TSTP Solution File: GEO111+1 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : GEO111+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n009.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 : Mon Mar 25 14:11:39 EDT 2024
% Result : Theorem 29.01s 29.19s
% Output : Proof 29.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO111+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Mar 21 10:59:44 EDT 2024
% 0.14/0.35 % CPUTime :
% 29.01/29.19 % SZS status Theorem for theBenchmark
% 29.01/29.19 % SZS output start Proof for theBenchmark
% 29.01/29.19
% 29.01/29.19 % Formula: part_of_defn ( axiom ) converted to clauses:
% 29.01/29.19 cnf(part_of_defn-1, axiom, ( ~part_of(_u4, _u6) | ~incident_c(_u0, _u4) | incident_c(_u0, _u6) )).
% 29.01/29.19 cnf(part_of_defn-2, axiom, ( part_of(_u5, _u7) | incident_c(skolem1(_u7, _u5), _u5) )).
% 29.01/29.19 cnf(part_of_defn-3, axiom, ( part_of(_u5, _u7) | ~incident_c(skolem1(_u7, _u5), _u7) )).
% 29.01/29.19
% 29.01/29.19 % Formula: sum_defn ( axiom ) converted to clauses:
% 29.01/29.19 cnf(sum_defn-1, axiom, ( ( _u21 != sum(_u19, _u17)) | ~incident_c(_u13, _u21) | incident_c(_u13, _u19) | incident_c(_u13, _u17) )).
% 29.01/29.19 cnf(sum_defn-2, axiom, ( ( _u21 != sum(_u19, _u17)) | incident_c(_u14, _u21) | ~incident_c(_u14, _u19) )).
% 29.01/29.19 cnf(sum_defn-3, axiom, ( ( _u21 != sum(_u19, _u17)) | incident_c(_u14, _u21) | ~incident_c(_u14, _u17) )).
% 29.01/29.19 cnf(sum_defn-4, axiom, ( ( _u22 = sum(_u20, _u18)) | incident_c(skolem2(_u22, _u20, _u18), _u22) | incident_c(skolem3(_u22, _u20, _u18), _u20) | incident_c(skolem3(_u22, _u20, _u18), _u18) )).
% 29.01/29.19 cnf(sum_defn-5, axiom, ( ( _u22 = sum(_u20, _u18)) | incident_c(skolem2(_u22, _u20, _u18), _u22) | ~incident_c(skolem3(_u22, _u20, _u18), _u22) )).
% 29.01/29.19 cnf(sum_defn-6, axiom, ( ( _u22 = sum(_u20, _u18)) | incident_c(skolem3(_u22, _u20, _u18), _u20) | incident_c(skolem3(_u22, _u20, _u18), _u18) | ~incident_c(skolem2(_u22, _u20, _u18), _u20) )).
% 29.01/29.19 cnf(sum_defn-7, axiom, ( ( _u22 = sum(_u20, _u18)) | incident_c(skolem3(_u22, _u20, _u18), _u20) | incident_c(skolem3(_u22, _u20, _u18), _u18) | ~incident_c(skolem2(_u22, _u20, _u18), _u18) )).
% 29.01/29.19 cnf(sum_defn-8, axiom, ( ( _u22 = sum(_u20, _u18)) | ~incident_c(skolem3(_u22, _u20, _u18), _u22) | ~incident_c(skolem2(_u22, _u20, _u18), _u20) )).
% 29.01/29.19 cnf(sum_defn-9, axiom, ( ( _u22 = sum(_u20, _u18)) | ~incident_c(skolem3(_u22, _u20, _u18), _u22) | ~incident_c(skolem2(_u22, _u20, _u18), _u18) )).
% 29.01/29.19
% 29.01/29.19 % Formula: end_point_defn ( axiom ) converted to clauses:
% 29.01/29.19 cnf(end_point_defn-1, axiom, ( ~end_point(_u31, _u29) | incident_c(_u31, _u29) )).
% 29.01/29.19 cnf(end_point_defn-2, axiom, ( ~end_point(_u31, _u29) | ~part_of(_u24, _u29) | ~part_of(_u23, _u29) | ~incident_c(_u31, _u24) | ~incident_c(_u31, _u23) | part_of(_u24, _u23) | part_of(_u23, _u24) )).
% 29.01/29.19 cnf(end_point_defn-3, axiom, ( end_point(_u32, _u30) | ~incident_c(_u32, _u30) | part_of(skolem4(_u32, _u30), _u30) )).
