%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV374+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.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 : Tue May 5 05:22:02 PM UTC 2026
% Result : Theorem 0.41s 1.52s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_78)
% Comments :
%------------------------------------------------------------------------------
fof(ax38,axiom,
! [X1,X2,X3,X4,X5] :
( strictly_less_than(X4,X5)
=> ( check_cpq(triple(X1,insert_slb(X2,pair(X4,X5)),X3))
<=> ~ $true ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax38) ).
fof(ax47,axiom,
! [X1,X2,X3,X4] :
( ( X2 != create_slb
& ~ contains_slb(X2,findmin_pqp_res(X1)) )
=> findmin_cpq_eff(triple(X1,X2,X3)) = triple(X1,update_slb(X2,findmin_pqp_res(X1)),bad) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax47) ).
fof(l10_co,conjecture,
! [X1,X2,X3] :
( ok(findmin_cpq_eff(triple(X1,X2,X3)))
=> ( X2 != create_slb
& contains_slb(X2,findmin_pqp_res(X1))
& less_than(lookup_slb(X2,findmin_pqp_res(X1)),findmin_pqp_res(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l10_co) ).
fof(ax43,axiom,
! [X1,X2,X3,X4] :
( ~ contains_slb(X2,X4)
=> remove_cpq(triple(X1,X2,X3),X4) = triple(X1,X2,bad) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax43) ).
fof(ax40,axiom,
! [X1,X2] :
( ok(triple(X1,X2,bad))
<=> ~ $true ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax40) ).
fof(ax41,axiom,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> X3 = bad ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax41) ).
fof(ax35,axiom,
! [X1,X2] :
( succ_cpq(X1,X2)
=> succ_cpq(X1,removemin_cpq_eff(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax35) ).
fof(ax52,axiom,
! [X1] : removemin_cpq_eff(X1) = remove_cpq(findmin_cpq_eff(X1),findmin_cpq_res(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax52) ).
fof(ax22,axiom,
! [X1,X2] : ~ pair_in_list(create_slb,X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax22) ).
fof(stricly_smaller_definition,axiom,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
fof(ax20,axiom,
! [X1] : ~ contains_slb(create_slb,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax20) ).
fof(ax37,axiom,
! [X1,X2,X3,X4,X5] :
( less_than(X5,X4)
=> ( check_cpq(triple(X1,insert_slb(X2,pair(X4,X5)),X3))
<=> check_cpq(triple(X1,X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax37) ).
fof(ax49,axiom,
! [X1,X2,X3,X4] :
( ( X2 != create_slb
& contains_slb(X2,findmin_pqp_res(X1))
& less_than(lookup_slb(X2,findmin_pqp_res(X1)),findmin_pqp_res(X1)) )
=> findmin_cpq_eff(triple(X1,X2,X3)) = triple(X1,update_slb(X2,findmin_pqp_res(X1)),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax49) ).
fof(ax48,axiom,
! [X1,X2,X3,X4] :
( ( X2 != create_slb
& contains_slb(X2,findmin_pqp_res(X1))
& strictly_less_than(findmin_pqp_res(X1),lookup_slb(X2,findmin_pqp_res(X1))) )
=> findmin_cpq_eff(triple(X1,X2,X3)) = triple(X1,update_slb(X2,findmin_pqp_res(X1)),bad) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax48) ).
fof(ax44,axiom,
! [X1,X2,X3,X4] :
( ( contains_slb(X2,X4)
& less_than(lookup_slb(X2,X4),X4) )
=> remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax44) ).
fof(ax45,axiom,
! [X1,X2,X3,X4] :
( ( contains_slb(X2,X4)
& strictly_less_than(X4,lookup_slb(X2,X4)) )
=> remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),bad) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax45) ).
fof(ax42,axiom,
! [X1,X2,X3,X4] : insert_cpq(triple(X1,X2,X3),X4) = triple(insert_pqp(X1,X4),insert_slb(X2,pair(X4,bottom)),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax42) ).
fof(ax23,axiom,
! [X1,X2,X3,X4,X5] :
( pair_in_list(insert_slb(X1,pair(X2,X4)),X3,X5)
<=> ( pair_in_list(X1,X3,X5)
| ( X2 = X3
& X4 = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax23) ).
fof(ax39,axiom,
! [X1,X2,X3,X4] :
( contains_cpq(triple(X1,X2,X3),X4)
<=> contains_slb(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax39) ).
fof(ax25,axiom,
! [X1,X2,X3,X4] :
( ( X2 != X3
& contains_slb(X1,X3) )
=> remove_slb(insert_slb(X1,pair(X2,X4)),X3) = insert_slb(remove_slb(X1,X3),pair(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax25) ).
fof(ax29,axiom,
! [X1,X2,X3,X4] :
( strictly_less_than(X4,X3)
=> update_slb(insert_slb(X1,pair(X2,X4)),X3) = insert_slb(update_slb(X1,X3),pair(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax29) ).
fof(ax30,axiom,
! [X1,X2,X3,X4] :
( less_than(X3,X4)
=> update_slb(insert_slb(X1,pair(X2,X4)),X3) = insert_slb(update_slb(X1,X3),pair(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax30) ).
fof(ax21,axiom,
! [X1,X2,X3,X4] :
( contains_slb(insert_slb(X1,pair(X2,X4)),X3)
<=> ( contains_slb(X1,X3)
| X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax21) ).
fof(ax46,axiom,
! [X1,X2] : findmin_cpq_eff(triple(X1,create_slb,X2)) = triple(X1,create_slb,bad),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax46) ).
fof(ax27,axiom,
! [X1,X2,X3,X4] :
( ( X2 != X3
& contains_slb(X1,X3) )
=> lookup_slb(insert_slb(X1,pair(X2,X4)),X3) = lookup_slb(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax27) ).
fof(ax51,axiom,
! [X1,X2,X3,X4] :
( X2 != create_slb
=> findmin_cpq_res(triple(X1,X2,X3)) = findmin_pqp_res(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax51) ).
fof(ax36,axiom,
! [X1,X2] : check_cpq(triple(X1,create_slb,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax36) ).
fof(ax50,axiom,
! [X1,X2] : findmin_cpq_res(triple(X1,create_slb,X2)) = bottom,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax50) ).
fof(ax26,axiom,
! [X1,X2,X3] : lookup_slb(insert_slb(X1,pair(X2,X3)),X2) = X3,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax26) ).
