TSTP Solution File: SET791+4 by ConnectPP---0.3.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET791+4 : TPTP v8.1.2. Released v3.2.0.
% 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 14:32:24 EDT 2024
% Result : Theorem 37.83s 38.01s
% Output : Proof 37.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET791+4 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.12 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Mar 20 21:44:29 EDT 2024
% 0.12/0.33 % CPUTime :
% 37.83/38.01 % SZS status Theorem for theBenchmark
% 37.83/38.01 % SZS output start Proof for theBenchmark
% 37.83/38.01
% 37.83/38.01 % Formula: order ( axiom ) converted to clauses:
% 37.83/38.01 cnf(order-1, axiom, ( ~order(_u16, _u14) | ~member(_u0, _u14) | apply(_u16, _u0, _u0) )).
% 37.83/38.01 cnf(order-2, axiom, ( ~order(_u16, _u14) | ~member(_u2, _u14) | ~member(_u1, _u14) | ~apply(_u16, _u2, _u1) | ~apply(_u16, _u1, _u2) | ( _u2 = _u1) )).
% 37.83/38.01 cnf(order-3, axiom, ( ~order(_u16, _u14) | ~member(_u5, _u14) | ~member(_u4, _u14) | ~member(_u3, _u14) | ~apply(_u16, _u5, _u4) | ~apply(_u16, _u4, _u3) | apply(_u16, _u5, _u3) )).
% 37.83/38.01 cnf(order-4, axiom, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-5, axiom, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-6, axiom, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-7, axiom, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.01 cnf(order-8, axiom, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-9, axiom, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-10, axiom, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-11, axiom, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-12, axiom, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.01 cnf(order-13, axiom, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-14, axiom, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-15, axiom, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-16, axiom, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-17, axiom, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.01 cnf(order-18, axiom, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-19, axiom, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-20, axiom, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-21, axiom, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-22, axiom, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.01 cnf(order-23, axiom, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-24, axiom, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-25, axiom, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-26, axiom, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-27, axiom, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.01 cnf(order-28, axiom, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-29, axiom, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-30, axiom, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-31, axiom, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-32, axiom, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.01 cnf(order-33, axiom, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-34, axiom, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-35, axiom, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-36, axiom, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-37, axiom, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.01 cnf(order-38, axiom, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-39, axiom, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-40, axiom, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-41, axiom, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-42, axiom, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.01 cnf(order-43, axiom, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-44, axiom, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-45, axiom, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-46, axiom, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-47, axiom, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.01 cnf(order-48, axiom, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-49, axiom, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-50, axiom, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-51, axiom, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-52, axiom, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.01 cnf(order-53, axiom, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-54, axiom, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-55, axiom, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-56, axiom, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-57, axiom, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.01 cnf(order-58, axiom, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-59, axiom, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-60, axiom, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(order-61, axiom, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(order-62, axiom, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.01 cnf(order-63, axiom, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.01
% 37.83/38.01 % Formula: total_order ( axiom ) converted to clauses:
% 37.83/38.01 cnf(total_order-1, axiom, ( ~total_order(_u26, _u24) | order(_u26, _u24) )).
% 37.83/38.01 cnf(total_order-2, axiom, ( ~total_order(_u26, _u24) | ~member(_u19, _u24) | ~member(_u18, _u24) | apply(_u26, _u19, _u18) | apply(_u26, _u18, _u19) )).
% 37.83/38.01 cnf(total_order-3, axiom, ( total_order(_u27, _u25) | ~order(_u27, _u25) | member(skolem7(_u27, _u25), _u25) )).
% 37.83/38.01 cnf(total_order-4, axiom, ( total_order(_u27, _u25) | ~order(_u27, _u25) | member(skolem8(_u27, _u25), _u25) )).
% 37.83/38.01 cnf(total_order-5, axiom, ( total_order(_u27, _u25) | ~order(_u27, _u25) | ~apply(_u27, skolem7(_u27, _u25), skolem8(_u27, _u25)) )).
% 37.83/38.01 cnf(total_order-6, axiom, ( total_order(_u27, _u25) | ~order(_u27, _u25) | ~apply(_u27, skolem8(_u27, _u25), skolem7(_u27, _u25)) )).