% 29.01/29.19 cnf(end_point_defn-4, axiom, ( end_point(_u32, _u30) | ~incident_c(_u32, _u30) | part_of(skolem5(_u32, _u30), _u30) )).
% 29.01/29.19 cnf(end_point_defn-5, axiom, ( end_point(_u32, _u30) | ~incident_c(_u32, _u30) | incident_c(_u32, skolem4(_u32, _u30)) )).
% 29.01/29.19 cnf(end_point_defn-6, axiom, ( end_point(_u32, _u30) | ~incident_c(_u32, _u30) | incident_c(_u32, skolem5(_u32, _u30)) )).
% 29.01/29.19 cnf(end_point_defn-7, axiom, ( end_point(_u32, _u30) | ~incident_c(_u32, _u30) | ~part_of(skolem4(_u32, _u30), skolem5(_u32, _u30)) )).
% 29.01/29.19 cnf(end_point_defn-8, axiom, ( end_point(_u32, _u30) | ~incident_c(_u32, _u30) | ~part_of(skolem5(_u32, _u30), skolem4(_u32, _u30)) )).
% 29.01/29.19
% 29.01/29.19 % Formula: inner_point_defn ( axiom ) converted to clauses:
% 29.01/29.19 cnf(inner_point_defn-1, axiom, ( ~inner_point(_u37, _u35) | incident_c(_u37, _u35) )).
% 29.01/29.19 cnf(inner_point_defn-2, axiom, ( ~inner_point(_u37, _u35) | ~end_point(_u37, _u35) )).
% 29.01/29.19 cnf(inner_point_defn-3, axiom, ( ~incident_c(_u38, _u36) | end_point(_u38, _u36) | inner_point(_u38, _u36) )).
% 29.01/29.19
% 29.01/29.19 % Formula: meet_defn ( axiom ) converted to clauses:
% 29.01/29.19 cnf(meet_defn-1, axiom, ( ~meet(_u48, _u46, _u44) | incident_c(_u48, _u46) )).
% 29.01/29.19 cnf(meet_defn-2, axiom, ( ~meet(_u48, _u46, _u44) | incident_c(_u48, _u44) )).
% 29.01/29.19 cnf(meet_defn-3, axiom, ( ~meet(_u48, _u46, _u44) | ~incident_c(_u39, _u46) | ~incident_c(_u39, _u44) | end_point(_u39, _u46) )).
% 29.01/29.19 cnf(meet_defn-4, axiom, ( ~meet(_u48, _u46, _u44) | ~incident_c(_u39, _u46) | ~incident_c(_u39, _u44) | end_point(_u39, _u44) )).
% 29.01/29.19 cnf(meet_defn-5, axiom, ( meet(_u49, _u47, _u45) | ~incident_c(_u49, _u47) | ~incident_c(_u49, _u45) | incident_c(skolem6(_u49, _u47, _u45), _u47) )).
% 29.01/29.19 cnf(meet_defn-6, axiom, ( meet(_u49, _u47, _u45) | ~incident_c(_u49, _u47) | ~incident_c(_u49, _u45) | incident_c(skolem6(_u49, _u47, _u45), _u45) )).
% 29.01/29.19 cnf(meet_defn-7, axiom, ( meet(_u49, _u47, _u45) | ~incident_c(_u49, _u47) | ~incident_c(_u49, _u45) | ~end_point(skolem6(_u49, _u47, _u45), _u47) | ~end_point(skolem6(_u49, _u47, _u45), _u45) )).
% 29.01/29.19
% 29.01/29.19 % Formula: closed_defn ( axiom ) converted to clauses:
% 29.01/29.19 cnf(closed_defn-1, axiom, ( ~closed(_u53) | ~end_point(_u50, _u53) )).
% 29.01/29.19 cnf(closed_defn-2, axiom, ( end_point(skolem7(_u54), _u54) | closed(_u54) )).
% 29.01/29.19
% 29.01/29.19 % Formula: open_defn ( axiom ) converted to clauses:
% 29.01/29.19 cnf(open_defn-1, axiom, ( ~open(_u58) | end_point(skolem8(_u58), _u58) )).
% 29.01/29.19 cnf(open_defn-2, axiom, ( ~end_point(_u56, _u59) | open(_u59) )).
