TSTP Solution File: SET810+4 by ConnectPP---0.3.0
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%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : SET810+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 : n029.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 14:32:26 EDT 2024
% Result : Theorem 33.71s 33.92s
% Output : Proof 33.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET810+4 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Mar 20 22:01:03 EDT 2024
% 0.13/0.34 % CPUTime :
% 33.71/33.92 % SZS status Theorem for theBenchmark
% 33.71/33.92 % SZS output start Proof for theBenchmark
% 33.71/33.92
% 33.71/33.92 % Formula: subset ( axiom ) converted to clauses:
% 33.71/33.92 cnf(subset-1, axiom, ( ~subset(_u6, _u4) | ~member(_u0, _u6) | member(_u0, _u4) )).
% 33.71/33.92 cnf(subset-2, axiom, ( subset(_u7, _u5) | member(skolem1(_u7, _u5), _u7) )).
% 33.71/33.92 cnf(subset-3, axiom, ( subset(_u7, _u5) | ~member(skolem1(_u7, _u5), _u5) )).
% 33.71/33.92
% 33.71/33.92 % Formula: equal_set ( axiom ) converted to clauses:
% 33.71/33.92 cnf(equal_set-1, axiom, ( ~equal_set(_u12, _u10) | subset(_u12, _u10) )).
% 33.71/33.92 cnf(equal_set-2, axiom, ( ~equal_set(_u12, _u10) | subset(_u10, _u12) )).
% 33.71/33.92 cnf(equal_set-3, axiom, ( ~subset(_u13, _u11) | ~subset(_u11, _u13) | equal_set(_u13, _u11) )).
% 33.71/33.92
% 33.71/33.92 % Formula: power_set ( axiom ) converted to clauses:
% 33.71/33.92 cnf(power_set-1, axiom, ( ~member(_u18, power_set(_u16)) | subset(_u18, _u16) )).
% 33.71/33.92 cnf(power_set-2, axiom, ( ~subset(_u19, _u17) | member(_u19, power_set(_u17)) )).
% 33.71/33.92
% 33.71/33.92 % Formula: intersection ( axiom ) converted to clauses:
% 33.71/33.92 cnf(intersection-1, axiom, ( ~member(_u27, intersection(_u25, _u23)) | member(_u27, _u25) )).
% 33.71/33.92 cnf(intersection-2, axiom, ( ~member(_u27, intersection(_u25, _u23)) | member(_u27, _u23) )).
% 33.71/33.92 cnf(intersection-3, axiom, ( ~member(_u28, _u26) | ~member(_u28, _u24) | member(_u28, intersection(_u26, _u24)) )).
% 33.71/33.92
% 33.71/33.92 % Formula: union ( axiom ) converted to clauses:
% 33.71/33.92 cnf(union-1, axiom, ( ~member(_u36, union(_u34, _u32)) | member(_u36, _u34) | member(_u36, _u32) )).
% 33.71/33.92 cnf(union-2, axiom, ( member(_u37, union(_u35, _u33)) | ~member(_u37, _u35) )).
% 33.71/33.92 cnf(union-3, axiom, ( member(_u37, union(_u35, _u33)) | ~member(_u37, _u33) )).
% 33.71/33.92
% 33.71/33.92 % Formula: empty_set ( axiom ) converted to clauses:
% 33.71/33.92 cnf(empty_set-1, axiom, ( ~member(_u38, empty_set) )).
% 33.71/33.92
% 33.71/33.92 % Formula: difference ( axiom ) converted to clauses:
% 33.71/33.92 cnf(difference-1, axiom, ( ~member(_u46, difference(_u42, _u44)) | member(_u46, _u42) )).
% 33.71/33.92 cnf(difference-2, axiom, ( ~member(_u46, difference(_u42, _u44)) | ~member(_u46, _u44) )).
% 33.71/33.92 cnf(difference-3, axiom, ( ~member(_u47, _u43) | member(_u47, _u45) | member(_u47, difference(_u43, _u45)) )).
% 33.71/33.92
% 33.71/33.92 % Formula: singleton ( axiom ) converted to clauses:
% 33.71/33.92 cnf(singleton-1, axiom, ( ~member(_u52, singleton(_u50)) | ( _u52 = _u50) )).
% 33.71/33.92 cnf(singleton-2, axiom, ( ( _u53 != _u51) | member(_u53, singleton(_u51)) )).
% 33.71/33.92
% 33.71/33.92 % Formula: unordered_pair ( axiom ) converted to clauses:
% 33.71/33.92 cnf(unordered_pair-1, axiom, ( ~member(_u61, unordered_pair(_u59, _u57)) | ( _u61 = _u59) | ( _u61 = _u57) )).
% 33.71/33.92 cnf(unordered_pair-2, axiom, ( member(_u62, unordered_pair(_u60, _u58)) | ( _u62 != _u60) )).
% 33.71/33.92 cnf(unordered_pair-3, axiom, ( member(_u62, unordered_pair(_u60, _u58)) | ( _u62 != _u58) )).