% 37.83/38.01
% 37.83/38.01 % Formula: upper_bound ( axiom ) converted to clauses:
% 37.83/38.01 cnf(upper_bound-1, axiom, ( ~upper_bound(_u33, _u37, _u35) | ~member(_u28, _u35) | apply(_u37, _u28, _u33) )).
% 37.83/38.01 cnf(upper_bound-2, axiom, ( upper_bound(_u34, _u38, _u36) | member(skolem9(_u38, _u36, _u34), _u36) )).
% 37.83/38.01 cnf(upper_bound-3, axiom, ( upper_bound(_u34, _u38, _u36) | ~apply(_u38, skolem9(_u38, _u36, _u34), _u34) )).
% 37.83/38.01
% 37.83/38.01 % Formula: lower_bound ( axiom ) converted to clauses:
% 37.83/38.01 cnf(lower_bound-1, axiom, ( ~lower_bound(_u44, _u48, _u46) | ~member(_u39, _u46) | apply(_u48, _u44, _u39) )).
% 37.83/38.01 cnf(lower_bound-2, axiom, ( lower_bound(_u45, _u49, _u47) | member(skolem10(_u49, _u47, _u45), _u47) )).
% 37.83/38.01 cnf(lower_bound-3, axiom, ( lower_bound(_u45, _u49, _u47) | ~apply(_u49, _u45, skolem10(_u49, _u47, _u45)) )).
% 37.83/38.01
% 37.83/38.01 % Formula: greatest ( axiom ) converted to clauses:
% 37.83/38.01 cnf(greatest-1, axiom, ( ~greatest(_u55, _u59, _u57) | member(_u55, _u57) )).
% 37.83/38.01 cnf(greatest-2, axiom, ( ~greatest(_u55, _u59, _u57) | ~member(_u50, _u57) | apply(_u59, _u50, _u55) )).
% 37.83/38.01 cnf(greatest-3, axiom, ( greatest(_u56, _u60, _u58) | ~member(_u56, _u58) | member(skolem11(_u60, _u58, _u56), _u58) )).
% 37.83/38.01 cnf(greatest-4, axiom, ( greatest(_u56, _u60, _u58) | ~member(_u56, _u58) | ~apply(_u60, skolem11(_u60, _u58, _u56), _u56) )).
% 37.83/38.01
% 37.83/38.01 % Formula: least ( axiom ) converted to clauses:
% 37.83/38.01 cnf(least-1, axiom, ( ~least(_u66, _u70, _u68) | member(_u66, _u68) )).
% 37.83/38.01 cnf(least-2, axiom, ( ~least(_u66, _u70, _u68) | ~member(_u61, _u68) | apply(_u70, _u66, _u61) )).
% 37.83/38.01 cnf(least-3, axiom, ( least(_u67, _u71, _u69) | ~member(_u67, _u69) | member(skolem12(_u71, _u69, _u67), _u69) )).
% 37.83/38.01 cnf(least-4, axiom, ( least(_u67, _u71, _u69) | ~member(_u67, _u69) | ~apply(_u71, _u67, skolem12(_u71, _u69, _u67)) )).
% 37.83/38.01
% 37.83/38.01 % Formula: max ( axiom ) converted to clauses:
% 37.83/38.01 cnf(max-1, axiom, ( ~max(_u77, _u81, _u79) | member(_u77, _u79) )).
% 37.83/38.01 cnf(max-2, axiom, ( ~max(_u77, _u81, _u79) | ~member(_u72, _u79) | ~apply(_u81, _u77, _u72) | ( _u77 = _u72) )).
% 37.83/38.01 cnf(max-3, axiom, ( max(_u78, _u82, _u80) | ~member(_u78, _u80) | member(skolem13(_u82, _u80, _u78), _u80) )).
% 37.83/38.01 cnf(max-4, axiom, ( max(_u78, _u82, _u80) | ~member(_u78, _u80) | apply(_u82, _u78, skolem13(_u82, _u80, _u78)) )).
% 37.83/38.01 cnf(max-5, axiom, ( max(_u78, _u82, _u80) | ~member(_u78, _u80) | ( _u78 != skolem13(_u82, _u80, _u78)) )).
% 37.83/38.01
% 37.83/38.01 % Formula: min ( axiom ) converted to clauses:
% 37.83/38.01 cnf(min-1, axiom, ( ~min(_u88, _u92, _u90) | member(_u88, _u90) )).