% 29.01/29.19
% 29.01/29.19 % Formula: c1 ( axiom ) converted to clauses:
% 29.01/29.19 cnf(c1-1, axiom, ( ~part_of(_u60, _u61) | ( _u60 = _u61) | open(_u60) )).
% 29.01/29.19
% 29.01/29.19 % Formula: c2 ( axiom ) converted to clauses:
% 29.01/29.19 cnf(c2-1, axiom, ( ~part_of(_u65, _u66) | ~part_of(_u64, _u66) | ~part_of(_u63, _u66) | ~end_point(_u62, _u65) | ~end_point(_u62, _u64) | ~end_point(_u62, _u63) | part_of(_u64, _u63) | part_of(_u63, _u64) | part_of(_u65, _u64) | part_of(_u64, _u65) | part_of(_u65, _u63) | part_of(_u63, _u65) )).
% 29.01/29.19
% 29.01/29.19 % Formula: c3 ( axiom ) converted to clauses:
% 29.01/29.19 cnf(c3-1, axiom, ( inner_point(skolem9(_u68), _u68) )).
% 29.01/29.19
% 29.01/29.19 % Formula: c4 ( axiom ) converted to clauses:
% 29.01/29.19 cnf(c4-1, axiom, ( ~inner_point(_u71, _u72) | meet(_u71, skolem10(_u72, _u71), skolem11(_u72, _u71)) )).
% 29.01/29.19 cnf(c4-2, axiom, ( ~inner_point(_u71, _u72) | ( _u72 = sum(skolem10(_u72, _u71), skolem11(_u72, _u71))) )).
% 29.01/29.19
% 29.01/29.19 % Formula: c5 ( axiom ) converted to clauses:
% 29.01/29.19 cnf(c5-1, axiom, ( ~end_point(_u75, _u76) | ~end_point(_u74, _u76) | ~end_point(_u73, _u76) | ( _u75 = _u74) | ( _u75 = _u73) | ( _u74 = _u73) )).
% 29.01/29.19
% 29.01/29.19 % Formula: c6 ( axiom ) converted to clauses:
% 29.01/29.19 cnf(c6-1, axiom, ( ~end_point(_u78, _u79) | end_point(skolem12(_u79, _u78), _u79) )).
% 29.01/29.19 cnf(c6-2, axiom, ( ~end_point(_u78, _u79) | ( _u78 != skolem12(_u79, _u78)) )).
% 29.01/29.19
% 29.01/29.19 % Formula: c7 ( axiom ) converted to clauses:
% 29.01/29.19 cnf(c7-1, axiom, ( ~end_point(_u80, _u83) | meet(_u80, _u83, _u82) | ~closed(_u84) | ( _u84 != sum(_u83, _u82)) | ~meet(_u81, _u83, _u82) )).
% 29.01/29.19
% 29.01/29.19 % Formula: c8 ( axiom ) converted to clauses:
% 29.01/29.19 cnf(c8-1, axiom, ( ~meet(_u85, _u88, _u87) | ( skolem13(_u88, _u87) = sum(_u88, _u87)) )).
% 29.01/29.19
% 29.01/29.19 % Formula: c9 ( axiom ) converted to clauses:
% 29.01/29.19 cnf(c9-1, axiom, ( ( _u91 = _u90) | incident_c(skolem14(_u91, _u90), _u91) | incident_c(skolem15(_u91, _u90), _u90) )).
% 29.01/29.19 cnf(c9-2, axiom, ( ( _u91 = _u90) | incident_c(skolem14(_u91, _u90), _u91) | ~incident_c(skolem15(_u91, _u90), _u91) )).
% 29.01/29.19 cnf(c9-3, axiom, ( ( _u91 = _u90) | ~incident_c(skolem14(_u91, _u90), _u90) | incident_c(skolem15(_u91, _u90), _u90) )).
% 29.01/29.19 cnf(c9-4, axiom, ( ( _u91 = _u90) | ~incident_c(skolem14(_u91, _u90), _u90) | ~incident_c(skolem15(_u91, _u90), _u91) )).
% 29.01/29.19
% 29.01/29.19 % Formula: between_c_defn ( axiom ) converted to clauses:
% 29.01/29.19 cnf(between_c_defn-1, axiom, ( ~between_c(_u106, _u104, _u102, _u100) | ( _u104 != _u100) )).