% 33.71/33.92
% 33.71/33.92 % Formula: sum ( axiom ) converted to clauses:
% 33.71/33.92 cnf(sum-1, axiom, ( ~member(_u69, sum(_u67)) | member(skolem2(_u69, _u67), _u67) )).
% 33.71/33.92 cnf(sum-2, axiom, ( ~member(_u69, sum(_u67)) | member(_u69, skolem2(_u69, _u67)) )).
% 33.71/33.92 cnf(sum-3, axiom, ( ~member(_u64, _u68) | ~member(_u70, _u64) | member(_u70, sum(_u68)) )).
% 33.71/33.92
% 33.71/33.92 % Formula: product ( axiom ) converted to clauses:
% 33.71/33.92 cnf(product-1, axiom, ( ~member(_u77, product(_u75)) | ~member(_u71, _u75) | member(_u77, _u71) )).
% 33.71/33.92 cnf(product-2, axiom, ( member(_u78, product(_u76)) | member(skolem3(_u78, _u76), _u76) )).
% 33.71/33.92 cnf(product-3, axiom, ( member(_u78, product(_u76)) | ~member(_u78, skolem3(_u78, _u76)) )).
% 33.71/33.92
% 33.71/33.92 % Formula: ordinal_number ( axiom ) converted to clauses:
% 33.71/33.92 cnf(ordinal_number-1, axiom, ( ~member(_u82, on) | set(_u82) )).
% 33.71/33.92 cnf(ordinal_number-2, axiom, ( ~member(_u82, on) | strict_well_order(member_predicate, _u82) )).
% 33.71/33.92 cnf(ordinal_number-3, axiom, ( ~member(_u82, on) | ~member(_u79, _u82) | subset(_u79, _u82) )).
% 33.71/33.92 cnf(ordinal_number-4, axiom, ( member(_u83, on) | ~set(_u83) | ~strict_well_order(member_predicate, _u83) | member(skolem4(_u83), _u83) )).
% 33.71/33.92 cnf(ordinal_number-5, axiom, ( member(_u83, on) | ~set(_u83) | ~strict_well_order(member_predicate, _u83) | ~subset(skolem4(_u83), _u83) )).
% 33.71/33.92
% 33.71/33.92 % Formula: strict_well_order ( axiom ) converted to clauses:
% 33.71/33.92 cnf(strict_well_order-1, axiom, ( ~strict_well_order(_u94, _u92) | strict_order(_u94, _u92) )).
% 33.71/33.92 cnf(strict_well_order-2, axiom, ( ~strict_well_order(_u94, _u92) | ~subset(_u86, _u92) | ~member(_u84, _u86) | least(skolem5(_u94, _u92, _u86), _u94, _u86) )).
% 33.71/33.92 cnf(strict_well_order-3, axiom, ( strict_well_order(_u95, _u93) | ~strict_order(_u95, _u93) | subset(skolem6(_u95, _u93), _u93) )).
% 33.71/33.92 cnf(strict_well_order-4, axiom, ( strict_well_order(_u95, _u93) | ~strict_order(_u95, _u93) | member(skolem7(_u95, _u93), skolem6(_u95, _u93)) )).
% 33.71/33.92 cnf(strict_well_order-5, axiom, ( strict_well_order(_u95, _u93) | ~strict_order(_u95, _u93) | ~least(_u88, _u95, skolem6(_u95, _u93)) )).
% 33.71/33.92
% 33.71/33.92 % Formula: least ( axiom ) converted to clauses:
% 33.71/33.92 cnf(least-1, axiom, ( ~least(_u101, _u105, _u103) | member(_u101, _u103) )).
% 33.71/33.92 cnf(least-2, axiom, ( ~least(_u101, _u105, _u103) | ~member(_u96, _u103) | ( _u101 = _u96) | apply(_u105, _u101, _u96) )).
% 33.71/33.92 cnf(least-3, axiom, ( least(_u102, _u106, _u104) | ~member(_u102, _u104) | member(skolem8(_u106, _u104, _u102), _u104) )).
% 33.71/33.92 cnf(least-4, axiom, ( least(_u102, _u106, _u104) | ~member(_u102, _u104) | ( _u102 != skolem8(_u106, _u104, _u102)) )).
% 33.71/33.92 cnf(least-5, axiom, ( least(_u102, _u106, _u104) | ~member(_u102, _u104) | ~apply(_u106, _u102, skolem8(_u106, _u104, _u102)) )).
% 33.71/33.92
% 33.71/33.92 % Formula: rel_member ( axiom ) converted to clauses:
% 33.71/33.92 cnf(rel_member-1, axiom, ( ~apply(member_predicate, _u111, _u109) | member(_u111, _u109) )).
% 33.71/33.92 cnf(rel_member-2, axiom, ( ~member(_u112, _u110) | apply(member_predicate, _u112, _u110) )).