fof(ax24,axiom,
! [X1,X2,X3] : remove_slb(insert_slb(X1,pair(X2,X3)),X2) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax24) ).
fof(ax19,axiom,
! [X1,X2,X3] : isnonempty_slb(insert_slb(X1,pair(X2,X3))),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax19) ).
fof(ax33,axiom,
! [X1,X2,X3] :
( succ_cpq(X1,X2)
=> succ_cpq(X1,remove_cpq(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax33) ).
fof(ax32,axiom,
! [X1,X2,X3] :
( succ_cpq(X1,X2)
=> succ_cpq(X1,insert_cpq(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax32) ).
fof(transitivity,axiom,
! [X1,X2,X3] :
( ( less_than(X1,X2)
& less_than(X2,X3) )
=> less_than(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',transitivity) ).
fof(ax34,axiom,
! [X1,X2] :
( succ_cpq(X1,X2)
=> succ_cpq(X1,findmin_cpq_eff(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax34) ).
fof(totality,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(ax31,axiom,
! [X1] : succ_cpq(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax31) ).
fof(reflexivity,axiom,
! [X1] : less_than(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',reflexivity) ).
fof(bottom_smallest,axiom,
! [X1] : less_than(bottom,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',bottom_smallest) ).
fof(ax28,axiom,
! [X1] : update_slb(create_slb,X1) = create_slb,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax28) ).
fof(ax18,axiom,
~ isnonempty_slb(create_slb),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax18) ).
fof(i_0_41,plain,
! [X1,X2,X3,X4,X5] :
( strictly_less_than(X4,X5)
=> ~ check_cpq(triple(X1,insert_slb(X2,pair(X4,X5)),X3)) ),
inference(fof_simplification,[status(thm)],[ax38]) ).
fof(i_0_42,plain,
! [X1,X2,X3,X4] :
( ( X2 != create_slb
& ~ contains_slb(X2,findmin_pqp_res(X1)) )
=> findmin_cpq_eff(triple(X1,X2,X3)) = triple(X1,update_slb(X2,findmin_pqp_res(X1)),bad) ),
inference(fof_simplification,[status(thm)],[ax47]) ).
fof(i_0_43,negated_conjecture,
~ ! [X1,X2,X3] :
( ok(findmin_cpq_eff(triple(X1,X2,X3)))
=> ( X2 != create_slb
& contains_slb(X2,findmin_pqp_res(X1))
& less_than(lookup_slb(X2,findmin_pqp_res(X1)),findmin_pqp_res(X1)) ) ),
inference(assume_negation,[status(cth)],[l10_co]) ).
fof(i_0_44,plain,
! [X1,X2,X3,X4] :
( ~ contains_slb(X2,X4)
=> remove_cpq(triple(X1,X2,X3),X4) = triple(X1,X2,bad) ),
inference(fof_simplification,[status(thm)],[ax43]) ).
fof(i_0_45,plain,
! [X1,X2] : ~ ok(triple(X1,X2,bad)),
inference(fof_simplification,[status(thm)],[ax40]) ).
fof(i_0_46,plain,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> X3 = bad ),
inference(fof_simplification,[status(thm)],[ax41]) ).
fof(i_0_47,plain,
! [X182,X183] :
( ~ succ_cpq(X182,X183)
| succ_cpq(X182,removemin_cpq_eff(X183)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax35])]) ).
fof(i_0_48,plain,
! [X237] : removemin_cpq_eff(X237) = remove_cpq(findmin_cpq_eff(X237),findmin_cpq_res(X237)),
inference(variable_rename,[status(thm)],[ax52]) ).
fof(i_0_49,plain,
! [X1,X2] : ~ pair_in_list(create_slb,X1,X2),
inference(fof_simplification,[status(thm)],[ax22]) ).
fof(i_0_50,plain,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[stricly_smaller_definition]) ).
fof(i_0_51,plain,
! [X1] : ~ contains_slb(create_slb,X1),
inference(fof_simplification,[status(thm)],[ax20]) ).
fof(i_0_52,plain,
! [X186,X187,X188,X189,X190] :
( ( ~ check_cpq(triple(X186,insert_slb(X187,pair(X189,X190)),X188))
| check_cpq(triple(X186,X187,X188))
| ~ less_than(X190,X189) )
& ( ~ check_cpq(triple(X186,X187,X188))
| check_cpq(triple(X186,insert_slb(X187,pair(X189,X190)),X188))
| ~ less_than(X190,X189) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])]) ).
fof(i_0_53,plain,
! [X191,X192,X193,X194,X195] :
( ~ strictly_less_than(X194,X195)
| ~ check_cpq(triple(X191,insert_slb(X192,pair(X194,X195)),X193)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_41])]) ).
fof(i_0_54,plain,
! [X229,X230,X231] :
( X230 = create_slb
| ~ contains_slb(X230,findmin_pqp_res(X229))
| ~ less_than(lookup_slb(X230,findmin_pqp_res(X229)),findmin_pqp_res(X229))
| findmin_cpq_eff(triple(X229,X230,X231)) = triple(X229,update_slb(X230,findmin_pqp_res(X229)),X231) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax49])])]) ).
fof(i_0_55,plain,
! [X226,X227,X228] :
( X227 = create_slb
| ~ contains_slb(X227,findmin_pqp_res(X226))
| ~ strictly_less_than(findmin_pqp_res(X226),lookup_slb(X227,findmin_pqp_res(X226)))
| findmin_cpq_eff(triple(X226,X227,X228)) = triple(X226,update_slb(X227,findmin_pqp_res(X226)),bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax48])])]) ).
fof(i_0_56,plain,
! [X213,X214,X215,X216] :
( ~ contains_slb(X214,X216)
| ~ less_than(lookup_slb(X214,X216),X216)
| remove_cpq(triple(X213,X214,X215),X216) = triple(remove_pqp(X213,X216),remove_slb(X214,X216),X215) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])]) ).
fof(i_0_57,plain,
! [X217,X218,X219,X220] :
( ~ contains_slb(X218,X220)
| ~ strictly_less_than(X220,lookup_slb(X218,X220))
| remove_cpq(triple(X217,X218,X219),X220) = triple(remove_pqp(X217,X220),remove_slb(X218,X220),bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
fof(i_0_58,plain,
! [X205,X206,X207,X208] : insert_cpq(triple(X205,X206,X207),X208) = triple(insert_pqp(X205,X208),insert_slb(X206,pair(X208,bottom)),X207),
inference(variable_rename,[status(thm)],[ax42]) ).