% 29.01/29.19 cnf(between_c_defn-2, axiom, ( ~between_c(_u106, _u104, _u102, _u100) | part_of(skolem16(_u106, _u104, _u102, _u100), _u106) )).
% 29.01/29.19 cnf(between_c_defn-3, axiom, ( ~between_c(_u106, _u104, _u102, _u100) | end_point(_u104, skolem16(_u106, _u104, _u102, _u100)) )).
% 29.01/29.19 cnf(between_c_defn-4, axiom, ( ~between_c(_u106, _u104, _u102, _u100) | end_point(_u100, skolem16(_u106, _u104, _u102, _u100)) )).
% 29.01/29.19 cnf(between_c_defn-5, axiom, ( ~between_c(_u106, _u104, _u102, _u100) | inner_point(_u102, skolem16(_u106, _u104, _u102, _u100)) )).
% 29.01/29.19 cnf(between_c_defn-6, axiom, ( ( _u105 = _u101) | ~part_of(_u95, _u107) | ~end_point(_u105, _u95) | ~end_point(_u101, _u95) | ~inner_point(_u103, _u95) | between_c(_u107, _u105, _u103, _u101) )).
% 29.01/29.19
% 29.01/29.19 % Formula: theorem_3_8_1 ( conjecture ) (definitionally) converted to clauses:
% 29.01/29.19 cnf(theorem_3_8_1-1, negated_conjecture, ( between_c(skolem17, skolem18, skolem19, skolem20) )).
% 29.01/29.19 cnf(theorem_3_8_1-2, negated_conjecture, ( ~incident_c(skolem18, skolem17) | ~incident_c(skolem19, skolem17) | ~incident_c(skolem20, skolem17) | ( skolem18 = skolem19) | ( skolem19 = skolem20) | ( skolem18 = skolem20) )).
% 29.01/29.19
% 29.01/29.19 % Problem matrix:
% 29.01/29.19 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 29.01/29.19 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 29.01/29.19 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 29.01/29.19 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( sum(__eqx_0, __eqx_1) = sum(__eqy_0, __eqy_1)) )).
% 29.01/29.19 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 29.01/29.19 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem2(__eqx_0, __eqx_1, __eqx_2) = skolem2(__eqy_0, __eqy_1, __eqy_2)) )).
% 29.01/29.19 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem3(__eqx_0, __eqx_1, __eqx_2) = skolem3(__eqy_0, __eqy_1, __eqy_2)) )).
% 29.01/29.19 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 29.01/29.19 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem5(__eqx_0, __eqx_1) = skolem5(__eqy_0, __eqy_1)) )).
% 29.01/29.19 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem6(__eqx_0, __eqx_1, __eqx_2) = skolem6(__eqy_0, __eqy_1, __eqy_2)) )).
% 29.01/29.19 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( skolem7(__eqx_0) = skolem7(__eqy_0)) )).
% 29.01/29.19 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( skolem8(__eqx_0) = skolem8(__eqy_0)) )).
% 29.01/29.19 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( skolem9(__eqx_0) = skolem9(__eqy_0)) )).
% 29.01/29.19 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem10(__eqx_0, __eqx_1) = skolem10(__eqy_0, __eqy_1)) )).
% 29.01/29.19 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem11(__eqx_0, __eqx_1) = skolem11(__eqy_0, __eqy_1)) )).
% 29.01/29.19 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem12(__eqx_0, __eqx_1) = skolem12(__eqy_0, __eqy_1)) )).
% 29.01/29.19 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem13(__eqx_0, __eqx_1) = skolem13(__eqy_0, __eqy_1)) )).
% 29.01/29.19 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem14(__eqx_0, __eqx_1) = skolem14(__eqy_0, __eqy_1)) )).
% 29.01/29.19 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem15(__eqx_0, __eqx_1) = skolem15(__eqy_0, __eqy_1)) )).
% 29.01/29.19 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( skolem16(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = skolem16(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 29.01/29.19 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~part_of(__eqx_0, __eqx_1) | part_of(__eqy_0, __eqy_1) )).
% 29.01/29.19 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~incident_c(__eqx_0, __eqx_1) | incident_c(__eqy_0, __eqy_1) )).
% 29.01/29.19 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~end_point(__eqx_0, __eqx_1) | end_point(__eqy_0, __eqy_1) )).
% 29.01/29.19 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~inner_point(__eqx_0, __eqx_1) | inner_point(__eqy_0, __eqy_1) )).