% 33.71/33.92
% 33.71/33.92 % Formula: strict_order ( axiom ) converted to clauses:
% 33.71/33.92 cnf(strict_order-1, axiom, ( ~strict_order(_u127, _u125) | ~member(_u114, _u125) | ~member(_u113, _u125) | ~apply(_u127, _u114, _u113) | ~apply(_u127, _u113, _u114) )).
% 33.71/33.92 cnf(strict_order-2, axiom, ( ~strict_order(_u127, _u125) | ~member(_u117, _u125) | ~member(_u116, _u125) | ~member(_u115, _u125) | ~apply(_u127, _u117, _u116) | ~apply(_u127, _u116, _u115) | apply(_u127, _u117, _u115) )).
% 33.71/33.92 cnf(strict_order-3, axiom, ( strict_order(_u128, _u126) | member(skolem9(_u128, _u126), _u126) | member(skolem11(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(strict_order-4, axiom, ( strict_order(_u128, _u126) | member(skolem9(_u128, _u126), _u126) | member(skolem12(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(strict_order-5, axiom, ( strict_order(_u128, _u126) | member(skolem9(_u128, _u126), _u126) | member(skolem13(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(strict_order-6, axiom, ( strict_order(_u128, _u126) | member(skolem10(_u128, _u126), _u126) | member(skolem11(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(strict_order-7, axiom, ( strict_order(_u128, _u126) | member(skolem10(_u128, _u126), _u126) | member(skolem12(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(strict_order-8, axiom, ( strict_order(_u128, _u126) | member(skolem10(_u128, _u126), _u126) | member(skolem13(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(strict_order-9, axiom, ( strict_order(_u128, _u126) | member(skolem9(_u128, _u126), _u126) | apply(_u128, skolem11(_u128, _u126), skolem12(_u128, _u126)) )).
% 33.71/33.92 cnf(strict_order-10, axiom, ( strict_order(_u128, _u126) | member(skolem9(_u128, _u126), _u126) | apply(_u128, skolem12(_u128, _u126), skolem13(_u128, _u126)) )).
% 33.71/33.92 cnf(strict_order-11, axiom, ( strict_order(_u128, _u126) | member(skolem9(_u128, _u126), _u126) | ~apply(_u128, skolem11(_u128, _u126), skolem13(_u128, _u126)) )).
% 33.71/33.92 cnf(strict_order-12, axiom, ( strict_order(_u128, _u126) | member(skolem10(_u128, _u126), _u126) | apply(_u128, skolem11(_u128, _u126), skolem12(_u128, _u126)) )).
% 33.71/33.92 cnf(strict_order-13, axiom, ( strict_order(_u128, _u126) | member(skolem10(_u128, _u126), _u126) | apply(_u128, skolem12(_u128, _u126), skolem13(_u128, _u126)) )).
% 33.71/33.92 cnf(strict_order-14, axiom, ( strict_order(_u128, _u126) | member(skolem10(_u128, _u126), _u126) | ~apply(_u128, skolem11(_u128, _u126), skolem13(_u128, _u126)) )).
% 33.71/33.92 cnf(strict_order-15, axiom, ( strict_order(_u128, _u126) | apply(_u128, skolem9(_u128, _u126), skolem10(_u128, _u126)) | member(skolem11(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(strict_order-16, axiom, ( strict_order(_u128, _u126) | apply(_u128, skolem9(_u128, _u126), skolem10(_u128, _u126)) | member(skolem12(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(strict_order-17, axiom, ( strict_order(_u128, _u126) | apply(_u128, skolem9(_u128, _u126), skolem10(_u128, _u126)) | member(skolem13(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(strict_order-18, axiom, ( strict_order(_u128, _u126) | apply(_u128, skolem10(_u128, _u126), skolem9(_u128, _u126)) | member(skolem11(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(strict_order-19, axiom, ( strict_order(_u128, _u126) | apply(_u128, skolem10(_u128, _u126), skolem9(_u128, _u126)) | member(skolem12(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(strict_order-20, axiom, ( strict_order(_u128, _u126) | apply(_u128, skolem10(_u128, _u126), skolem9(_u128, _u126)) | member(skolem13(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(strict_order-21, axiom, ( strict_order(_u128, _u126) | apply(_u128, skolem9(_u128, _u126), skolem10(_u128, _u126)) | apply(_u128, skolem11(_u128, _u126), skolem12(_u128, _u126)) )).
% 33.71/33.92 cnf(strict_order-22, axiom, ( strict_order(_u128, _u126) | apply(_u128, skolem9(_u128, _u126), skolem10(_u128, _u126)) | apply(_u128, skolem12(_u128, _u126), skolem13(_u128, _u126)) )).
% 33.71/33.92 cnf(strict_order-23, axiom, ( strict_order(_u128, _u126) | apply(_u128, skolem9(_u128, _u126), skolem10(_u128, _u126)) | ~apply(_u128, skolem11(_u128, _u126), skolem13(_u128, _u126)) )).