% 37.83/38.01 cnf(min-2, axiom, ( ~min(_u88, _u92, _u90) | ~member(_u83, _u90) | ~apply(_u92, _u83, _u88) | ( _u88 = _u83) )).
% 37.83/38.01 cnf(min-3, axiom, ( min(_u89, _u93, _u91) | ~member(_u89, _u91) | member(skolem14(_u93, _u91, _u89), _u91) )).
% 37.83/38.01 cnf(min-4, axiom, ( min(_u89, _u93, _u91) | ~member(_u89, _u91) | apply(_u93, skolem14(_u93, _u91, _u89), _u89) )).
% 37.83/38.01 cnf(min-5, axiom, ( min(_u89, _u93, _u91) | ~member(_u89, _u91) | ( _u89 != skolem14(_u93, _u91, _u89)) )).
% 37.83/38.01
% 37.83/38.01 % Formula: least_upper_bound ( axiom ) converted to clauses:
% 37.83/38.01 cnf(least_upper_bound-1, axiom, ( ~least_upper_bound(_u106, _u104, _u102, _u100) | member(_u106, _u104) )).
% 37.83/38.01 cnf(least_upper_bound-2, axiom, ( ~least_upper_bound(_u106, _u104, _u102, _u100) | upper_bound(_u106, _u102, _u104) )).
% 37.83/38.01 cnf(least_upper_bound-3, axiom, ( ~least_upper_bound(_u106, _u104, _u102, _u100) | ~member(_u94, _u100) | ~upper_bound(_u94, _u102, _u104) | apply(_u102, _u106, _u94) )).
% 37.83/38.01 cnf(least_upper_bound-4, axiom, ( least_upper_bound(_u107, _u105, _u103, _u101) | ~member(_u107, _u105) | ~upper_bound(_u107, _u103, _u105) | member(skolem15(_u107, _u105, _u103, _u101), _u101) )).
% 37.83/38.01 cnf(least_upper_bound-5, axiom, ( least_upper_bound(_u107, _u105, _u103, _u101) | ~member(_u107, _u105) | ~upper_bound(_u107, _u103, _u105) | upper_bound(skolem15(_u107, _u105, _u103, _u101), _u103, _u105) )).
% 37.83/38.01 cnf(least_upper_bound-6, axiom, ( least_upper_bound(_u107, _u105, _u103, _u101) | ~member(_u107, _u105) | ~upper_bound(_u107, _u103, _u105) | ~apply(_u103, _u107, skolem15(_u107, _u105, _u103, _u101)) )).
% 37.83/38.01
% 37.83/38.01 % Formula: greatest_lower_bound ( axiom ) converted to clauses:
% 37.83/38.01 cnf(greatest_lower_bound-1, axiom, ( ~greatest_lower_bound(_u120, _u118, _u116, _u114) | member(_u120, _u118) )).
% 37.83/38.01 cnf(greatest_lower_bound-2, axiom, ( ~greatest_lower_bound(_u120, _u118, _u116, _u114) | lower_bound(_u120, _u116, _u118) )).
% 37.83/38.01 cnf(greatest_lower_bound-3, axiom, ( ~greatest_lower_bound(_u120, _u118, _u116, _u114) | ~member(_u108, _u114) | ~lower_bound(_u108, _u116, _u118) | apply(_u116, _u108, _u120) )).
% 37.83/38.01 cnf(greatest_lower_bound-4, axiom, ( greatest_lower_bound(_u121, _u119, _u117, _u115) | ~member(_u121, _u119) | ~lower_bound(_u121, _u117, _u119) | member(skolem16(_u121, _u119, _u117, _u115), _u115) )).
% 37.83/38.01 cnf(greatest_lower_bound-5, axiom, ( greatest_lower_bound(_u121, _u119, _u117, _u115) | ~member(_u121, _u119) | ~lower_bound(_u121, _u117, _u119) | lower_bound(skolem16(_u121, _u119, _u117, _u115), _u117, _u119) )).
% 37.83/38.01 cnf(greatest_lower_bound-6, axiom, ( greatest_lower_bound(_u121, _u119, _u117, _u115) | ~member(_u121, _u119) | ~lower_bound(_u121, _u117, _u119) | ~apply(_u117, skolem16(_u121, _u119, _u117, _u115), _u121) )).