% 29.01/29.19 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~meet(__eqx_0, __eqx_1, __eqx_2) | meet(__eqy_0, __eqy_1, __eqy_2) )).
% 29.01/29.20 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ~closed(__eqx_0) | closed(__eqy_0) )).
% 29.01/29.20 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ~open(__eqx_0) | open(__eqy_0) )).
% 29.01/29.20 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ~between_c(__eqx_0, __eqx_1, __eqx_2, __eqx_3) | between_c(__eqy_0, __eqy_1, __eqy_2, __eqy_3) )).
% 29.01/29.20 cnf(matrix-28, plain, ( ~part_of(_u4, _u6) | ~incident_c(_u0, _u4) | incident_c(_u0, _u6) )).
% 29.01/29.20 cnf(matrix-29, plain, ( part_of(_u5, _u7) | incident_c(skolem1(_u7, _u5), _u5) )).
% 29.01/29.20 cnf(matrix-30, plain, ( part_of(_u5, _u7) | ~incident_c(skolem1(_u7, _u5), _u7) )).
% 29.01/29.20 cnf(matrix-31, plain, ( ( _u21 != sum(_u19, _u17)) | ~incident_c(_u13, _u21) | incident_c(_u13, _u19) | incident_c(_u13, _u17) )).
% 29.01/29.20 cnf(matrix-32, plain, ( ( _u21 != sum(_u19, _u17)) | incident_c(_u14, _u21) | ~incident_c(_u14, _u19) )).
% 29.01/29.20 cnf(matrix-33, plain, ( ( _u21 != sum(_u19, _u17)) | incident_c(_u14, _u21) | ~incident_c(_u14, _u17) )).
% 29.01/29.20 cnf(matrix-34, plain, ( ( _u22 = sum(_u20, _u18)) | incident_c(skolem2(_u22, _u20, _u18), _u22) | incident_c(skolem3(_u22, _u20, _u18), _u20) | incident_c(skolem3(_u22, _u20, _u18), _u18) )).
% 29.01/29.20 cnf(matrix-35, plain, ( ( _u22 = sum(_u20, _u18)) | incident_c(skolem2(_u22, _u20, _u18), _u22) | ~incident_c(skolem3(_u22, _u20, _u18), _u22) )).
% 29.01/29.20 cnf(matrix-36, plain, ( ( _u22 = sum(_u20, _u18)) | incident_c(skolem3(_u22, _u20, _u18), _u20) | incident_c(skolem3(_u22, _u20, _u18), _u18) | ~incident_c(skolem2(_u22, _u20, _u18), _u20) )).
% 29.01/29.20 cnf(matrix-37, plain, ( ( _u22 = sum(_u20, _u18)) | incident_c(skolem3(_u22, _u20, _u18), _u20) | incident_c(skolem3(_u22, _u20, _u18), _u18) | ~incident_c(skolem2(_u22, _u20, _u18), _u18) )).
% 29.01/29.20 cnf(matrix-38, plain, ( ( _u22 = sum(_u20, _u18)) | ~incident_c(skolem3(_u22, _u20, _u18), _u22) | ~incident_c(skolem2(_u22, _u20, _u18), _u20) )).
% 29.01/29.20 cnf(matrix-39, plain, ( ( _u22 = sum(_u20, _u18)) | ~incident_c(skolem3(_u22, _u20, _u18), _u22) | ~incident_c(skolem2(_u22, _u20, _u18), _u18) )).
% 29.01/29.20 cnf(matrix-40, plain, ( ~end_point(_u31, _u29) | incident_c(_u31, _u29) )).
% 29.01/29.20 cnf(matrix-41, plain, ( ~end_point(_u31, _u29) | ~part_of(_u24, _u29) | ~part_of(_u23, _u29) | ~incident_c(_u31, _u24) | ~incident_c(_u31, _u23) | part_of(_u24, _u23) | part_of(_u23, _u24) )).
% 29.01/29.20 cnf(matrix-42, plain, ( end_point(_u32, _u30) | ~incident_c(_u32, _u30) | part_of(skolem4(_u32, _u30), _u30) )).
% 29.01/29.20 cnf(matrix-43, plain, ( end_point(_u32, _u30) | ~incident_c(_u32, _u30) | part_of(skolem5(_u32, _u30), _u30) )).
% 29.01/29.20 cnf(matrix-44, plain, ( end_point(_u32, _u30) | ~incident_c(_u32, _u30) | incident_c(_u32, skolem4(_u32, _u30)) )).