% 33.71/33.92 cnf(strict_order-24, axiom, ( strict_order(_u128, _u126) | apply(_u128, skolem10(_u128, _u126), skolem9(_u128, _u126)) | apply(_u128, skolem11(_u128, _u126), skolem12(_u128, _u126)) )).
% 33.71/33.92 cnf(strict_order-25, axiom, ( strict_order(_u128, _u126) | apply(_u128, skolem10(_u128, _u126), skolem9(_u128, _u126)) | apply(_u128, skolem12(_u128, _u126), skolem13(_u128, _u126)) )).
% 33.71/33.92 cnf(strict_order-26, axiom, ( strict_order(_u128, _u126) | apply(_u128, skolem10(_u128, _u126), skolem9(_u128, _u126)) | ~apply(_u128, skolem11(_u128, _u126), skolem13(_u128, _u126)) )).
% 33.71/33.92
% 33.71/33.92 % Formula: set_member ( axiom ) converted to clauses:
% 33.71/33.92 cnf(set_member-1, axiom, ( ~set(_u130) | ~member(_u129, _u130) | set(_u129) )).
% 33.71/33.92
% 33.71/33.92 % Formula: initial_segment ( axiom ) converted to clauses:
% 33.71/33.92 cnf(initial_segment-1, axiom, ( ~member(_u135, initial_segment(_u141, _u139, _u137)) | member(_u135, _u137) )).
% 33.71/33.92 cnf(initial_segment-2, axiom, ( ~member(_u135, initial_segment(_u141, _u139, _u137)) | apply(_u139, _u135, _u141) )).
% 33.71/33.92 cnf(initial_segment-3, axiom, ( ~member(_u136, _u138) | ~apply(_u140, _u136, _u142) | member(_u136, initial_segment(_u142, _u140, _u138)) )).
% 33.71/33.92
% 33.71/33.92 % Formula: successor ( axiom ) converted to clauses:
% 33.71/33.92 cnf(successor-1, axiom, ( ~member(_u145, suc(_u147)) | member(_u145, union(_u147, singleton(_u147))) )).
% 33.71/33.92 cnf(successor-2, axiom, ( ~member(_u146, union(_u148, singleton(_u148))) | member(_u146, suc(_u148)) )).
% 33.71/33.92
% 33.71/33.92 % Formula: thV3 ( conjecture ) (definitionally) converted to clauses:
% 33.71/33.92 cnf(thV3-1, negated_conjecture, ( member(skolem14, on) )).
% 33.71/33.92 cnf(thV3-2, negated_conjecture, ( member(skolem15, on) )).
% 33.71/33.92 cnf(thV3-3, negated_conjecture, ( member(skolem14, skolem15) )).
% 33.71/33.92 cnf(thV3-4, negated_conjecture, ( member(skolem15, skolem14) )).
% 33.71/33.92
% 33.71/33.92 % Problem matrix:
% 33.71/33.92 cnf(matrix-0, plain, ( ( __eqx_0 = __eqx_0) )).
% 33.71/33.92 cnf(matrix-1, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 = __eqx_0) )).
% 33.71/33.92 cnf(matrix-2, plain, ( ( __eqx_0 != __eqx_1) | ( __eqx_1 != __eqx_2) | ( __eqx_0 = __eqx_2) )).
% 33.71/33.92 cnf(matrix-3, plain, ( ( __eqx_0 != __eqy_0) | ( power_set(__eqx_0) = power_set(__eqy_0)) )).
% 33.71/33.92 cnf(matrix-4, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( intersection(__eqx_0, __eqx_1) = intersection(__eqy_0, __eqy_1)) )).
% 33.71/33.92 cnf(matrix-5, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( union(__eqx_0, __eqx_1) = union(__eqy_0, __eqy_1)) )).
% 33.71/33.92 cnf(matrix-6, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( difference(__eqx_0, __eqx_1) = difference(__eqy_0, __eqy_1)) )).
% 33.71/33.92 cnf(matrix-7, plain, ( ( __eqx_0 != __eqy_0) | ( singleton(__eqx_0) = singleton(__eqy_0)) )).
% 33.71/33.92 cnf(matrix-8, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( unordered_pair(__eqx_0, __eqx_1) = unordered_pair(__eqy_0, __eqy_1)) )).
% 33.71/33.92 cnf(matrix-9, plain, ( ( __eqx_0 != __eqy_0) | ( sum(__eqx_0) = sum(__eqy_0)) )).
% 33.71/33.92 cnf(matrix-10, plain, ( ( __eqx_0 != __eqy_0) | ( product(__eqx_0) = product(__eqy_0)) )).
% 33.71/33.92 cnf(matrix-11, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( initial_segment(__eqx_0, __eqx_1, __eqx_2) = initial_segment(__eqy_0, __eqy_1, __eqy_2)) )).
% 33.71/33.92 cnf(matrix-12, plain, ( ( __eqx_0 != __eqy_0) | ( suc(__eqx_0) = suc(__eqy_0)) )).