fof(i_0_59,plain,
! [X145,X146,X147,X148,X149] :
( ( X146 = X147
| pair_in_list(X145,X147,X149)
| ~ pair_in_list(insert_slb(X145,pair(X146,X148)),X147,X149) )
& ( X148 = X149
| pair_in_list(X145,X147,X149)
| ~ pair_in_list(insert_slb(X145,pair(X146,X148)),X147,X149) )
& ( ~ pair_in_list(X145,X147,X149)
| pair_in_list(insert_slb(X145,pair(X146,X148)),X147,X149) )
& ( X146 != X147
| X148 != X149
| pair_in_list(insert_slb(X145,pair(X146,X148)),X147,X149) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
fof(i_0_60,plain,
! [X223,X224,X225] :
( X224 = create_slb
| contains_slb(X224,findmin_pqp_res(X223))
| findmin_cpq_eff(triple(X223,X224,X225)) = triple(X223,update_slb(X224,findmin_pqp_res(X223)),bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[i_0_42])])]) ).
fof(i_0_61,negated_conjecture,
( ok(findmin_cpq_eff(triple(esk1_0,esk2_0,esk3_0)))
& ( esk2_0 = create_slb
| ~ contains_slb(esk2_0,findmin_pqp_res(esk1_0))
| ~ less_than(lookup_slb(esk2_0,findmin_pqp_res(esk1_0)),findmin_pqp_res(esk1_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_43])])]) ).
fof(i_0_62,plain,
! [X196,X197,X198,X199] :
( ( ~ contains_cpq(triple(X196,X197,X198),X199)
| contains_slb(X197,X199) )
& ( ~ contains_slb(X197,X199)
| contains_cpq(triple(X196,X197,X198),X199) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax39])]) ).
fof(i_0_63,plain,
! [X209,X210,X211,X212] :
( contains_slb(X210,X212)
| remove_cpq(triple(X209,X210,X211),X212) = triple(X209,X210,bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_44])]) ).
fof(i_0_64,plain,
! [X153,X154,X155,X156] :
( X154 = X155
| ~ contains_slb(X153,X155)
| remove_slb(insert_slb(X153,pair(X154,X156)),X155) = insert_slb(remove_slb(X153,X155),pair(X154,X156)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])]) ).
fof(i_0_65,plain,
! [X165,X166,X167,X168] :
( ~ strictly_less_than(X168,X167)
| update_slb(insert_slb(X165,pair(X166,X168)),X167) = insert_slb(update_slb(X165,X167),pair(X166,X167)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax29])]) ).
fof(i_0_66,plain,
! [X169,X170,X171,X172] :
( ~ less_than(X171,X172)
| update_slb(insert_slb(X169,pair(X170,X172)),X171) = insert_slb(update_slb(X169,X171),pair(X170,X172)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax30])]) ).
fof(i_0_67,plain,
! [X200,X201] : ~ ok(triple(X200,X201,bad)),
inference(variable_rename,[status(thm)],[i_0_45]) ).
fof(i_0_68,plain,
! [X139,X140,X141,X142] :
( ( ~ contains_slb(insert_slb(X139,pair(X140,X142)),X141)
| contains_slb(X139,X141)
| X140 = X141 )
& ( ~ contains_slb(X139,X141)
| contains_slb(insert_slb(X139,pair(X140,X142)),X141) )
& ( X140 != X141
| contains_slb(insert_slb(X139,pair(X140,X142)),X141) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
fof(i_0_69,plain,
! [X221,X222] : findmin_cpq_eff(triple(X221,create_slb,X222)) = triple(X221,create_slb,bad),
inference(variable_rename,[status(thm)],[ax46]) ).
fof(i_0_70,plain,
! [X160,X161,X162,X163] :
( X161 = X162
| ~ contains_slb(X160,X162)
| lookup_slb(insert_slb(X160,pair(X161,X163)),X162) = lookup_slb(X160,X162) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])]) ).
fof(i_0_71,plain,
! [X234,X235,X236] :
( X235 = create_slb
| findmin_cpq_res(triple(X234,X235,X236)) = findmin_pqp_res(X234) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax51])])]) ).
fof(i_0_72,plain,
! [X202,X203,X204] :
( ok(triple(X202,X203,X204))
| X204 = bad ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_46])]) ).
fof(i_0_73,plain,
! [X184,X185] : check_cpq(triple(X184,create_slb,X185)),
inference(variable_rename,[status(thm)],[ax36]) ).
fof(i_0_74,plain,
! [X232,X233] : findmin_cpq_res(triple(X232,create_slb,X233)) = bottom,
inference(variable_rename,[status(thm)],[ax50]) ).
fof(i_0_75,plain,
! [X157,X158,X159] : lookup_slb(insert_slb(X157,pair(X158,X159)),X158) = X159,
inference(variable_rename,[status(thm)],[ax26]) ).
fof(i_0_76,plain,
! [X150,X151,X152] : remove_slb(insert_slb(X150,pair(X151,X152)),X151) = X150,
inference(variable_rename,[status(thm)],[ax24]) ).
cnf(i_0_77,plain,
( succ_cpq(X1,removemin_cpq_eff(X2))
| ~ succ_cpq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_47]) ).
cnf(i_0_78,plain,
removemin_cpq_eff(X1) = remove_cpq(findmin_cpq_eff(X1),findmin_cpq_res(X1)),
inference(split_conjunct,[status(thm)],[i_0_48]) ).
fof(i_0_79,plain,
! [X143,X144] : ~ pair_in_list(create_slb,X143,X144),
inference(variable_rename,[status(thm)],[i_0_49]) ).
fof(i_0_80,plain,
! [X135,X136,X137] : isnonempty_slb(insert_slb(X135,pair(X136,X137))),
inference(variable_rename,[status(thm)],[ax19]) ).
fof(i_0_81,plain,
! [X177,X178,X179] :
( ~ succ_cpq(X177,X178)
| succ_cpq(X177,remove_cpq(X178,X179)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax33])]) ).
fof(i_0_82,plain,
! [X174,X175,X176] :
( ~ succ_cpq(X174,X175)
| succ_cpq(X174,insert_cpq(X175,X176)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax32])]) ).