% 29.01/29.20 cnf(matrix-45, plain, ( end_point(_u32, _u30) | ~incident_c(_u32, _u30) | incident_c(_u32, skolem5(_u32, _u30)) )).
% 29.01/29.20 cnf(matrix-46, plain, ( end_point(_u32, _u30) | ~incident_c(_u32, _u30) | ~part_of(skolem4(_u32, _u30), skolem5(_u32, _u30)) )).
% 29.01/29.20 cnf(matrix-47, plain, ( end_point(_u32, _u30) | ~incident_c(_u32, _u30) | ~part_of(skolem5(_u32, _u30), skolem4(_u32, _u30)) )).
% 29.01/29.20 cnf(matrix-48, plain, ( ~inner_point(_u37, _u35) | incident_c(_u37, _u35) )).
% 29.01/29.20 cnf(matrix-49, plain, ( ~inner_point(_u37, _u35) | ~end_point(_u37, _u35) )).
% 29.01/29.20 cnf(matrix-50, plain, ( ~incident_c(_u38, _u36) | end_point(_u38, _u36) | inner_point(_u38, _u36) )).
% 29.01/29.20 cnf(matrix-51, plain, ( ~meet(_u48, _u46, _u44) | incident_c(_u48, _u46) )).
% 29.01/29.20 cnf(matrix-52, plain, ( ~meet(_u48, _u46, _u44) | incident_c(_u48, _u44) )).
% 29.01/29.20 cnf(matrix-53, plain, ( ~meet(_u48, _u46, _u44) | ~incident_c(_u39, _u46) | ~incident_c(_u39, _u44) | end_point(_u39, _u46) )).
% 29.01/29.20 cnf(matrix-54, plain, ( ~meet(_u48, _u46, _u44) | ~incident_c(_u39, _u46) | ~incident_c(_u39, _u44) | end_point(_u39, _u44) )).
% 29.01/29.20 cnf(matrix-55, plain, ( meet(_u49, _u47, _u45) | ~incident_c(_u49, _u47) | ~incident_c(_u49, _u45) | incident_c(skolem6(_u49, _u47, _u45), _u47) )).
% 29.01/29.20 cnf(matrix-56, plain, ( meet(_u49, _u47, _u45) | ~incident_c(_u49, _u47) | ~incident_c(_u49, _u45) | incident_c(skolem6(_u49, _u47, _u45), _u45) )).
% 29.01/29.20 cnf(matrix-57, plain, ( meet(_u49, _u47, _u45) | ~incident_c(_u49, _u47) | ~incident_c(_u49, _u45) | ~end_point(skolem6(_u49, _u47, _u45), _u47) | ~end_point(skolem6(_u49, _u47, _u45), _u45) )).
% 29.01/29.20 cnf(matrix-58, plain, ( ~closed(_u53) | ~end_point(_u50, _u53) )).
% 29.01/29.20 cnf(matrix-59, plain, ( end_point(skolem7(_u54), _u54) | closed(_u54) )).
% 29.01/29.20 cnf(matrix-60, plain, ( ~open(_u58) | end_point(skolem8(_u58), _u58) )).
% 29.01/29.20 cnf(matrix-61, plain, ( ~end_point(_u56, _u59) | open(_u59) )).
% 29.01/29.20 cnf(matrix-62, plain, ( ~part_of(_u60, _u61) | ( _u60 = _u61) | open(_u60) )).
% 29.01/29.20 cnf(matrix-63, plain, ( ~part_of(_u65, _u66) | ~part_of(_u64, _u66) | ~part_of(_u63, _u66) | ~end_point(_u62, _u65) | ~end_point(_u62, _u64) | ~end_point(_u62, _u63) | part_of(_u64, _u63) | part_of(_u63, _u64) | part_of(_u65, _u64) | part_of(_u64, _u65) | part_of(_u65, _u63) | part_of(_u63, _u65) )).
% 29.01/29.20 cnf(matrix-64, plain, ( inner_point(skolem9(_u68), _u68) )).
% 29.01/29.20 cnf(matrix-65, plain, ( ~inner_point(_u71, _u72) | meet(_u71, skolem10(_u72, _u71), skolem11(_u72, _u71)) )).
% 29.01/29.20 cnf(matrix-66, plain, ( ~inner_point(_u71, _u72) | ( _u72 = sum(skolem10(_u72, _u71), skolem11(_u72, _u71))) )).