% 33.71/33.92 cnf(matrix-13, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem1(__eqx_0, __eqx_1) = skolem1(__eqy_0, __eqy_1)) )).
% 33.71/33.92 cnf(matrix-14, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem2(__eqx_0, __eqx_1) = skolem2(__eqy_0, __eqy_1)) )).
% 33.71/33.92 cnf(matrix-15, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem3(__eqx_0, __eqx_1) = skolem3(__eqy_0, __eqy_1)) )).
% 33.71/33.92 cnf(matrix-16, plain, ( ( __eqx_0 != __eqy_0) | ( skolem4(__eqx_0) = skolem4(__eqy_0)) )).
% 33.71/33.92 cnf(matrix-17, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem5(__eqx_0, __eqx_1, __eqx_2) = skolem5(__eqy_0, __eqy_1, __eqy_2)) )).
% 33.71/33.92 cnf(matrix-18, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem6(__eqx_0, __eqx_1) = skolem6(__eqy_0, __eqy_1)) )).
% 33.71/33.92 cnf(matrix-19, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem7(__eqx_0, __eqx_1) = skolem7(__eqy_0, __eqy_1)) )).
% 33.71/33.92 cnf(matrix-20, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( __eqx_2 != __eqy_2) | ( skolem8(__eqx_0, __eqx_1, __eqx_2) = skolem8(__eqy_0, __eqy_1, __eqy_2)) )).
% 33.71/33.92 cnf(matrix-21, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem9(__eqx_0, __eqx_1) = skolem9(__eqy_0, __eqy_1)) )).
% 33.71/33.92 cnf(matrix-22, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem10(__eqx_0, __eqx_1) = skolem10(__eqy_0, __eqy_1)) )).
% 33.71/33.92 cnf(matrix-23, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem11(__eqx_0, __eqx_1) = skolem11(__eqy_0, __eqy_1)) )).
% 33.71/33.92 cnf(matrix-24, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem12(__eqx_0, __eqx_1) = skolem12(__eqy_0, __eqy_1)) )).
% 33.71/33.92 cnf(matrix-25, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ( skolem13(__eqx_0, __eqx_1) = skolem13(__eqy_0, __eqy_1)) )).
% 33.71/33.92 cnf(matrix-26, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~subset(__eqx_0, __eqx_1) | subset(__eqy_0, __eqy_1) )).
% 33.71/33.92 cnf(matrix-27, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~member(__eqx_0, __eqx_1) | member(__eqy_0, __eqy_1) )).
% 33.71/33.92 cnf(matrix-28, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~equal_set(__eqx_0, __eqx_1) | equal_set(__eqy_0, __eqy_1) )).
% 33.71/33.92 cnf(matrix-29, plain, ( ( __eqx_0 != __eqy_0) | ~set(__eqx_0) | set(__eqy_0) )).
% 33.71/33.92 cnf(matrix-30, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~strict_well_order(__eqx_0, __eqx_1) | strict_well_order(__eqy_0, __eqy_1) )).
% 33.71/33.92 cnf(matrix-31, plain, ( ( __eqx_0 != __eqy_0) | ( __eqx_1 != __eqy_1) | ~strict_order(__eqx_0, __eqx_1) | strict_order(__eqy_0, __eqy_1) )).
% 33.71/33.92 cnf(matrix-32, 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) )).
% 33.71/33.92 cnf(matrix-33, 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) )).
% 33.71/33.92 cnf(matrix-34, plain, ( ~subset(_u6, _u4) | ~member(_u0, _u6) | member(_u0, _u4) )).
% 33.71/33.92 cnf(matrix-35, plain, ( subset(_u7, _u5) | member(skolem1(_u7, _u5), _u7) )).
% 33.71/33.92 cnf(matrix-36, plain, ( subset(_u7, _u5) | ~member(skolem1(_u7, _u5), _u5) )).
% 33.71/33.92 cnf(matrix-37, plain, ( ~equal_set(_u12, _u10) | subset(_u12, _u10) )).
% 33.71/33.92 cnf(matrix-38, plain, ( ~equal_set(_u12, _u10) | subset(_u10, _u12) )).
% 33.71/33.92 cnf(matrix-39, plain, ( ~subset(_u13, _u11) | ~subset(_u11, _u13) | equal_set(_u13, _u11) )).
% 33.71/33.92 cnf(matrix-40, plain, ( ~member(_u18, power_set(_u16)) | subset(_u18, _u16) )).
% 33.71/33.92 cnf(matrix-41, plain, ( ~subset(_u19, _u17) | member(_u19, power_set(_u17)) )).
% 33.71/33.92 cnf(matrix-42, plain, ( ~member(_u27, intersection(_u25, _u23)) | member(_u27, _u25) )).
% 33.71/33.92 cnf(matrix-43, plain, ( ~member(_u27, intersection(_u25, _u23)) | member(_u27, _u23) )).
