23, #103 ), references = 1, size of lhs = 5:
% 0.55/0.83 P_implies-{F}(V0,V1,V2), P_implies-{F}(V1,V3,V4), P_implies-{F}(V0,V3,V5), P_implies-{F}(V4,V5,V6), P_implies-{F}(V2,V6,V7) | P_y-{T}(V7)
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 #114: #94+#32+#7+#35+#98+#104+#16, references = 1, size of lhs = 1:
% 0.55/0.83 #-{F} V0 | FALSE
% 0.55/0.83 (used 0 times, uses = {})
% 0.55/0.83
% 0.55/0.83 number of learnt formulas = 21
% 0.55/0.83
% 0.55/0.83
% 0.55/0.83 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.55/0.83
% 0.55/0.83 randbase = 1
%------------------------------------------------------------------------------