fof(i_0_83,plain,
! [X126,X127,X128] :
( ~ less_than(X126,X127)
| ~ less_than(X127,X128)
| less_than(X126,X128) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity])]) ).
fof(i_0_84,plain,
! [X132,X133] :
( ( less_than(X132,X133)
| ~ strictly_less_than(X132,X133) )
& ( ~ less_than(X133,X132)
| ~ strictly_less_than(X132,X133) )
& ( ~ less_than(X132,X133)
| less_than(X133,X132)
| strictly_less_than(X132,X133) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_50])])]) ).
fof(i_0_85,plain,
! [X180,X181] :
( ~ succ_cpq(X180,X181)
| succ_cpq(X180,findmin_cpq_eff(X181)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax34])]) ).
fof(i_0_86,plain,
! [X129,X130] :
( less_than(X129,X130)
| less_than(X130,X129) ),
inference(variable_rename,[status(thm)],[totality]) ).
fof(i_0_87,plain,
! [X138] : ~ contains_slb(create_slb,X138),
inference(variable_rename,[status(thm)],[i_0_51]) ).
fof(i_0_88,plain,
! [X173] : succ_cpq(X173,X173),
inference(variable_rename,[status(thm)],[ax31]) ).
fof(i_0_89,plain,
! [X131] : less_than(X131,X131),
inference(variable_rename,[status(thm)],[reflexivity]) ).
fof(i_0_90,plain,
! [X134] : less_than(bottom,X134),
inference(variable_rename,[status(thm)],[bottom_smallest]) ).
fof(i_0_91,plain,
! [X164] : update_slb(create_slb,X164) = create_slb,
inference(variable_rename,[status(thm)],[ax28]) ).
fof(i_0_92,plain,
~ isnonempty_slb(create_slb),
inference(fof_simplification,[status(thm)],[ax18]) ).
cnf(i_0_93,plain,
( check_cpq(triple(X1,X2,X5))
| ~ check_cpq(triple(X1,insert_slb(X2,pair(X3,X4)),X5))
| ~ less_than(X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_94,plain,
( check_cpq(triple(X1,insert_slb(X2,pair(X4,X5)),X3))
| ~ check_cpq(triple(X1,X2,X3))
| ~ less_than(X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_95,plain,
( ~ strictly_less_than(X1,X2)
| ~ check_cpq(triple(X3,insert_slb(X4,pair(X1,X2)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_96,plain,
( X1 = create_slb
| findmin_cpq_eff(triple(X2,X1,X3)) = triple(X2,update_slb(X1,findmin_pqp_res(X2)),X3)
| ~ contains_slb(X1,findmin_pqp_res(X2))
| ~ less_than(lookup_slb(X1,findmin_pqp_res(X2)),findmin_pqp_res(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_97,plain,
( X1 = create_slb
| findmin_cpq_eff(triple(X2,X1,X3)) = triple(X2,update_slb(X1,findmin_pqp_res(X2)),bad)
| ~ contains_slb(X1,findmin_pqp_res(X2))
| ~ strictly_less_than(findmin_pqp_res(X2),lookup_slb(X1,findmin_pqp_res(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_98,plain,
( remove_cpq(triple(X3,X1,X4),X2) = triple(remove_pqp(X3,X2),remove_slb(X1,X2),X4)
| ~ contains_slb(X1,X2)
| ~ less_than(lookup_slb(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_99,plain,
( remove_cpq(triple(X3,X1,X4),X2) = triple(remove_pqp(X3,X2),remove_slb(X1,X2),bad)
| ~ contains_slb(X1,X2)
| ~ strictly_less_than(X2,lookup_slb(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_100,plain,
insert_cpq(triple(X1,X2,X3),X4) = triple(insert_pqp(X1,X4),insert_slb(X2,pair(X4,bottom)),X3),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_101,plain,
( X1 = X2
| pair_in_list(X3,X2,X4)
| ~ pair_in_list(insert_slb(X3,pair(X1,X5)),X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_102,plain,
( X1 = X2
| pair_in_list(X3,X4,X2)
| ~ pair_in_list(insert_slb(X3,pair(X5,X1)),X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_103,plain,
( X1 = create_slb
| contains_slb(X1,findmin_pqp_res(X2))
| findmin_cpq_eff(triple(X2,X1,X3)) = triple(X2,update_slb(X1,findmin_pqp_res(X2)),bad) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_104,plain,
( pair_in_list(insert_slb(X1,pair(X4,X5)),X2,X3)
| ~ pair_in_list(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_105,negated_conjecture,
ok(findmin_cpq_eff(triple(esk1_0,esk2_0,esk3_0))),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_106,plain,
( contains_slb(X2,X4)
| ~ contains_cpq(triple(X1,X2,X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_107,plain,
( contains_slb(X1,X2)
| remove_cpq(triple(X3,X1,X4),X2) = triple(X3,X1,bad) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_108,plain,
( X1 = X2
| remove_slb(insert_slb(X3,pair(X1,X4)),X2) = insert_slb(remove_slb(X3,X2),pair(X1,X4))
| ~ contains_slb(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_109,plain,
( update_slb(insert_slb(X3,pair(X4,X1)),X2) = insert_slb(update_slb(X3,X2),pair(X4,X2))
| ~ strictly_less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_110,plain,
( update_slb(insert_slb(X3,pair(X4,X2)),X1) = insert_slb(update_slb(X3,X1),pair(X4,X2))
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_111,plain,
~ ok(triple(X1,X2,bad)),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_112,plain,
( contains_slb(X1,X4)
| X2 = X4
| ~ contains_slb(insert_slb(X1,pair(X2,X3)),X4) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_113,plain,
findmin_cpq_eff(triple(X1,create_slb,X2)) = triple(X1,create_slb,bad),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_114,plain,
( contains_cpq(triple(X3,X1,X4),X2)
| ~ contains_slb(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_115,plain,
( pair_in_list(insert_slb(X5,pair(X1,X3)),X2,X4)
| X1 != X2
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_116,plain,
( X1 = X2
| lookup_slb(insert_slb(X3,pair(X1,X4)),X2) = lookup_slb(X3,X2)
| ~ contains_slb(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_117,plain,
( X1 = create_slb
| findmin_cpq_res(triple(X2,X1,X3)) = findmin_pqp_res(X2) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_118,plain,
( contains_slb(insert_slb(X1,pair(X3,X4)),X2)
| ~ contains_slb(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_119,plain,
( ok(triple(X1,X2,X3))
| X3 = bad ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_120,plain,
check_cpq(triple(X1,create_slb,X2)),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_121,plain,
findmin_cpq_res(triple(X1,create_slb,X2)) = bottom,
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_122,negated_conjecture,
( esk2_0 = create_slb
| ~ contains_slb(esk2_0,findmin_pqp_res(esk1_0))
| ~ less_than(lookup_slb(esk2_0,findmin_pqp_res(esk1_0)),findmin_pqp_res(esk1_0)) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_123,plain,
( contains_slb(insert_slb(X3,pair(X1,X4)),X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_124,plain,
lookup_slb(insert_slb(X1,pair(X2,X3)),X2) = X3,
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_125,plain,
remove_slb(insert_slb(X1,pair(X2,X3)),X2) = X1,
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_126,plain,
( succ_cpq(X1,remove_cpq(findmin_cpq_eff(X2),findmin_cpq_res(X2)))
| ~ succ_cpq(X1,X2) ),
inference(rw,[status(thm)],[i_0_77,c_0_78]),
[final] ).
