TSTP Solution File: SEU028+1 by leanCoP---2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : leanCoP---2.2
% Problem : SEU028+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leancop_casc.sh %s %d
% Computer : n017.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 : 600s
% DateTime : Tue Jul 19 11:59:50 EDT 2022
% Result : Theorem 0.42s 1.42s
% Output : Proof 0.42s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU028+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : leancop_casc.sh %s %d
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 20 08:45:44 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.42/1.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/1.43 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/1.43
% 0.42/1.43 %-----------------------------------------------------
% 0.42/1.43 fof(t61_funct_1, conjecture, ! [_72768] : (relation(_72768) & function(_72768) => one_to_one(_72768) => relation_composition(_72768, function_inverse(_72768)) = identity_relation(relation_dom(_72768)) & relation_composition(function_inverse(_72768), _72768) = identity_relation(relation_rng(_72768))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', t61_funct_1)).
% 0.42/1.43 fof(dt_k2_funct_1, axiom, ! [_73110] : (relation(_73110) & function(_73110) => relation(function_inverse(_73110)) & function(function_inverse(_73110))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dt_k2_funct_1)).
% 0.42/1.43 fof(dt_k5_relat_1, axiom, ! [_73303, _73306] : (relation(_73303) & relation(_73306) => relation(relation_composition(_73303, _73306))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dt_k5_relat_1)).
% 0.42/1.43 fof(fc1_funct_1, axiom, ! [_73480, _73483] : (relation(_73480) & function(_73480) & relation(_73483) & function(_73483) => relation(relation_composition(_73480, _73483)) & function(relation_composition(_73480, _73483))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', fc1_funct_1)).
% 0.42/1.43 fof(t34_funct_1, axiom, ! [_73767, _73770] : (relation(_73770) & function(_73770) => (_73770 = identity_relation(_73767) <=> relation_dom(_73770) = _73767 & ! [_73812] : (in(_73812, _73767) => apply(_73770, _73812) = _73812))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', t34_funct_1)).
% 0.42/1.43 fof(t56_funct_1, axiom, ! [_74079, _74082] : (relation(_74082) & function(_74082) => one_to_one(_74082) & in(_74079, relation_dom(_74082)) => _74079 = apply(function_inverse(_74082), apply(_74082, _74079)) & _74079 = apply(relation_composition(_74082, function_inverse(_74082)), _74079)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', t56_funct_1)).
% 0.42/1.43 fof(t57_funct_1, axiom, ! [_74400, _74403] : (relation(_74403) & function(_74403) => one_to_one(_74403) & in(_74400, relation_rng(_74403)) => _74400 = apply(_74403, apply(function_inverse(_74403), _74400)) & _74400 = apply(relation_composition(function_inverse(_74403), _74403), _74400)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', t57_funct_1)).
% 0.42/1.43 fof(t58_funct_1, axiom, ! [_74720] : (relation(_74720) & function(_74720) => one_to_one(_74720) => relation_dom(relation_composition(_74720, function_inverse(_74720))) = relation_dom(_74720) & relation_rng(relation_composition(_74720, function_inverse(_74720))) = relation_dom(_74720)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', t58_funct_1)).
% 0.42/1.43 fof(t59_funct_1, axiom, ! [_74997] : (relation(_74997) & function(_74997) => one_to_one(_74997) => relation_dom(relation_composition(function_inverse(_74997), _74997)) = relation_rng(_74997) & relation_rng(relation_composition(function_inverse(_74997), _74997)) = relation_rng(_74997)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', t59_funct_1)).
% 0.42/1.43
% 0.42/1.43 cnf(1, plain, [-(relation(13 ^ []))], clausify(t61_funct_1)).
% 0.42/1.43 cnf(2, plain, [-(function(13 ^ []))], clausify(t61_funct_1)).
% 0.42/1.43 cnf(3, plain, [-(one_to_one(13 ^ []))], clausify(t61_funct_1)).
% 0.42/1.43 cnf(4, plain, [relation_composition(13 ^ [], function_inverse(13 ^ [])) = identity_relation(relation_dom(13 ^ [])), relation_composition(function_inverse(13 ^ []), 13 ^ []) = identity_relation(relation_rng(13 ^ []))], clausify(t61_funct_1)).
% 0.42/1.43 cnf(5, plain, [_20596 = _20641, -(_20641 = _20596)], theory(equality)).
% 0.42/1.43 cnf(6, plain, [-(relation(function_inverse(_29179))), relation(_29179), function(_29179)], clausify(dt_k2_funct_1)).