% 29.01/29.20 cnf(matrix-67, plain, ( ~end_point(_u75, _u76) | ~end_point(_u74, _u76) | ~end_point(_u73, _u76) | ( _u75 = _u74) | ( _u75 = _u73) | ( _u74 = _u73) )).
% 29.01/29.20 cnf(matrix-68, plain, ( ~end_point(_u78, _u79) | end_point(skolem12(_u79, _u78), _u79) )).
% 29.01/29.20 cnf(matrix-69, plain, ( ~end_point(_u78, _u79) | ( _u78 != skolem12(_u79, _u78)) )).
% 29.01/29.20 cnf(matrix-70, plain, ( ~end_point(_u80, _u83) | meet(_u80, _u83, _u82) | ~closed(_u84) | ( _u84 != sum(_u83, _u82)) | ~meet(_u81, _u83, _u82) )).
% 29.01/29.20 cnf(matrix-71, plain, ( ~meet(_u85, _u88, _u87) | ( skolem13(_u88, _u87) = sum(_u88, _u87)) )).
% 29.01/29.20 cnf(matrix-72, plain, ( ( _u91 = _u90) | incident_c(skolem14(_u91, _u90), _u91) | incident_c(skolem15(_u91, _u90), _u90) )).
% 29.01/29.20 cnf(matrix-73, plain, ( ( _u91 = _u90) | incident_c(skolem14(_u91, _u90), _u91) | ~incident_c(skolem15(_u91, _u90), _u91) )).
% 29.01/29.20 cnf(matrix-74, plain, ( ( _u91 = _u90) | ~incident_c(skolem14(_u91, _u90), _u90) | incident_c(skolem15(_u91, _u90), _u90) )).
% 29.01/29.20 cnf(matrix-75, plain, ( ( _u91 = _u90) | ~incident_c(skolem14(_u91, _u90), _u90) | ~incident_c(skolem15(_u91, _u90), _u91) )).
% 29.01/29.20 cnf(matrix-76, plain, ( ~between_c(_u106, _u104, _u102, _u100) | ( _u104 != _u100) )).
% 29.01/29.20 cnf(matrix-77, plain, ( ~between_c(_u106, _u104, _u102, _u100) | part_of(skolem16(_u106, _u104, _u102, _u100), _u106) )).
% 29.01/29.20 cnf(matrix-78, plain, ( ~between_c(_u106, _u104, _u102, _u100) | end_point(_u104, skolem16(_u106, _u104, _u102, _u100)) )).
% 29.01/29.20 cnf(matrix-79, plain, ( ~between_c(_u106, _u104, _u102, _u100) | end_point(_u100, skolem16(_u106, _u104, _u102, _u100)) )).
% 29.01/29.20 cnf(matrix-80, plain, ( ~between_c(_u106, _u104, _u102, _u100) | inner_point(_u102, skolem16(_u106, _u104, _u102, _u100)) )).
% 29.01/29.20 cnf(matrix-81, plain, ( ( _u105 = _u101) | ~part_of(_u95, _u107) | ~end_point(_u105, _u95) | ~end_point(_u101, _u95) | ~inner_point(_u103, _u95) | between_c(_u107, _u105, _u103, _u101) )).
% 29.01/29.20 cnf(matrix-82, plain, ( between_c(skolem17, skolem18, skolem19, skolem20) )).
% 29.01/29.20 cnf(matrix-83, plain, ( ~incident_c(skolem18, skolem17) | ~incident_c(skolem19, skolem17) | ~incident_c(skolem20, skolem17) | ( skolem18 = skolem19) | ( skolem19 = skolem20) | ( skolem18 = skolem20) )).