cnf(i_0_127,plain,
~ pair_in_list(create_slb,X1,X2),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_128,plain,
isnonempty_slb(insert_slb(X1,pair(X2,X3))),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_129,plain,
( succ_cpq(X1,remove_cpq(X2,X3))
| ~ succ_cpq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_130,plain,
( succ_cpq(X1,insert_cpq(X2,X3))
| ~ succ_cpq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_131,plain,
( less_than(X1,X3)
| ~ less_than(X1,X2)
| ~ less_than(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_132,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_133,plain,
( ~ less_than(X1,X2)
| ~ strictly_less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_134,plain,
( succ_cpq(X1,findmin_cpq_eff(X2))
| ~ succ_cpq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_135,plain,
( less_than(X1,X2)
| ~ strictly_less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_136,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_137,plain,
~ contains_slb(create_slb,X1),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_138,plain,
succ_cpq(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_139,plain,
less_than(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_140,plain,
less_than(bottom,X1),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_141,plain,
update_slb(create_slb,X1) = create_slb,
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_142,plain,
~ isnonempty_slb(create_slb),
inference(split_conjunct,[status(thm)],[i_0_92]),
[final] ).
cnf(i_0_143,axiom,
X1 = X1 ).
cnf(i_0_144,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_145,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_146,axiom,
( X1 != X2
| triple(X1,X3,X4) = triple(X2,X3,X4) ) ).
cnf(i_0_147,axiom,
( X1 != X2
| triple(X3,X1,X4) = triple(X3,X2,X4) ) ).
cnf(i_0_148,axiom,
( X1 != X2
| triple(X3,X4,X1) = triple(X3,X4,X2) ) ).
cnf(i_0_149,axiom,
( X1 != X2
| remove_slb(X1,X3) = remove_slb(X2,X3) ) ).
cnf(i_0_150,axiom,
( X1 != X2
| remove_slb(X3,X1) = remove_slb(X3,X2) ) ).
cnf(i_0_151,axiom,
( X1 != X2
| insert_cpq(X1,X3) = insert_cpq(X2,X3) ) ).
cnf(i_0_152,axiom,
( X1 != X2
| insert_cpq(X3,X1) = insert_cpq(X3,X2) ) ).
cnf(i_0_153,axiom,
( X1 != X2
| findmin_cpq_res(X1) = findmin_cpq_res(X2) ) ).
cnf(i_0_154,axiom,
( X1 != X2
| insert_slb(X1,X3) = insert_slb(X2,X3) ) ).
cnf(i_0_155,axiom,
( X1 != X2
| insert_slb(X3,X1) = insert_slb(X3,X2) ) ).
cnf(i_0_156,axiom,
( X1 != X2
| findmin_cpq_eff(X1) = findmin_cpq_eff(X2) ) ).
cnf(i_0_157,axiom,
( X1 != X2
| update_slb(X1,X3) = update_slb(X2,X3) ) ).
cnf(i_0_158,axiom,
( X1 != X2
| update_slb(X3,X1) = update_slb(X3,X2) ) ).
cnf(i_0_159,axiom,
( X1 != X2
| findmin_pqp_res(X1) = findmin_pqp_res(X2) ) ).
cnf(i_0_160,axiom,
( X1 != X2
| lookup_slb(X1,X3) = lookup_slb(X2,X3) ) ).
cnf(i_0_161,axiom,
( X1 != X2
| lookup_slb(X3,X1) = lookup_slb(X3,X2) ) ).
cnf(i_0_162,axiom,
( X1 != X2
| remove_cpq(X1,X3) = remove_cpq(X2,X3) ) ).
cnf(i_0_163,axiom,
( X1 != X2
| remove_cpq(X3,X1) = remove_cpq(X3,X2) ) ).
cnf(i_0_164,axiom,
( X1 != X2
| ~ check_cpq(X1)
| check_cpq(X2) ) ).
cnf(i_0_165,axiom,
( X1 != X2
| ~ less_than(X1,X3)
| less_than(X2,X3) ) ).
cnf(i_0_166,axiom,
( X1 != X2
| ~ less_than(X3,X1)
| less_than(X3,X2) ) ).
cnf(i_0_167,axiom,
( X1 != X2
| ~ strictly_less_than(X1,X3)
| strictly_less_than(X2,X3) ) ).
cnf(i_0_168,axiom,
( X1 != X2
| ~ strictly_less_than(X3,X1)
| strictly_less_than(X3,X2) ) ).
cnf(i_0_169,axiom,
( X1 != X2
| ~ contains_slb(X1,X3)
| contains_slb(X2,X3) ) ).
cnf(i_0_170,axiom,
( X1 != X2
| ~ contains_slb(X3,X1)
| contains_slb(X3,X2) ) ).
cnf(i_0_171,axiom,
( X1 != X2
| ~ pair_in_list(X1,X3,X4)
| pair_in_list(X2,X3,X4) ) ).
cnf(i_0_172,axiom,
( X1 != X2
| ~ pair_in_list(X3,X1,X4)
| pair_in_list(X3,X2,X4) ) ).
cnf(i_0_173,axiom,
( X1 != X2
| ~ pair_in_list(X3,X4,X1)
| pair_in_list(X3,X4,X2) ) ).
cnf(i_0_174,axiom,
( X1 != X2
| ~ ok(X1)
| ok(X2) ) ).