% 0.42/1.43 cnf(7, plain, [-(function(function_inverse(_29179))), relation(_29179), function(_29179)], clausify(dt_k2_funct_1)).
% 0.42/1.43 cnf(8, plain, [-(relation(relation_composition(_29541, _29592))), relation(_29541), relation(_29592)], clausify(dt_k5_relat_1)).
% 0.42/1.43 cnf(9, plain, [-(function(relation_composition(_31000, _31069))), relation(_31000), function(_31000), relation(_31069), function(_31069)], clausify(fc1_funct_1)).
% 0.42/1.43 cnf(10, plain, [function(_37463), relation(_37463), -(_37463 = identity_relation(_37384)), relation_dom(_37463) = _37384, -(in(12 ^ [_37463, _37384], _37384))], clausify(t34_funct_1)).
% 0.42/1.43 cnf(11, plain, [function(_37463), relation(_37463), -(_37463 = identity_relation(_37384)), relation_dom(_37463) = _37384, apply(_37463, 12 ^ [_37463, _37384]) = 12 ^ [_37463, _37384]], clausify(t34_funct_1)).
% 0.42/1.43 cnf(12, plain, [function(_39046), relation(_39046), -(_38962 = apply(relation_composition(_39046, function_inverse(_39046)), _38962)), one_to_one(_39046), in(_38962, relation_dom(_39046))], clausify(t56_funct_1)).
% 0.42/1.43 cnf(13, plain, [function(_39863), relation(_39863), -(_39779 = apply(relation_composition(function_inverse(_39863), _39863), _39779)), one_to_one(_39863), in(_39779, relation_rng(_39863))], clausify(t57_funct_1)).
% 0.42/1.43 cnf(14, plain, [function(_40596), relation(_40596), one_to_one(_40596), -(relation_dom(relation_composition(_40596, function_inverse(_40596))) = relation_dom(_40596))], clausify(t58_funct_1)).
% 0.42/1.43 cnf(15, plain, [function(_41212), relation(_41212), one_to_one(_41212), -(relation_dom(relation_composition(function_inverse(_41212), _41212)) = relation_rng(_41212))], clausify(t59_funct_1)).
% 0.42/1.43
% 0.42/1.43 cnf('1',plain,[relation_composition(13 ^ [], function_inverse(13 ^ [])) = identity_relation(relation_dom(13 ^ [])), relation_composition(function_inverse(13 ^ []), 13 ^ []) = identity_relation(relation_rng(13 ^ []))],start(4)).
% 0.42/1.43 cnf('1.1',plain,[-(relation_composition(13 ^ [], function_inverse(13 ^ [])) = identity_relation(relation_dom(13 ^ []))), function(relation_composition(13 ^ [], function_inverse(13 ^ []))), relation(relation_composition(13 ^ [], function_inverse(13 ^ []))), relation_dom(relation_composition(13 ^ [], function_inverse(13 ^ []))) = relation_dom(13 ^ []), -(in(12 ^ [relation_composition(13 ^ [], function_inverse(13 ^ [])), relation_dom(13 ^ [])], relation_dom(13 ^ [])))],extension(10,bind([[_37463, _37384], [relation_composition(13 ^ [], function_inverse(13 ^ [])), relation_dom(13 ^ [])]]))).
% 0.42/1.43 cnf('1.1.1',plain,[-(function(relation_composition(13 ^ [], function_inverse(13 ^ [])))), relation(13 ^ []), function(13 ^ []), relation(function_inverse(13 ^ [])), function(function_inverse(13 ^ []))],extension(9,bind([[_31000, _31069], [13 ^ [], function_inverse(13 ^ [])]]))).
% 0.42/1.43 cnf('1.1.1.1',plain,[-(relation(13 ^ []))],extension(1)).
% 0.42/1.43 cnf('1.1.1.2',plain,[-(function(13 ^ []))],extension(2)).
% 0.42/1.43 cnf('1.1.1.3',plain,[-(relation(function_inverse(13 ^ []))), relation(13 ^ []), function(13 ^ [])],extension(6,bind([[_29179], [13 ^ []]]))).
% 0.42/1.43 cnf('1.1.1.3.1',plain,[-(relation(13 ^ []))],extension(1)).
% 0.42/1.43 cnf('1.1.1.3.2',plain,[-(function(13 ^ []))],extension(2)).
% 0.42/1.43 cnf('1.1.1.4',plain,[-(function(function_inverse(13 ^ []))), relation(13 ^ []), function(13 ^ [])],extension(7,bind([[_29179], [13 ^ []]]))).
% 0.42/1.43 cnf('1.1.1.4.1',plain,[-(relation(13 ^ []))],extension(1)).