% 37.83/38.01
% 37.83/38.01 % Formula: thIV3 ( conjecture ) (definitionally) converted to clauses:
% 37.83/38.01 cnf(thIV3-1, negated_conjecture, ( order(skolem17, skolem18) )).
% 37.83/38.01 cnf(thIV3-2, negated_conjecture, ( greatest(skolem19, skolem17, skolem18) )).
% 37.83/38.01 cnf(thIV3-3, negated_conjecture, ( ~max(skolem19, skolem17, skolem18) )).
% 37.83/38.01
% 37.83/38.01 % Problem matrix:
% 37.83/38.01 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 37.83/38.01 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 37.83/38.01 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 37.83/38.01 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 37.83/38.01 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 37.83/38.01 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 37.83/38.01 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem4(__eqx_0, __eqx_1) = skolem4(__eqy_0, __eqy_1)) )).
% 37.83/38.01 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem5(__eqx_0, __eqx_1) = skolem5(__eqy_0, __eqy_1)) )).
% 37.83/38.01 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem6(__eqx_0, __eqx_1) = skolem6(__eqy_0, __eqy_1)) )).
% 37.83/38.01 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem7(__eqx_0, __eqx_1) = skolem7(__eqy_0, __eqy_1)) )).
% 37.83/38.01 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem8(__eqx_0, __eqx_1) = skolem8(__eqy_0, __eqy_1)) )).
% 37.83/38.01 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem9(__eqx_0, __eqx_1, __eqx_2) = skolem9(__eqy_0, __eqy_1, __eqy_2)) )).
% 37.83/38.01 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem10(__eqx_0, __eqx_1, __eqx_2) = skolem10(__eqy_0, __eqy_1, __eqy_2)) )).
% 37.83/38.01 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem11(__eqx_0, __eqx_1, __eqx_2) = skolem11(__eqy_0, __eqy_1, __eqy_2)) )).
% 37.83/38.01 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem12(__eqx_0, __eqx_1, __eqx_2) = skolem12(__eqy_0, __eqy_1, __eqy_2)) )).
% 37.83/38.01 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem13(__eqx_0, __eqx_1, __eqx_2) = skolem13(__eqy_0, __eqy_1, __eqy_2)) )).
% 37.83/38.01 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem14(__eqx_0, __eqx_1, __eqx_2) = skolem14(__eqy_0, __eqy_1, __eqy_2)) )).
% 37.83/38.01 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ( skolem15(__eqx_0, __eqx_1, __eqx_2, __eqx_3) = skolem15(__eqy_0, __eqy_1, __eqy_2, __eqy_3)) )).
% 37.83/38.01 cnf(matrix-18, 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)) )).
% 37.83/38.01 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~order(__eqx_0, __eqx_1) | order(__eqy_0, __eqy_1) )).
% 37.83/38.01 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~member(__eqx_0, __eqx_1) | member(__eqy_0, __eqy_1) )).
% 37.83/38.01 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~apply(__eqx_0, __eqx_1, __eqx_2) | apply(__eqy_0, __eqy_1, __eqy_2) )).
% 37.83/38.01 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~total_order(__eqx_0, __eqx_1) | total_order(__eqy_0, __eqy_1) )).
% 37.83/38.01 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~upper_bound(__eqx_0, __eqx_1, __eqx_2) | upper_bound(__eqy_0, __eqy_1, __eqy_2) )).
% 37.83/38.01 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~lower_bound(__eqx_0, __eqx_1, __eqx_2) | lower_bound(__eqy_0, __eqy_1, __eqy_2) )).
% 37.83/38.01 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~greatest(__eqx_0, __eqx_1, __eqx_2) | greatest(__eqy_0, __eqy_1, __eqy_2) )).
% 37.83/38.01 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~least(__eqx_0, __eqx_1, __eqx_2) | least(__eqy_0, __eqy_1, __eqy_2) )).
% 37.83/38.01 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~max(__eqx_0, __eqx_1, __eqx_2) | max(__eqy_0, __eqy_1, __eqy_2) )).
% 37.83/38.01 cnf(matrix-28, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ~min(__eqx_0, __eqx_1, __eqx_2) | min(__eqy_0, __eqy_1, __eqy_2) )).
% 37.83/38.01 cnf(matrix-29, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ~least_upper_bound(__eqx_0, __eqx_1, __eqx_2, __eqx_3) | least_upper_bound(__eqy_0, __eqy_1, __eqy_2, __eqy_3) )).