cnf(i_0_175,axiom,
( X1 != X2
| ~ contains_cpq(X1,X3)
| contains_cpq(X2,X3) ) ).
cnf(i_0_176,axiom,
( X1 != X2
| ~ contains_cpq(X3,X1)
| contains_cpq(X3,X2) ) ).
cnf(i_0_177,axiom,
( X1 != X2
| ~ succ_cpq(X1,X3)
| succ_cpq(X2,X3) ) ).
cnf(i_0_178,axiom,
( X1 != X2
| ~ succ_cpq(X3,X1)
| succ_cpq(X3,X2) ) ).
cnf(i_0_179,axiom,
( X1 != X2
| ~ isnonempty_slb(X1)
| isnonempty_slb(X2) ) ).
cnf(i_0_143_001,axiom,
X1 = X1 ).
cnf(i_0_144_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_145_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_146_004,axiom,
( X1 != X2
| triple(X1,X3,X4) = triple(X2,X3,X4) ) ).
cnf(i_0_147_005,axiom,
( X1 != X2
| triple(X3,X1,X4) = triple(X3,X2,X4) ) ).
cnf(i_0_148_006,axiom,
( X1 != X2
| triple(X3,X4,X1) = triple(X3,X4,X2) ) ).
cnf(i_0_149_007,axiom,
( X1 != X2
| remove_slb(X1,X3) = remove_slb(X2,X3) ) ).
cnf(i_0_150_008,axiom,
( X1 != X2
| remove_slb(X3,X1) = remove_slb(X3,X2) ) ).
cnf(i_0_151_009,axiom,
( X1 != X2
| insert_cpq(X1,X3) = insert_cpq(X2,X3) ) ).
cnf(i_0_152_010,axiom,
( X1 != X2
| insert_cpq(X3,X1) = insert_cpq(X3,X2) ) ).
cnf(i_0_153_011,axiom,
( X1 != X2
| findmin_cpq_res(X1) = findmin_cpq_res(X2) ) ).
cnf(i_0_154_012,axiom,
( X1 != X2
| insert_slb(X1,X3) = insert_slb(X2,X3) ) ).
cnf(i_0_155_013,axiom,
( X1 != X2
| insert_slb(X3,X1) = insert_slb(X3,X2) ) ).
cnf(i_0_156_014,axiom,
( X1 != X2
| findmin_cpq_eff(X1) = findmin_cpq_eff(X2) ) ).
cnf(i_0_157_015,axiom,
( X1 != X2
| update_slb(X1,X3) = update_slb(X2,X3) ) ).
cnf(i_0_158_016,axiom,
( X1 != X2
| update_slb(X3,X1) = update_slb(X3,X2) ) ).
cnf(i_0_159_017,axiom,
( X1 != X2
| findmin_pqp_res(X1) = findmin_pqp_res(X2) ) ).
cnf(i_0_160_018,axiom,
( X1 != X2
| lookup_slb(X1,X3) = lookup_slb(X2,X3) ) ).
cnf(i_0_161_019,axiom,
( X1 != X2
| lookup_slb(X3,X1) = lookup_slb(X3,X2) ) ).
cnf(i_0_162_020,axiom,
( X1 != X2
| remove_cpq(X1,X3) = remove_cpq(X2,X3) ) ).
cnf(i_0_163_021,axiom,
( X1 != X2
| remove_cpq(X3,X1) = remove_cpq(X3,X2) ) ).
cnf(i_0_164_022,axiom,
( X1 != X2
| ~ check_cpq(X1)
| check_cpq(X2) ) ).
cnf(i_0_165_023,axiom,
( X1 != X2
| ~ less_than(X1,X3)
| less_than(X2,X3) ) ).
cnf(i_0_166_024,axiom,
( X1 != X2
| ~ less_than(X3,X1)
| less_than(X3,X2) ) ).
cnf(i_0_167_025,axiom,
( X1 != X2
| ~ strictly_less_than(X1,X3)
| strictly_less_than(X2,X3) ) ).
cnf(i_0_168_026,axiom,
( X1 != X2
| ~ strictly_less_than(X3,X1)
| strictly_less_than(X3,X2) ) ).
cnf(i_0_169_027,axiom,
( X1 != X2
| ~ contains_slb(X1,X3)
| contains_slb(X2,X3) ) ).
cnf(i_0_170_028,axiom,
( X1 != X2
| ~ contains_slb(X3,X1)
| contains_slb(X3,X2) ) ).
cnf(i_0_171_029,axiom,
( X1 != X2
| ~ pair_in_list(X1,X3,X4)
| pair_in_list(X2,X3,X4) ) ).
cnf(i_0_172_030,axiom,
( X1 != X2
| ~ pair_in_list(X3,X1,X4)
| pair_in_list(X3,X2,X4) ) ).
cnf(i_0_173_031,axiom,
( X1 != X2
| ~ pair_in_list(X3,X4,X1)
| pair_in_list(X3,X4,X2) ) ).
cnf(i_0_174_032,axiom,
( X1 != X2
| ~ ok(X1)
| ok(X2) ) ).
cnf(i_0_175_033,axiom,
( X1 != X2
| ~ contains_cpq(X1,X3)
| contains_cpq(X2,X3) ) ).
cnf(i_0_176_034,axiom,
( X1 != X2
| ~ contains_cpq(X3,X1)
| contains_cpq(X3,X2) ) ).
cnf(i_0_177_035,axiom,
( X1 != X2
| ~ succ_cpq(X1,X3)
| succ_cpq(X2,X3) ) ).
cnf(i_0_178_036,axiom,
( X1 != X2
| ~ succ_cpq(X3,X1)
| succ_cpq(X3,X2) ) ).
cnf(i_0_179_037,axiom,
( X1 != X2
| ~ isnonempty_slb(X1)
| isnonempty_slb(X2) ) ).
cnf(i_0_180,plain,
contains_slb(insert_slb(X1,pair(X2,X3)),X2),
inference(equality_inference,[],[123]) ).
cnf(i_0_181,plain,
create_slb = update_slb(create_slb,X1),
inference(scs_inference,[],[i_0_141,i_0_144]) ).
cnf(i_0_182,plain,
findmin_cpq_eff(triple(esk1_0,esk2_0,esk3_0)) != triple(X1,X2,bad),
inference(scs_inference,[],[i_0_105,i_0_141,i_0_111,i_0_144,i_0_174]) ).