% 0.42/1.43 cnf('1.1.1.4.2',plain,[-(function(13 ^ []))],extension(2)).
% 0.42/1.43 cnf('1.1.2',plain,[-(relation(relation_composition(13 ^ [], function_inverse(13 ^ [])))), relation(13 ^ []), relation(function_inverse(13 ^ []))],extension(8,bind([[_29541, _29592], [13 ^ [], function_inverse(13 ^ [])]]))).
% 0.42/1.43 cnf('1.1.2.1',plain,[-(relation(13 ^ []))],extension(1)).
% 0.42/1.43 cnf('1.1.2.2',plain,[-(relation(function_inverse(13 ^ []))), relation(13 ^ []), function(13 ^ [])],extension(6,bind([[_29179], [13 ^ []]]))).
% 0.42/1.43 cnf('1.1.2.2.1',plain,[-(relation(13 ^ []))],extension(1)).
% 0.42/1.43 cnf('1.1.2.2.2',plain,[-(function(13 ^ []))],extension(2)).
% 0.42/1.43 cnf('1.1.3',plain,[-(relation_dom(relation_composition(13 ^ [], function_inverse(13 ^ []))) = relation_dom(13 ^ [])), function(13 ^ []), relation(13 ^ []), one_to_one(13 ^ [])],extension(14,bind([[_40596], [13 ^ []]]))).
% 0.42/1.43 cnf('1.1.3.1',plain,[-(function(13 ^ []))],extension(2)).
% 0.42/1.43 cnf('1.1.3.2',plain,[-(relation(13 ^ []))],extension(1)).
% 0.42/1.43 cnf('1.1.3.3',plain,[-(one_to_one(13 ^ []))],extension(3)).
% 0.42/1.43 cnf('1.1.4',plain,[in(12 ^ [relation_composition(13 ^ [], function_inverse(13 ^ [])), relation_dom(13 ^ [])], relation_dom(13 ^ [])), function(13 ^ []), relation(13 ^ []), -(12 ^ [relation_composition(13 ^ [], function_inverse(13 ^ [])), relation_dom(13 ^ [])] = apply(relation_composition(13 ^ [], function_inverse(13 ^ [])), 12 ^ [relation_composition(13 ^ [], function_inverse(13 ^ [])), relation_dom(13 ^ [])])), one_to_one(13 ^ [])],extension(12,bind([[_38962, _39046], [12 ^ [relation_composition(13 ^ [], function_inverse(13 ^ [])), relation_dom(13 ^ [])], 13 ^ []]]))).
% 0.42/1.43 cnf('1.1.4.1',plain,[-(function(13 ^ []))],extension(2)).
% 0.42/1.43 cnf('1.1.4.2',plain,[-(relation(13 ^ []))],extension(1)).
% 0.42/1.43 cnf('1.1.4.3',plain,[12 ^ [relation_composition(13 ^ [], function_inverse(13 ^ [])), relation_dom(13 ^ [])] = apply(relation_composition(13 ^ [], function_inverse(13 ^ [])), 12 ^ [relation_composition(13 ^ [], function_inverse(13 ^ [])), relation_dom(13 ^ [])]), -(apply(relation_composition(13 ^ [], function_inverse(13 ^ [])), 12 ^ [relation_composition(13 ^ [], function_inverse(13 ^ [])), relation_dom(13 ^ [])]) = 12 ^ [relation_composition(13 ^ [], function_inverse(13 ^ [])), relation_dom(13 ^ [])])],extension(5,bind([[_20641, _20596], [apply(relation_composition(13 ^ [], function_inverse(13 ^ [])), 12 ^ [relation_composition(13 ^ [], function_inverse(13 ^ [])), relation_dom(13 ^ [])]), 12 ^ [relation_composition(13 ^ [], function_inverse(13 ^ [])), relation_dom(13 ^ [])]]]))).
% 0.42/1.43 cnf('1.1.4.3.1',plain,[apply(relation_composition(13 ^ [], function_inverse(13 ^ [])), 12 ^ [relation_composition(13 ^ [], function_inverse(13 ^ [])), relation_dom(13 ^ [])]) = 12 ^ [relation_composition(13 ^ [], function_inverse(13 ^ [])), relation_dom(13 ^ [])], function(relation_composition(13 ^ [], function_inverse(13 ^ []))), relation(relation_composition(13 ^ [], function_inverse(13 ^ []))), -(relation_composition(13 ^ [], function_inverse(13 ^ [])) = identity_relation(relation_dom(13 ^ []))), relation_dom(relation_composition(13 ^ [], function_inverse(13 ^ []))) = relation_dom(13 ^ [])],extension(11,bind([[_37463, _37384], [relation_composition(13 ^ [], function_inverse(13 ^ [])), relation_dom(13 ^ [])]]))).