% 37.83/38.01 cnf(matrix-30, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( __eqx_3 != __eqy_3) | ~greatest_lower_bound(__eqx_0, __eqx_1, __eqx_2, __eqx_3) | greatest_lower_bound(__eqy_0, __eqy_1, __eqy_2, __eqy_3) )).
% 37.83/38.01 cnf(matrix-31, plain, ( ~order(_u16, _u14) | ~member(_u0, _u14) | apply(_u16, _u0, _u0) )).
% 37.83/38.01 cnf(matrix-32, plain, ( ~order(_u16, _u14) | ~member(_u2, _u14) | ~member(_u1, _u14) | ~apply(_u16, _u2, _u1) | ~apply(_u16, _u1, _u2) | ( _u2 = _u1) )).
% 37.83/38.01 cnf(matrix-33, plain, ( ~order(_u16, _u14) | ~member(_u5, _u14) | ~member(_u4, _u14) | ~member(_u3, _u14) | ~apply(_u16, _u5, _u4) | ~apply(_u16, _u4, _u3) | apply(_u16, _u5, _u3) )).
% 37.83/38.01 cnf(matrix-34, plain, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(matrix-35, plain, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(matrix-36, plain, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(matrix-37, plain, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.01 cnf(matrix-38, plain, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(matrix-39, plain, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(matrix-40, plain, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(matrix-41, plain, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(matrix-42, plain, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.01 cnf(matrix-43, plain, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(matrix-44, plain, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(matrix-45, plain, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.01 cnf(matrix-46, plain, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(matrix-47, plain, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.01 cnf(matrix-48, plain, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | member(skolem1(_u17, _u15), _u15) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.01 cnf(matrix-49, plain, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-50, plain, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-51, plain, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-52, plain, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-53, plain, ( order(_u17, _u15) | member(skolem4(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-54, plain, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-55, plain, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-56, plain, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-57, plain, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-58, plain, ( order(_u17, _u15) | member(skolem5(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-59, plain, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-60, plain, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-61, plain, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-62, plain, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-63, plain, ( order(_u17, _u15) | member(skolem6(_u17, _u15), _u15) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-64, plain, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-65, plain, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-66, plain, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-67, plain, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-68, plain, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-69, plain, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-70, plain, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-71, plain, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-72, plain, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-73, plain, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-74, plain, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-75, plain, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-76, plain, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-77, plain, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-78, plain, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | member(skolem1(_u17, _u15), _u15) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-79, plain, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-80, plain, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-81, plain, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-82, plain, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-83, plain, ( order(_u17, _u15) | apply(_u17, skolem4(_u17, _u15), skolem5(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-84, plain, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-85, plain, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-86, plain, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-87, plain, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-88, plain, ( order(_u17, _u15) | apply(_u17, skolem5(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-89, plain, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem2(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-90, plain, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | member(skolem3(_u17, _u15), _u15) )).
% 37.83/38.02 cnf(matrix-91, plain, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem2(_u17, _u15), skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-92, plain, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | apply(_u17, skolem3(_u17, _u15), skolem2(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-93, plain, ( order(_u17, _u15) | ~apply(_u17, skolem4(_u17, _u15), skolem6(_u17, _u15)) | ~apply(_u17, skolem1(_u17, _u15), skolem1(_u17, _u15)) | ( skolem2(_u17, _u15) != skolem3(_u17, _u15)) )).
% 37.83/38.02 cnf(matrix-94, plain, ( ~total_order(_u26, _u24) | order(_u26, _u24) )).
% 37.83/38.02 cnf(matrix-95, plain, ( ~total_order(_u26, _u24) | ~member(_u19, _u24) | ~member(_u18, _u24) | apply(_u26, _u19, _u18) | apply(_u26, _u18, _u19) )).
% 37.83/38.02 cnf(matrix-96, plain, ( total_order(_u27, _u25) | ~order(_u27, _u25) | member(skolem7(_u27, _u25), _u25) )).
% 37.83/38.02 cnf(matrix-97, plain, ( total_order(_u27, _u25) | ~order(_u27, _u25) | member(skolem8(_u27, _u25), _u25) )).
% 37.83/38.02 cnf(matrix-98, plain, ( total_order(_u27, _u25) | ~order(_u27, _u25) | ~apply(_u27, skolem7(_u27, _u25), skolem8(_u27, _u25)) )).