% 33.71/33.92 cnf(matrix-44, plain, ( ~member(_u28, _u26) | ~member(_u28, _u24) | member(_u28, intersection(_u26, _u24)) )).
% 33.71/33.92 cnf(matrix-45, plain, ( ~member(_u36, union(_u34, _u32)) | member(_u36, _u34) | member(_u36, _u32) )).
% 33.71/33.92 cnf(matrix-46, plain, ( member(_u37, union(_u35, _u33)) | ~member(_u37, _u35) )).
% 33.71/33.92 cnf(matrix-47, plain, ( member(_u37, union(_u35, _u33)) | ~member(_u37, _u33) )).
% 33.71/33.92 cnf(matrix-48, plain, ( ~member(_u38, empty_set) )).
% 33.71/33.92 cnf(matrix-49, plain, ( ~member(_u46, difference(_u42, _u44)) | member(_u46, _u42) )).
% 33.71/33.92 cnf(matrix-50, plain, ( ~member(_u46, difference(_u42, _u44)) | ~member(_u46, _u44) )).
% 33.71/33.92 cnf(matrix-51, plain, ( ~member(_u47, _u43) | member(_u47, _u45) | member(_u47, difference(_u43, _u45)) )).
% 33.71/33.92 cnf(matrix-52, plain, ( ~member(_u52, singleton(_u50)) | ( _u52 = _u50) )).
% 33.71/33.92 cnf(matrix-53, plain, ( ( _u53 != _u51) | member(_u53, singleton(_u51)) )).
% 33.71/33.92 cnf(matrix-54, plain, ( ~member(_u61, unordered_pair(_u59, _u57)) | ( _u61 = _u59) | ( _u61 = _u57) )).
% 33.71/33.92 cnf(matrix-55, plain, ( member(_u62, unordered_pair(_u60, _u58)) | ( _u62 != _u60) )).
% 33.71/33.92 cnf(matrix-56, plain, ( member(_u62, unordered_pair(_u60, _u58)) | ( _u62 != _u58) )).
% 33.71/33.92 cnf(matrix-57, plain, ( ~member(_u69, sum(_u67)) | member(skolem2(_u69, _u67), _u67) )).
% 33.71/33.92 cnf(matrix-58, plain, ( ~member(_u69, sum(_u67)) | member(_u69, skolem2(_u69, _u67)) )).
% 33.71/33.92 cnf(matrix-59, plain, ( ~member(_u64, _u68) | ~member(_u70, _u64) | member(_u70, sum(_u68)) )).
% 33.71/33.92 cnf(matrix-60, plain, ( ~member(_u77, product(_u75)) | ~member(_u71, _u75) | member(_u77, _u71) )).
% 33.71/33.92 cnf(matrix-61, plain, ( member(_u78, product(_u76)) | member(skolem3(_u78, _u76), _u76) )).
% 33.71/33.92 cnf(matrix-62, plain, ( member(_u78, product(_u76)) | ~member(_u78, skolem3(_u78, _u76)) )).
% 33.71/33.92 cnf(matrix-63, plain, ( ~member(_u82, on) | set(_u82) )).
% 33.71/33.92 cnf(matrix-64, plain, ( ~member(_u82, on) | strict_well_order(member_predicate, _u82) )).
% 33.71/33.92 cnf(matrix-65, plain, ( ~member(_u82, on) | ~member(_u79, _u82) | subset(_u79, _u82) )).
% 33.71/33.92 cnf(matrix-66, plain, ( member(_u83, on) | ~set(_u83) | ~strict_well_order(member_predicate, _u83) | member(skolem4(_u83), _u83) )).
% 33.71/33.92 cnf(matrix-67, plain, ( member(_u83, on) | ~set(_u83) | ~strict_well_order(member_predicate, _u83) | ~subset(skolem4(_u83), _u83) )).
% 33.71/33.92 cnf(matrix-68, plain, ( ~strict_well_order(_u94, _u92) | strict_order(_u94, _u92) )).
% 33.71/33.92 cnf(matrix-69, plain, ( ~strict_well_order(_u94, _u92) | ~subset(_u86, _u92) | ~member(_u84, _u86) | least(skolem5(_u94, _u92, _u86), _u94, _u86) )).
% 33.71/33.92 cnf(matrix-70, plain, ( strict_well_order(_u95, _u93) | ~strict_order(_u95, _u93) | subset(skolem6(_u95, _u93), _u93) )).
% 33.71/33.92 cnf(matrix-71, plain, ( strict_well_order(_u95, _u93) | ~strict_order(_u95, _u93) | member(skolem7(_u95, _u93), skolem6(_u95, _u93)) )).
% 33.71/33.92 cnf(matrix-72, plain, ( strict_well_order(_u95, _u93) | ~strict_order(_u95, _u93) | ~least(_u88, _u95, skolem6(_u95, _u93)) )).
% 33.71/33.92 cnf(matrix-73, plain, ( ~least(_u101, _u105, _u103) | member(_u101, _u103) )).