% 0.42/1.43 cnf('1.1.4.3.1.1',plain,[-(function(relation_composition(13 ^ [], function_inverse(13 ^ []))))],lemmata('1.1')).
% 0.42/1.43 cnf('1.1.4.3.1.2',plain,[-(relation(relation_composition(13 ^ [], function_inverse(13 ^ []))))],lemmata('1.1')).
% 0.42/1.43 cnf('1.1.4.3.1.3',plain,[relation_composition(13 ^ [], function_inverse(13 ^ [])) = identity_relation(relation_dom(13 ^ []))],reduction('1')).
% 0.42/1.43 cnf('1.1.4.3.1.4',plain,[-(relation_dom(relation_composition(13 ^ [], function_inverse(13 ^ []))) = relation_dom(13 ^ []))],lemmata('1.1')).
% 0.42/1.43 cnf('1.1.4.4',plain,[-(one_to_one(13 ^ []))],extension(3)).
% 0.42/1.43 cnf('1.2',plain,[-(relation_composition(function_inverse(13 ^ []), 13 ^ []) = identity_relation(relation_rng(13 ^ []))), function(relation_composition(function_inverse(13 ^ []), 13 ^ [])), relation(relation_composition(function_inverse(13 ^ []), 13 ^ [])), relation_dom(relation_composition(function_inverse(13 ^ []), 13 ^ [])) = relation_rng(13 ^ []), -(in(12 ^ [relation_composition(function_inverse(13 ^ []), 13 ^ []), relation_rng(13 ^ [])], relation_rng(13 ^ [])))],extension(10,bind([[_37463, _37384], [relation_composition(function_inverse(13 ^ []), 13 ^ []), relation_rng(13 ^ [])]]))).
% 0.42/1.43 cnf('1.2.1',plain,[-(function(relation_composition(function_inverse(13 ^ []), 13 ^ []))), relation(function_inverse(13 ^ [])), function(function_inverse(13 ^ [])), relation(13 ^ []), function(13 ^ [])],extension(9,bind([[_31000, _31069], [function_inverse(13 ^ []), 13 ^ []]]))).
% 0.42/1.43 cnf('1.2.1.1',plain,[-(relation(function_inverse(13 ^ []))), relation(13 ^ []), function(13 ^ [])],extension(6,bind([[_29179], [13 ^ []]]))).
% 0.42/1.43 cnf('1.2.1.1.1',plain,[-(relation(13 ^ []))],extension(1)).
% 0.42/1.43 cnf('1.2.1.1.2',plain,[-(function(13 ^ []))],extension(2)).
% 0.42/1.43 cnf('1.2.1.2',plain,[-(function(function_inverse(13 ^ []))), relation(13 ^ []), function(13 ^ [])],extension(7,bind([[_29179], [13 ^ []]]))).
% 0.42/1.43 cnf('1.2.1.2.1',plain,[-(relation(13 ^ []))],extension(1)).
% 0.42/1.43 cnf('1.2.1.2.2',plain,[-(function(13 ^ []))],extension(2)).
% 0.42/1.43 cnf('1.2.1.3',plain,[-(relation(13 ^ []))],extension(1)).
% 0.42/1.43 cnf('1.2.1.4',plain,[-(function(13 ^ []))],extension(2)).
% 0.42/1.43 cnf('1.2.2',plain,[-(relation(relation_composition(function_inverse(13 ^ []), 13 ^ []))), relation(function_inverse(13 ^ [])), relation(13 ^ [])],extension(8,bind([[_29541, _29592], [function_inverse(13 ^ []), 13 ^ []]]))).
% 0.42/1.43 cnf('1.2.2.1',plain,[-(relation(function_inverse(13 ^ []))), relation(13 ^ []), function(13 ^ [])],extension(6,bind([[_29179], [13 ^ []]]))).
% 0.42/1.43 cnf('1.2.2.1.1',plain,[-(relation(13 ^ []))],extension(1)).
% 0.42/1.43 cnf('1.2.2.1.2',plain,[-(function(13 ^ []))],extension(2)).
% 0.42/1.43 cnf('1.2.2.2',plain,[-(relation(13 ^ []))],extension(1)).
% 0.42/1.43 cnf('1.2.3',plain,[-(relation_dom(relation_composition(function_inverse(13 ^ []), 13 ^ [])) = relation_rng(13 ^ [])), function(13 ^ []), relation(13 ^ []), one_to_one(13 ^ [])],extension(15,bind([[_41212], [13 ^ []]]))).