cnf(i_0_183,plain,
findmin_cpq_eff(triple(esk1_0,esk2_0,esk3_0)) != findmin_cpq_eff(triple(X1,create_slb,X2)),
inference(scs_inference,[],[i_0_105,i_0_141,i_0_111,i_0_113,i_0_144,i_0_174,i_0_145]) ).
cnf(i_0_184,plain,
findmin_cpq_eff(triple(X1,create_slb,X2)) = triple(X1,create_slb,bad),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_185,plain,
~ contains_slb(update_slb(create_slb,X1),X2),
inference(scs_inference,[],[i_0_105,i_0_137,i_0_141,i_0_111,i_0_113,i_0_144,i_0_174,i_0_145,i_0_169]) ).
cnf(i_0_186,plain,
~ pair_in_list(update_slb(create_slb,X1),X2,X3),
inference(scs_inference,[],[i_0_105,i_0_127,i_0_137,i_0_141,i_0_111,i_0_113,i_0_144,i_0_174,i_0_145,i_0_169,i_0_171]) ).
cnf(i_0_187,plain,
insert_slb(X1,pair(X2,X3)) != create_slb,
inference(scs_inference,[],[i_0_105,i_0_127,i_0_137,i_0_142,i_0_141,i_0_111,i_0_113,i_0_128,i_0_144,i_0_174,i_0_145,i_0_169,i_0_171,i_0_179]) ).
cnf(i_0_188,plain,
triple(esk1_0,esk2_0,esk3_0) != triple(X1,create_slb,X2),
inference(scs_inference,[],[i_0_105,i_0_127,i_0_137,i_0_142,i_0_141,i_0_111,i_0_113,i_0_128,i_0_144,i_0_174,i_0_145,i_0_169,i_0_171,i_0_179,i_0_156]) ).
cnf(i_0_189,plain,
( check_cpq(X1)
| triple(X2,create_slb,X3) != X1 ),
inference(scs_inference,[],[i_0_105,i_0_127,i_0_137,i_0_142,i_0_141,i_0_111,i_0_120,i_0_113,i_0_128,i_0_144,i_0_174,i_0_145,i_0_169,i_0_171,i_0_179,i_0_156,i_0_164]) ).
cnf(i_0_190,plain,
( triple(X1,create_slb,X2) != triple(X3,insert_slb(X4,pair(X5,X5)),X6)
| check_cpq(triple(X3,X4,X6)) ),
inference(scs_inference,[],[i_0_105,i_0_139,i_0_127,i_0_137,i_0_142,i_0_141,i_0_111,i_0_120,i_0_113,i_0_128,i_0_144,i_0_174,i_0_145,i_0_169,i_0_171,i_0_179,i_0_156,i_0_164,i_0_93]) ).
cnf(i_0_191,plain,
( ~ check_cpq(triple(X1,insert_slb(X2,pair(X3,X4)),X5))
| check_cpq(triple(X1,X2,X5))
| ~ less_than(X4,X3) ),
inference(rename_variables,[],[i_0_93]) ).
cnf(i_0_192,plain,
( esk2_0 != create_slb
| triple(X1,create_slb,X2) != triple(X3,insert_slb(X4,pair(X5,X5)),X6) ),
inference(scs_inference,[],[i_0_105,i_0_139,i_0_127,i_0_137,i_0_142,i_0_141,i_0_111,i_0_120,i_0_113,i_0_128,i_0_144,i_0_174,i_0_145,i_0_169,i_0_171,i_0_179,i_0_156,i_0_164,i_0_93,i_0_147]) ).
cnf(i_0_193,plain,
( ~ strictly_less_than(X1,X1)
| triple(X2,create_slb,X3) != triple(X4,insert_slb(X5,pair(X1,X1)),X6) ),
inference(scs_inference,[],[i_0_105,i_0_139,i_0_127,i_0_137,i_0_142,i_0_141,i_0_111,i_0_120,i_0_113,i_0_128,i_0_144,i_0_174,i_0_145,i_0_169,i_0_171,i_0_179,i_0_156,i_0_164,i_0_93,i_0_147,i_0_95]) ).
cnf(i_0_194,plain,
( ~ check_cpq(triple(X1,insert_slb(X2,pair(X3,X4)),X5))
| ~ strictly_less_than(X3,X4) ),
inference(rename_variables,[],[i_0_95]) ).
cnf(i_0_195,plain,
( triple(X1,create_slb,X2) != triple(X3,insert_slb(X4,pair(create_slb,create_slb)),X5)
| ~ strictly_less_than(update_slb(create_slb,X6),create_slb) ),
inference(scs_inference,[],[i_0_105,i_0_139,i_0_127,i_0_137,i_0_142,i_0_141,i_0_111,i_0_120,i_0_113,i_0_128,i_0_144,i_0_174,i_0_145,i_0_169,i_0_171,i_0_179,i_0_156,i_0_164,i_0_93,i_0_147,i_0_95,i_0_167]) ).
cnf(i_0_196,plain,
( triple(X1,create_slb,X2) != triple(X3,insert_slb(X4,pair(create_slb,create_slb)),X5)
| ~ strictly_less_than(create_slb,update_slb(create_slb,X6)) ),
inference(scs_inference,[],[i_0_105,i_0_139,i_0_127,i_0_137,i_0_142,i_0_141,i_0_111,i_0_120,i_0_113,i_0_128,i_0_144,i_0_174,i_0_145,i_0_169,i_0_171,i_0_179,i_0_156,i_0_164,i_0_93,i_0_147,i_0_95,i_0_167,i_0_168]) ).
cnf(i_0_197,plain,
( strictly_less_than(X1,X2)
| ~ less_than(X1,X2)
| less_than(X2,X1) ),
inference(rename_variables,[],[i_0_132]) ).
cnf(i_0_198,plain,
( ~ less_than(update_slb(create_slb,X1),create_slb)
| triple(X2,create_slb,X3) != triple(X4,insert_slb(X5,pair(create_slb,create_slb)),X6)
| less_than(create_slb,update_slb(create_slb,X1)) ),
inference(scs_inference,[],[i_0_105,i_0_139,i_0_127,i_0_137,i_0_142,i_0_141,i_0_111,i_0_120,i_0_113,i_0_128,i_0_144,i_0_174,i_0_145,i_0_169,i_0_171,i_0_179,i_0_156,i_0_164,i_0_93,i_0_147,i_0_95,i_0_167,i_0_168,i_0_132]) ).