% 37.83/38.02 cnf(matrix-99, plain, ( total_order(_u27, _u25) | ~order(_u27, _u25) | ~apply(_u27, skolem8(_u27, _u25), skolem7(_u27, _u25)) )).
% 37.83/38.02 cnf(matrix-100, plain, ( ~upper_bound(_u33, _u37, _u35) | ~member(_u28, _u35) | apply(_u37, _u28, _u33) )).
% 37.83/38.02 cnf(matrix-101, plain, ( upper_bound(_u34, _u38, _u36) | member(skolem9(_u38, _u36, _u34), _u36) )).
% 37.83/38.02 cnf(matrix-102, plain, ( upper_bound(_u34, _u38, _u36) | ~apply(_u38, skolem9(_u38, _u36, _u34), _u34) )).
% 37.83/38.02 cnf(matrix-103, plain, ( ~lower_bound(_u44, _u48, _u46) | ~member(_u39, _u46) | apply(_u48, _u44, _u39) )).
% 37.83/38.02 cnf(matrix-104, plain, ( lower_bound(_u45, _u49, _u47) | member(skolem10(_u49, _u47, _u45), _u47) )).
% 37.83/38.02 cnf(matrix-105, plain, ( lower_bound(_u45, _u49, _u47) | ~apply(_u49, _u45, skolem10(_u49, _u47, _u45)) )).
% 37.83/38.02 cnf(matrix-106, plain, ( ~greatest(_u55, _u59, _u57) | member(_u55, _u57) )).
% 37.83/38.02 cnf(matrix-107, plain, ( ~greatest(_u55, _u59, _u57) | ~member(_u50, _u57) | apply(_u59, _u50, _u55) )).
% 37.83/38.02 cnf(matrix-108, plain, ( greatest(_u56, _u60, _u58) | ~member(_u56, _u58) | member(skolem11(_u60, _u58, _u56), _u58) )).
% 37.83/38.02 cnf(matrix-109, plain, ( greatest(_u56, _u60, _u58) | ~member(_u56, _u58) | ~apply(_u60, skolem11(_u60, _u58, _u56), _u56) )).
% 37.83/38.02 cnf(matrix-110, plain, ( ~least(_u66, _u70, _u68) | member(_u66, _u68) )).
% 37.83/38.02 cnf(matrix-111, plain, ( ~least(_u66, _u70, _u68) | ~member(_u61, _u68) | apply(_u70, _u66, _u61) )).
% 37.83/38.02 cnf(matrix-112, plain, ( least(_u67, _u71, _u69) | ~member(_u67, _u69) | member(skolem12(_u71, _u69, _u67), _u69) )).
% 37.83/38.02 cnf(matrix-113, plain, ( least(_u67, _u71, _u69) | ~member(_u67, _u69) | ~apply(_u71, _u67, skolem12(_u71, _u69, _u67)) )).
% 37.83/38.02 cnf(matrix-114, plain, ( ~max(_u77, _u81, _u79) | member(_u77, _u79) )).
% 37.83/38.02 cnf(matrix-115, plain, ( ~max(_u77, _u81, _u79) | ~member(_u72, _u79) | ~apply(_u81, _u77, _u72) | ( _u77 = _u72) )).
% 37.83/38.02 cnf(matrix-116, plain, ( max(_u78, _u82, _u80) | ~member(_u78, _u80) | member(skolem13(_u82, _u80, _u78), _u80) )).
% 37.83/38.02 cnf(matrix-117, plain, ( max(_u78, _u82, _u80) | ~member(_u78, _u80) | apply(_u82, _u78, skolem13(_u82, _u80, _u78)) )).
% 37.83/38.02 cnf(matrix-118, plain, ( max(_u78, _u82, _u80) | ~member(_u78, _u80) | ( _u78 != skolem13(_u82, _u80, _u78)) )).
% 37.83/38.02 cnf(matrix-119, plain, ( ~min(_u88, _u92, _u90) | member(_u88, _u90) )).
% 37.83/38.02 cnf(matrix-120, plain, ( ~min(_u88, _u92, _u90) | ~member(_u83, _u90) | ~apply(_u92, _u83, _u88) | ( _u88 = _u83) )).
% 37.83/38.02 cnf(matrix-121, plain, ( min(_u89, _u93, _u91) | ~member(_u89, _u91) | member(skolem14(_u93, _u91, _u89), _u91) )).