% 33.71/33.92 cnf(matrix-74, plain, ( ~least(_u101, _u105, _u103) | ~member(_u96, _u103) | ( _u101 = _u96) | apply(_u105, _u101, _u96) )).
% 33.71/33.92 cnf(matrix-75, plain, ( least(_u102, _u106, _u104) | ~member(_u102, _u104) | member(skolem8(_u106, _u104, _u102), _u104) )).
% 33.71/33.92 cnf(matrix-76, plain, ( least(_u102, _u106, _u104) | ~member(_u102, _u104) | ( _u102 != skolem8(_u106, _u104, _u102)) )).
% 33.71/33.92 cnf(matrix-77, plain, ( least(_u102, _u106, _u104) | ~member(_u102, _u104) | ~apply(_u106, _u102, skolem8(_u106, _u104, _u102)) )).
% 33.71/33.92 cnf(matrix-78, plain, ( ~apply(member_predicate, _u111, _u109) | member(_u111, _u109) )).
% 33.71/33.92 cnf(matrix-79, plain, ( ~member(_u112, _u110) | apply(member_predicate, _u112, _u110) )).
% 33.71/33.92 cnf(matrix-80, plain, ( ~strict_order(_u127, _u125) | ~member(_u114, _u125) | ~member(_u113, _u125) | ~apply(_u127, _u114, _u113) | ~apply(_u127, _u113, _u114) )).
% 33.71/33.92 cnf(matrix-81, plain, ( ~strict_order(_u127, _u125) | ~member(_u117, _u125) | ~member(_u116, _u125) | ~member(_u115, _u125) | ~apply(_u127, _u117, _u116) | ~apply(_u127, _u116, _u115) | apply(_u127, _u117, _u115) )).
% 33.71/33.92 cnf(matrix-82, plain, ( strict_order(_u128, _u126) | member(skolem9(_u128, _u126), _u126) | member(skolem11(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(matrix-83, plain, ( strict_order(_u128, _u126) | member(skolem9(_u128, _u126), _u126) | member(skolem12(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(matrix-84, plain, ( strict_order(_u128, _u126) | member(skolem9(_u128, _u126), _u126) | member(skolem13(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(matrix-85, plain, ( strict_order(_u128, _u126) | member(skolem10(_u128, _u126), _u126) | member(skolem11(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(matrix-86, plain, ( strict_order(_u128, _u126) | member(skolem10(_u128, _u126), _u126) | member(skolem12(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(matrix-87, plain, ( strict_order(_u128, _u126) | member(skolem10(_u128, _u126), _u126) | member(skolem13(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(matrix-88, plain, ( strict_order(_u128, _u126) | member(skolem9(_u128, _u126), _u126) | apply(_u128, skolem11(_u128, _u126), skolem12(_u128, _u126)) )).
% 33.71/33.92 cnf(matrix-89, plain, ( strict_order(_u128, _u126) | member(skolem9(_u128, _u126), _u126) | apply(_u128, skolem12(_u128, _u126), skolem13(_u128, _u126)) )).
% 33.71/33.92 cnf(matrix-90, plain, ( strict_order(_u128, _u126) | member(skolem9(_u128, _u126), _u126) | ~apply(_u128, skolem11(_u128, _u126), skolem13(_u128, _u126)) )).
% 33.71/33.92 cnf(matrix-91, plain, ( strict_order(_u128, _u126) | member(skolem10(_u128, _u126), _u126) | apply(_u128, skolem11(_u128, _u126), skolem12(_u128, _u126)) )).
% 33.71/33.92 cnf(matrix-92, plain, ( strict_order(_u128, _u126) | member(skolem10(_u128, _u126), _u126) | apply(_u128, skolem12(_u128, _u126), skolem13(_u128, _u126)) )).
% 33.71/33.92 cnf(matrix-93, plain, ( strict_order(_u128, _u126) | member(skolem10(_u128, _u126), _u126) | ~apply(_u128, skolem11(_u128, _u126), skolem13(_u128, _u126)) )).
% 33.71/33.92 cnf(matrix-94, plain, ( strict_order(_u128, _u126) | apply(_u128, skolem9(_u128, _u126), skolem10(_u128, _u126)) | member(skolem11(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(matrix-95, plain, ( strict_order(_u128, _u126) | apply(_u128, skolem9(_u128, _u126), skolem10(_u128, _u126)) | member(skolem12(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(matrix-96, plain, ( strict_order(_u128, _u126) | apply(_u128, skolem9(_u128, _u126), skolem10(_u128, _u126)) | member(skolem13(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(matrix-97, plain, ( strict_order(_u128, _u126) | apply(_u128, skolem10(_u128, _u126), skolem9(_u128, _u126)) | member(skolem11(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(matrix-98, plain, ( strict_order(_u128, _u126) | apply(_u128, skolem10(_u128, _u126), skolem9(_u128, _u126)) | member(skolem12(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(matrix-99, plain, ( strict_order(_u128, _u126) | apply(_u128, skolem10(_u128, _u126), skolem9(_u128, _u126)) | member(skolem13(_u128, _u126), _u126) )).