% 29.01/29.20
% 29.01/29.20 % Proof stack:
% 29.01/29.20 cnf(proof-stack, plain,
% 29.01/29.20 proof_stack(
% 29.01/29.20 start(83),
% 29.01/29.20 left_branch(0, 28, 2, 2),
% 29.01/29.20 left_branch(0, 77, 1, 3),
% 29.01/29.20 left_branch(0, 82, 0, 4),
% 29.01/29.20 right_branch(4),
% 29.01/29.20 right_branch(3),
% 29.01/29.20 left_branch(0, 40, 1, 4),
% 29.01/29.20 left_branch(0, 78, 1, 5),
% 29.01/29.20 left_branch(0, 82, 0, 6),
% 29.01/29.20 right_branch(6),
% 29.01/29.20 right_branch(5),
% 29.01/29.20 right_branch(4),
% 29.01/29.20 right_branch(2),
% 29.01/29.20 left_branch(0, 76, 1, 3),
% 29.01/29.20 left_branch(0, 82, 0, 4),
% 29.01/29.20 right_branch(4),
% 29.01/29.20 right_branch(3),
% 29.01/29.20 left_branch(0, 23, 0, 4),
% 29.01/29.20 left_branch(0, 49, 0, 5),
% 29.01/29.20 left_branch(0, 79, 1, 6),
% 29.01/29.20 left_branch(0, 82, 0, 7),
% 29.01/29.20 right_branch(7),
% 29.01/29.20 right_branch(6),
% 29.01/29.20 right_branch(5),
% 29.01/29.20 left_branch(0, 80, 1, 6),
% 29.01/29.20 left_branch(0, 82, 0, 7),
% 29.01/29.20 right_branch(7),
% 29.01/29.20 right_branch(6),
% 29.01/29.20 left_branch(0, 19, 4, 7),
% 29.01/29.20 left_branch(0, 0, 0, 8),
% 29.01/29.20 right_branch(8),
% 29.01/29.20 left_branch(0, 0, 0, 9),
% 29.01/29.20 right_branch(9),
% 29.01/29.20 left_branch(0, 0, 0, 10),
% 29.01/29.20 right_branch(10),
% 29.01/29.20 left_branch(0, 0, 0, 11),
% 29.01/29.20 right_branch(11),
% 29.01/29.20 right_branch(7),
% 29.01/29.20 right_branch(4),
% 29.01/29.20 left_branch(0, 22, 0, 5),
% 29.01/29.20 left_branch(0, 49, 1, 6),
% 29.01/29.20 left_branch(0, 80, 1, 7),
% 29.01/29.20 left_branch(0, 82, 0, 8),
% 29.01/29.20 right_branch(8),
% 29.01/29.20 right_branch(7),
% 29.01/29.20 right_branch(6),
% 29.01/29.20 left_branch(0, 78, 1, 7),
% 29.01/29.20 left_branch(0, 82, 0, 8),
% 29.01/29.20 right_branch(8),
% 29.01/29.20 right_branch(7),
% 29.01/29.20 left_branch(0, 19, 4, 8),
% 29.01/29.20 left_branch(0, 0, 0, 9),
% 29.01/29.20 right_branch(9),
% 29.01/29.20 left_branch(0, 0, 0, 10),
% 29.01/29.20 right_branch(10),
% 29.01/29.20 left_branch(0, 0, 0, 11),
% 29.01/29.20 right_branch(11),
% 29.01/29.20 left_branch(0, 0, 0, 12),
% 29.01/29.20 right_branch(12),
% 29.01/29.20 right_branch(8),
% 29.01/29.20 right_branch(5),
% 29.01/29.20 left_branch(0, 28, 2, 6),
% 29.01/29.20 left_branch(0, 77, 1, 7),
% 29.01/29.20 left_branch(0, 82, 0, 8),
% 29.01/29.20 right_branch(8),
% 29.01/29.20 right_branch(7),
% 29.01/29.20 left_branch(0, 40, 1, 8),
% 29.01/29.20 left_branch(0, 79, 1, 9),
% 29.01/29.20 left_branch(0, 82, 0, 10),
% 29.01/29.20 right_branch(10),
% 29.01/29.20 right_branch(9),
% 29.01/29.20 right_branch(8),
% 29.01/29.20 right_branch(6),
% 29.01/29.20 left_branch(0, 28, 2, 7),
% 29.01/29.20 left_branch(0, 77, 1, 8),
% 29.01/29.20 left_branch(0, 82, 0, 9),
% 29.01/29.20 right_branch(9),
% 29.01/29.20 right_branch(8),
% 29.01/29.20 left_branch(0, 48, 1, 9),
% 29.01/29.20 left_branch(0, 80, 1, 10),
% 29.01/29.20 left_branch(0, 82, 0, 11),
% 29.01/29.20 right_branch(11),
% 29.01/29.20 right_branch(10),
% 29.01/29.20 right_branch(9),
% 29.01/29.20 right_branch(7)
% 29.01/29.20 )).
% 29.01/29.20 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------