% 0.42/1.43 cnf('1.2.3.1',plain,[-(function(13 ^ []))],extension(2)).
% 0.42/1.43 cnf('1.2.3.2',plain,[-(relation(13 ^ []))],extension(1)).
% 0.42/1.43 cnf('1.2.3.3',plain,[-(one_to_one(13 ^ []))],extension(3)).
% 0.42/1.43 cnf('1.2.4',plain,[in(12 ^ [relation_composition(function_inverse(13 ^ []), 13 ^ []), relation_rng(13 ^ [])], relation_rng(13 ^ [])), function(13 ^ []), relation(13 ^ []), -(12 ^ [relation_composition(function_inverse(13 ^ []), 13 ^ []), relation_rng(13 ^ [])] = apply(relation_composition(function_inverse(13 ^ []), 13 ^ []), 12 ^ [relation_composition(function_inverse(13 ^ []), 13 ^ []), relation_rng(13 ^ [])])), one_to_one(13 ^ [])],extension(13,bind([[_39779, _39863], [12 ^ [relation_composition(function_inverse(13 ^ []), 13 ^ []), relation_rng(13 ^ [])], 13 ^ []]]))).
% 0.42/1.43 cnf('1.2.4.1',plain,[-(function(13 ^ []))],extension(2)).
% 0.42/1.43 cnf('1.2.4.2',plain,[-(relation(13 ^ []))],extension(1)).
% 0.42/1.43 cnf('1.2.4.3',plain,[12 ^ [relation_composition(function_inverse(13 ^ []), 13 ^ []), relation_rng(13 ^ [])] = apply(relation_composition(function_inverse(13 ^ []), 13 ^ []), 12 ^ [relation_composition(function_inverse(13 ^ []), 13 ^ []), relation_rng(13 ^ [])]), -(apply(relation_composition(function_inverse(13 ^ []), 13 ^ []), 12 ^ [relation_composition(function_inverse(13 ^ []), 13 ^ []), relation_rng(13 ^ [])]) = 12 ^ [relation_composition(function_inverse(13 ^ []), 13 ^ []), relation_rng(13 ^ [])])],extension(5,bind([[_20641, _20596], [apply(relation_composition(function_inverse(13 ^ []), 13 ^ []), 12 ^ [relation_composition(function_inverse(13 ^ []), 13 ^ []), relation_rng(13 ^ [])]), 12 ^ [relation_composition(function_inverse(13 ^ []), 13 ^ []), relation_rng(13 ^ [])]]]))).
% 0.42/1.43 cnf('1.2.4.3.1',plain,[apply(relation_composition(function_inverse(13 ^ []), 13 ^ []), 12 ^ [relation_composition(function_inverse(13 ^ []), 13 ^ []), relation_rng(13 ^ [])]) = 12 ^ [relation_composition(function_inverse(13 ^ []), 13 ^ []), relation_rng(13 ^ [])], function(relation_composition(function_inverse(13 ^ []), 13 ^ [])), relation(relation_composition(function_inverse(13 ^ []), 13 ^ [])), -(relation_composition(function_inverse(13 ^ []), 13 ^ []) = identity_relation(relation_rng(13 ^ []))), relation_dom(relation_composition(function_inverse(13 ^ []), 13 ^ [])) = relation_rng(13 ^ [])],extension(11,bind([[_37463, _37384], [relation_composition(function_inverse(13 ^ []), 13 ^ []), relation_rng(13 ^ [])]]))).
% 0.42/1.43 cnf('1.2.4.3.1.1',plain,[-(function(relation_composition(function_inverse(13 ^ []), 13 ^ [])))],lemmata('1.2')).
% 0.42/1.43 cnf('1.2.4.3.1.2',plain,[-(relation(relation_composition(function_inverse(13 ^ []), 13 ^ [])))],lemmata('1.2')).
% 0.42/1.43 cnf('1.2.4.3.1.3',plain,[relation_composition(function_inverse(13 ^ []), 13 ^ []) = identity_relation(relation_rng(13 ^ []))],reduction('1')).
% 0.42/1.43 cnf('1.2.4.3.1.4',plain,[-(relation_dom(relation_composition(function_inverse(13 ^ []), 13 ^ [])) = relation_rng(13 ^ []))],lemmata('1.2')).
% 0.42/1.43 cnf('1.2.4.4',plain,[-(one_to_one(13 ^ []))],extension(3)).
% 0.42/1.43 %-----------------------------------------------------
% 0.42/1.44
% 0.42/1.44 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------