cnf(i_0_199,plain,
check_cpq(triple(X1,create_slb,X2)),
inference(equality_inference,[],[189]) ).
cnf(i_0_200,plain,
X1 = lookup_slb(insert_slb(X2,pair(X3,X1)),X3),
inference(scs_inference,[],[i_0_124,i_0_144]) ).
cnf(i_0_201,plain,
esk2_0 != create_slb,
inference(scs_inference,[],[i_0_188,i_0_124,i_0_144,i_0_147]) ).
cnf(i_0_202,plain,
triple(esk1_0,esk2_0,esk3_0) != triple(X1,create_slb,X2),
inference(rename_variables,[],[i_0_188]) ).
cnf(i_0_203,plain,
contains_slb(esk2_0,findmin_pqp_res(esk1_0)),
inference(scs_inference,[],[i_0_182,i_0_188,i_0_124,i_0_144,i_0_147,i_0_103]) ).
cnf(i_0_204,plain,
findmin_cpq_eff(triple(esk1_0,esk2_0,esk3_0)) != triple(X1,X2,bad),
inference(rename_variables,[],[i_0_182]) ).
cnf(i_0_205,plain,
( findmin_cpq_eff(triple(X1,X2,X3)) = triple(X1,update_slb(X2,findmin_pqp_res(X1)),bad)
| X2 = create_slb
| contains_slb(X2,findmin_pqp_res(X1)) ),
inference(rename_variables,[],[i_0_103]) ).
cnf(i_0_206,plain,
lookup_slb(insert_slb(X1,pair(X2,create_slb)),X2) = update_slb(create_slb,X3),
inference(scs_inference,[],[i_0_182,i_0_188,i_0_181,i_0_124,i_0_144,i_0_147,i_0_103,i_0_145]) ).
cnf(i_0_207,plain,
lookup_slb(insert_slb(X1,pair(X2,X3)),X2) = X3,
inference(rename_variables,[],[i_0_124]) ).
cnf(i_0_208,plain,
~ contains_slb(lookup_slb(insert_slb(X1,pair(X2,create_slb)),X2),X3),
inference(scs_inference,[],[i_0_182,i_0_188,i_0_181,i_0_137,i_0_124,i_0_207,i_0_144,i_0_147,i_0_103,i_0_145,i_0_169]) ).
cnf(i_0_209,plain,
lookup_slb(insert_slb(X1,pair(X2,X3)),X2) = X3,
inference(rename_variables,[],[i_0_124]) ).
cnf(i_0_210,plain,
~ pair_in_list(lookup_slb(insert_slb(X1,pair(X2,create_slb)),X2),X3,X4),
inference(scs_inference,[],[i_0_182,i_0_188,i_0_181,i_0_127,i_0_137,i_0_124,i_0_207,i_0_209,i_0_144,i_0_147,i_0_103,i_0_145,i_0_169,i_0_171]) ).
cnf(i_0_211,plain,
lookup_slb(insert_slb(X1,pair(X2,X3)),X2) = X3,
inference(rename_variables,[],[i_0_124]) ).
cnf(i_0_212,plain,
~ strictly_less_than(findmin_pqp_res(esk1_0),lookup_slb(esk2_0,findmin_pqp_res(esk1_0))),
inference(scs_inference,[],[i_0_182,i_0_204,i_0_188,i_0_181,i_0_127,i_0_137,i_0_124,i_0_207,i_0_209,i_0_144,i_0_147,i_0_103,i_0_145,i_0_169,i_0_171,i_0_97]) ).
cnf(i_0_213,plain,
findmin_cpq_eff(triple(esk1_0,esk2_0,esk3_0)) != triple(X1,X2,bad),
inference(rename_variables,[],[i_0_182]) ).
cnf(i_0_214,plain,
( findmin_cpq_eff(triple(X1,X2,X3)) = triple(X1,update_slb(X2,findmin_pqp_res(X1)),bad)
| ~ strictly_less_than(findmin_pqp_res(X1),lookup_slb(X2,findmin_pqp_res(X1)))
| ~ contains_slb(X2,findmin_pqp_res(X1))
| X2 = create_slb ),
inference(rename_variables,[],[i_0_97]) ).
cnf(i_0_215,plain,
( ~ less_than(findmin_pqp_res(esk1_0),lookup_slb(esk2_0,findmin_pqp_res(esk1_0)))
| less_than(lookup_slb(esk2_0,findmin_pqp_res(esk1_0)),findmin_pqp_res(esk1_0)) ),
inference(scs_inference,[],[i_0_182,i_0_204,i_0_188,i_0_181,i_0_127,i_0_137,i_0_124,i_0_207,i_0_209,i_0_144,i_0_147,i_0_103,i_0_145,i_0_169,i_0_171,i_0_97,i_0_132]) ).
cnf(i_0_216,plain,
( strictly_less_than(X1,X2)
| ~ less_than(X1,X2)
| less_than(X2,X1) ),
inference(rename_variables,[],[i_0_132]) ).
cnf(i_0_217,plain,
less_than(lookup_slb(esk2_0,findmin_pqp_res(esk1_0)),findmin_pqp_res(esk1_0)),
inference(scs_inference,[],[i_0_182,i_0_204,i_0_188,i_0_181,i_0_127,i_0_137,i_0_124,i_0_207,i_0_209,i_0_144,i_0_147,i_0_103,i_0_145,i_0_169,i_0_171,i_0_97,i_0_132,i_0_136]) ).
cnf(i_0_218,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(rename_variables,[],[i_0_136]) ).
cnf(i_0_220,plain,
update_slb(create_slb,X1) = lookup_slb(insert_slb(X2,pair(X3,create_slb)),X3),
inference(scs_inference,[],[i_0_206,i_0_144]) ).
cnf(i_0_221,plain,
$false,
inference(scs_inference,[],[i_0_217,i_0_206,i_0_201,i_0_203,i_0_144,i_0_122]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SWV374+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue May 5 05:07:31 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.26 % start to proof: theBenchmark
% 0.41/1.52 % Version : CSE_E---1.7
% 0.41/1.52 % Problem : theBenchmark.p
% 0.41/1.52 % SZS status Theorem for theBenchmark.p
% 0.41/1.52 % SZS output start CNFRefutation
% See solution above
% 0.50/1.61 % Total time : 1.264s
%------------------------------------------------------------------------------