% 37.83/38.02 cnf(matrix-122, plain, ( min(_u89, _u93, _u91) | ~member(_u89, _u91) | apply(_u93, skolem14(_u93, _u91, _u89), _u89) )).
% 37.83/38.02 cnf(matrix-123, plain, ( min(_u89, _u93, _u91) | ~member(_u89, _u91) | ( _u89 != skolem14(_u93, _u91, _u89)) )).
% 37.83/38.02 cnf(matrix-124, plain, ( ~least_upper_bound(_u106, _u104, _u102, _u100) | member(_u106, _u104) )).
% 37.83/38.02 cnf(matrix-125, plain, ( ~least_upper_bound(_u106, _u104, _u102, _u100) | upper_bound(_u106, _u102, _u104) )).
% 37.83/38.02 cnf(matrix-126, plain, ( ~least_upper_bound(_u106, _u104, _u102, _u100) | ~member(_u94, _u100) | ~upper_bound(_u94, _u102, _u104) | apply(_u102, _u106, _u94) )).
% 37.83/38.02 cnf(matrix-127, plain, ( least_upper_bound(_u107, _u105, _u103, _u101) | ~member(_u107, _u105) | ~upper_bound(_u107, _u103, _u105) | member(skolem15(_u107, _u105, _u103, _u101), _u101) )).
% 37.83/38.02 cnf(matrix-128, plain, ( least_upper_bound(_u107, _u105, _u103, _u101) | ~member(_u107, _u105) | ~upper_bound(_u107, _u103, _u105) | upper_bound(skolem15(_u107, _u105, _u103, _u101), _u103, _u105) )).
% 37.83/38.02 cnf(matrix-129, plain, ( least_upper_bound(_u107, _u105, _u103, _u101) | ~member(_u107, _u105) | ~upper_bound(_u107, _u103, _u105) | ~apply(_u103, _u107, skolem15(_u107, _u105, _u103, _u101)) )).
% 37.83/38.02 cnf(matrix-130, plain, ( ~greatest_lower_bound(_u120, _u118, _u116, _u114) | member(_u120, _u118) )).
% 37.83/38.02 cnf(matrix-131, plain, ( ~greatest_lower_bound(_u120, _u118, _u116, _u114) | lower_bound(_u120, _u116, _u118) )).
% 37.83/38.02 cnf(matrix-132, plain, ( ~greatest_lower_bound(_u120, _u118, _u116, _u114) | ~member(_u108, _u114) | ~lower_bound(_u108, _u116, _u118) | apply(_u116, _u108, _u120) )).
% 37.83/38.02 cnf(matrix-133, plain, ( greatest_lower_bound(_u121, _u119, _u117, _u115) | ~member(_u121, _u119) | ~lower_bound(_u121, _u117, _u119) | member(skolem16(_u121, _u119, _u117, _u115), _u115) )).
% 37.83/38.02 cnf(matrix-134, plain, ( greatest_lower_bound(_u121, _u119, _u117, _u115) | ~member(_u121, _u119) | ~lower_bound(_u121, _u117, _u119) | lower_bound(skolem16(_u121, _u119, _u117, _u115), _u117, _u119) )).
% 37.83/38.02 cnf(matrix-135, plain, ( greatest_lower_bound(_u121, _u119, _u117, _u115) | ~member(_u121, _u119) | ~lower_bound(_u121, _u117, _u119) | ~apply(_u117, skolem16(_u121, _u119, _u117, _u115), _u121) )).
% 37.83/38.02 cnf(matrix-136, plain, ( order(skolem17, skolem18) )).
% 37.83/38.02 cnf(matrix-137, plain, ( greatest(skolem19, skolem17, skolem18) )).
% 37.83/38.02 cnf(matrix-138, plain, ( ~max(skolem19, skolem17, skolem18) )).