% 33.71/33.92 cnf(matrix-100, plain, ( strict_order(_u128, _u126) | apply(_u128, skolem9(_u128, _u126), skolem10(_u128, _u126)) | apply(_u128, skolem11(_u128, _u126), skolem12(_u128, _u126)) )).
% 33.71/33.92 cnf(matrix-101, plain, ( strict_order(_u128, _u126) | apply(_u128, skolem9(_u128, _u126), skolem10(_u128, _u126)) | apply(_u128, skolem12(_u128, _u126), skolem13(_u128, _u126)) )).
% 33.71/33.92 cnf(matrix-102, plain, ( strict_order(_u128, _u126) | apply(_u128, skolem9(_u128, _u126), skolem10(_u128, _u126)) | ~apply(_u128, skolem11(_u128, _u126), skolem13(_u128, _u126)) )).
% 33.71/33.92 cnf(matrix-103, plain, ( strict_order(_u128, _u126) | apply(_u128, skolem10(_u128, _u126), skolem9(_u128, _u126)) | apply(_u128, skolem11(_u128, _u126), skolem12(_u128, _u126)) )).
% 33.71/33.92 cnf(matrix-104, plain, ( strict_order(_u128, _u126) | apply(_u128, skolem10(_u128, _u126), skolem9(_u128, _u126)) | apply(_u128, skolem12(_u128, _u126), skolem13(_u128, _u126)) )).
% 33.71/33.92 cnf(matrix-105, plain, ( strict_order(_u128, _u126) | apply(_u128, skolem10(_u128, _u126), skolem9(_u128, _u126)) | ~apply(_u128, skolem11(_u128, _u126), skolem13(_u128, _u126)) )).
% 33.71/33.92 cnf(matrix-106, plain, ( ~set(_u130) | ~member(_u129, _u130) | set(_u129) )).
% 33.71/33.92 cnf(matrix-107, plain, ( ~member(_u135, initial_segment(_u141, _u139, _u137)) | member(_u135, _u137) )).
% 33.71/33.92 cnf(matrix-108, plain, ( ~member(_u135, initial_segment(_u141, _u139, _u137)) | apply(_u139, _u135, _u141) )).
% 33.71/33.92 cnf(matrix-109, plain, ( ~member(_u136, _u138) | ~apply(_u140, _u136, _u142) | member(_u136, initial_segment(_u142, _u140, _u138)) )).
% 33.71/33.92 cnf(matrix-110, plain, ( ~member(_u145, suc(_u147)) | member(_u145, union(_u147, singleton(_u147))) )).
% 33.71/33.92 cnf(matrix-111, plain, ( ~member(_u146, union(_u148, singleton(_u148))) | member(_u146, suc(_u148)) )).
% 33.71/33.92 cnf(matrix-112, plain, ( member(skolem14, on) )).
% 33.71/33.92 cnf(matrix-113, plain, ( member(skolem15, on) )).
% 33.71/33.92 cnf(matrix-114, plain, ( member(skolem14, skolem15) )).
% 33.71/33.92 cnf(matrix-115, plain, ( member(skolem15, skolem14) )).
% 33.71/33.92
% 33.71/33.92 % Proof stack:
% 33.71/33.92 cnf(proof-stack, plain,
% 33.71/33.92 proof_stack(
% 33.71/33.92 start(114),
% 33.71/33.92 left_branch(0, 80, 2, 2),
% 33.71/33.92 left_branch(0, 68, 1, 3),
% 33.71/33.92 left_branch(0, 64, 1, 4),
% 33.71/33.92 left_branch(0, 113, 0, 5),
% 33.71/33.92 right_branch(5),
% 33.71/33.92 right_branch(4),
% 33.71/33.92 right_branch(3),
% 33.71/33.92 left_branch(0, 79, 1, 4),
% 33.71/33.92 left_branch(0, 115, 0, 5),
% 33.71/33.92 right_branch(5),
% 33.71/33.92 right_branch(4),
% 33.71/33.92 left_branch(0, 79, 1, 5),
% 33.71/33.92 reduction(0, 0),
% 33.71/33.92 right_branch(5),
% 33.71/33.92 left_branch(0, 34, 2, 6),
% 33.71/33.92 left_branch(0, 65, 2, 7),
% 33.71/33.92 left_branch(0, 113, 0, 8),
% 33.71/33.92 right_branch(8),
% 33.71/33.92 reduction(0, 0),
% 33.71/33.92 right_branch(7),
% 33.71/33.92 left_branch(0, 115, 0, 8),
% 33.71/33.92 right_branch(8),
% 33.71/33.92 right_branch(6),
% 33.71/33.92 right_branch(2)
% 33.71/33.92 )).
% 33.71/33.92 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------