% 37.83/38.02
% 37.83/38.02 % Proof stack:
% 37.83/38.02 cnf(proof-stack, plain,
% 37.83/38.02 proof_stack(
% 37.83/38.02 start(136),
% 37.83/38.02 left_branch(0, 33, 0, 2),
% 37.83/38.02 left_branch(0, 32, 4, 3),
% 37.83/38.02 reduction(0, 0),
% 37.83/38.02 left_branch(0, 118, 2, 5),
% 37.83/38.02 left_branch(0, 138, 0, 6),
% 37.83/38.02 right_branch(6),
% 37.83/38.02 left_branch(0, 106, 1, 7),
% 37.83/38.02 left_branch(0, 137, 0, 8),
% 37.83/38.02 right_branch(8),
% 37.83/38.02 right_branch(7),
% 37.83/38.02 right_branch(5),
% 37.83/38.02 left_branch(0, 117, 2, 6),
% 37.83/38.02 left_branch(0, 138, 0, 7),
% 37.83/38.02 right_branch(7),
% 37.83/38.02 left_branch(0, 106, 1, 8),
% 37.83/38.02 left_branch(0, 137, 0, 9),
% 37.83/38.02 right_branch(9),
% 37.83/38.02 right_branch(8),
% 37.83/38.02 right_branch(6),
% 37.83/38.02 left_branch(0, 116, 2, 7),
% 37.83/38.02 left_branch(0, 138, 0, 8),
% 37.83/38.02 right_branch(8),
% 37.83/38.02 left_branch(0, 106, 1, 9),
% 37.83/38.02 left_branch(0, 137, 0, 10),
% 37.83/38.02 right_branch(10),
% 37.83/38.02 right_branch(9),
% 37.83/38.02 right_branch(7),
% 37.83/38.02 left_branch(0, 106, 1, 8),
% 37.83/38.02 left_branch(0, 137, 0, 9),
% 37.83/38.02 right_branch(9),
% 37.83/38.02 right_branch(8),
% 37.83/38.02 right_branch(3),
% 37.83/38.02 left_branch(0, 107, 2, 4),
% 37.83/38.02 left_branch(0, 137, 0, 5),
% 37.83/38.02 right_branch(5),
% 37.83/38.02 left_branch(0, 116, 2, 6),
% 37.83/38.02 left_branch(0, 138, 0, 7),
% 37.83/38.02 right_branch(7),
% 37.83/38.02 left_branch(0, 106, 1, 8),
% 37.83/38.02 left_branch(0, 137, 0, 9),
% 37.83/38.02 right_branch(9),
% 37.83/38.02 right_branch(8),
% 37.83/38.02 right_branch(6),
% 37.83/38.02 right_branch(4),
% 37.83/38.02 left_branch(0, 33, 6, 5),
% 37.83/38.02 reduction(0, 0),
% 37.83/38.02 left_branch(0, 117, 2, 7),
% 37.83/38.02 left_branch(0, 138, 0, 8),
% 37.83/38.02 right_branch(8),
% 37.83/38.02 left_branch(0, 106, 1, 9),
% 37.83/38.02 left_branch(0, 137, 0, 10),
% 37.83/38.02 right_branch(10),
% 37.83/38.02 right_branch(9),
% 37.83/38.02 right_branch(7),
% 37.83/38.02 lemmata(0, 1),
% 37.83/38.02 left_branch(0, 116, 2, 9),
% 37.83/38.02 left_branch(0, 138, 0, 10),
% 37.83/38.02 right_branch(10),
% 37.83/38.02 left_branch(0, 106, 1, 11),
% 37.83/38.02 left_branch(0, 137, 0, 12),
% 37.83/38.02 right_branch(12),
% 37.83/38.02 right_branch(11),
% 37.83/38.02 right_branch(9),
% 37.83/38.02 left_branch(0, 106, 1, 10),
% 37.83/38.02 left_branch(0, 137, 0, 11),
% 37.83/38.02 right_branch(11),
% 37.83/38.02 right_branch(10),
% 37.83/38.02 lemmata(0, 4),
% 37.83/38.02 right_branch(5),
% 37.83/38.02 left_branch(0, 106, 1, 6),
% 37.83/38.02 left_branch(0, 137, 0, 7),
% 37.83/38.02 right_branch(7),
% 37.83/38.02 right_branch(6),
% 37.83/38.02 left_branch(0, 116, 2, 7),
% 37.83/38.02 left_branch(0, 138, 0, 8),
% 37.83/38.02 right_branch(8),
% 37.83/38.02 lemmata(0, 3),
% 37.83/38.02 right_branch(7),
% 37.83/38.02 lemmata(0, 4),
% 37.83/38.02 right_branch(2)
% 37.83/38.02 )).
% 37.83/38.02 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------