%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV385+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n002.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 05:22:03 PM UTC 2026
% Result : Theorem 0.25s 1.61s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_84)
% Comments :
%------------------------------------------------------------------------------
fof(l21_li2225,lemma,
! [X1,X2,X3] :
( ~ check_cpq(triple(X1,X2,X3))
=> ( ~ check_cpq(im_succ_cpq(triple(X1,X2,X3)))
| ~ ok(im_succ_cpq(triple(X1,X2,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_li2225) ).
fof(l21_li1316,lemma,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> ~ ok(im_succ_cpq(triple(X1,X2,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_li1316) ).
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/sandbox/benchmark/Axioms/SWV007+3.ax',ax38) ).
fof(l21_co,conjecture,
! [X1,X2,X3] :
( ( ~ check_cpq(triple(X1,X2,X3))
| ~ ok(triple(X1,X2,X3)) )
=> ( ~ check_cpq(im_succ_cpq(triple(X1,X2,X3)))
| ~ ok(im_succ_cpq(triple(X1,X2,X3))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_co) ).
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/sandbox/benchmark/Axioms/SWV007+3.ax',ax47) ).
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/sandbox/benchmark/Axioms/SWV007+3.ax',ax43) ).
fof(ax40,axiom,
! [X1,X2] :
( ok(triple(X1,X2,bad))
<=> ~ $true ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax40) ).
fof(ax41,axiom,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> X3 = bad ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SWV007+3.ax',ax52) ).
fof(ax22,axiom,
! [X1,X2] : ~ pair_in_list(create_slb,X1,X2),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
fof(ax20,axiom,
! [X1] : ~ contains_slb(create_slb,X1),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SWV007+3.ax',ax51) ).
fof(ax36,axiom,
! [X1,X2] : check_cpq(triple(X1,create_slb,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax36) ).
fof(ax50,axiom,
! [X1,X2] : findmin_cpq_res(triple(X1,create_slb,X2)) = bottom,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SWV007+2.ax',ax24) ).
fof(ax19,axiom,
! [X1,X2,X3] : isnonempty_slb(insert_slb(X1,pair(X2,X3))),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/SWV007+3.ax',ax34) ).
fof(totality,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(ax31,axiom,
! [X1] : succ_cpq(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax31) ).
fof(reflexivity,axiom,
! [X1] : less_than(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',reflexivity) ).
fof(bottom_smallest,axiom,
! [X1] : less_than(bottom,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',bottom_smallest) ).
fof(ax28,axiom,
! [X1] : update_slb(create_slb,X1) = create_slb,
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax28) ).
fof(ax18,axiom,
~ isnonempty_slb(create_slb),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax18) ).
fof(i_0_43,lemma,
! [X1,X2,X3] :
( ~ check_cpq(triple(X1,X2,X3))
=> ( ~ check_cpq(im_succ_cpq(triple(X1,X2,X3)))
| ~ ok(im_succ_cpq(triple(X1,X2,X3))) ) ),
inference(fof_simplification,[status(thm)],[l21_li2225]) ).
fof(i_0_44,lemma,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> ~ ok(im_succ_cpq(triple(X1,X2,X3))) ),
inference(fof_simplification,[status(thm)],[l21_li1316]) ).
fof(i_0_45,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_46,negated_conjecture,
~ ! [X1,X2,X3] :
( ( ~ check_cpq(triple(X1,X2,X3))
| ~ ok(triple(X1,X2,X3)) )
=> ( ~ check_cpq(im_succ_cpq(triple(X1,X2,X3)))
| ~ ok(im_succ_cpq(triple(X1,X2,X3))) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l21_co])]) ).
fof(i_0_47,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_48,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_49,plain,
! [X1,X2] : ~ ok(triple(X1,X2,bad)),
inference(fof_simplification,[status(thm)],[ax40]) ).
fof(i_0_50,plain,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> X3 = bad ),
inference(fof_simplification,[status(thm)],[ax41]) ).
fof(i_0_51,plain,
! [X188,X189] :
( ~ succ_cpq(X188,X189)
| succ_cpq(X188,removemin_cpq_eff(X189)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax35])]) ).
fof(i_0_52,plain,
! [X243] : removemin_cpq_eff(X243) = remove_cpq(findmin_cpq_eff(X243),findmin_cpq_res(X243)),
inference(variable_rename,[status(thm)],[ax52]) ).
fof(i_0_53,plain,
! [X1,X2] : ~ pair_in_list(create_slb,X1,X2),
inference(fof_simplification,[status(thm)],[ax22]) ).
fof(i_0_54,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_55,plain,
! [X1] : ~ contains_slb(create_slb,X1),
inference(fof_simplification,[status(thm)],[ax20]) ).
fof(i_0_56,lemma,
! [X248,X249,X250] :
( check_cpq(triple(X248,X249,X250))
| ~ check_cpq(im_succ_cpq(triple(X248,X249,X250)))
| ~ ok(im_succ_cpq(triple(X248,X249,X250))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_43])]) ).
fof(i_0_57,plain,
! [X192,X193,X194,X195,X196] :
( ( ~ check_cpq(triple(X192,insert_slb(X193,pair(X195,X196)),X194))
| check_cpq(triple(X192,X193,X194))
| ~ less_than(X196,X195) )
& ( ~ check_cpq(triple(X192,X193,X194))
| check_cpq(triple(X192,insert_slb(X193,pair(X195,X196)),X194))
| ~ less_than(X196,X195) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])]) ).
fof(i_0_58,lemma,
! [X245,X246,X247] :
( ok(triple(X245,X246,X247))
| ~ ok(im_succ_cpq(triple(X245,X246,X247))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_44])]) ).
fof(i_0_59,plain,
! [X197,X198,X199,X200,X201] :
( ~ strictly_less_than(X200,X201)
| ~ check_cpq(triple(X197,insert_slb(X198,pair(X200,X201)),X199)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_45])]) ).
fof(i_0_60,plain,
! [X235,X236,X237] :
( X236 = create_slb
| ~ contains_slb(X236,findmin_pqp_res(X235))
| ~ less_than(lookup_slb(X236,findmin_pqp_res(X235)),findmin_pqp_res(X235))
| findmin_cpq_eff(triple(X235,X236,X237)) = triple(X235,update_slb(X236,findmin_pqp_res(X235)),X237) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax49])])]) ).
fof(i_0_61,plain,
! [X232,X233,X234] :
( X233 = create_slb
| ~ contains_slb(X233,findmin_pqp_res(X232))
| ~ strictly_less_than(findmin_pqp_res(X232),lookup_slb(X233,findmin_pqp_res(X232)))
| findmin_cpq_eff(triple(X232,X233,X234)) = triple(X232,update_slb(X233,findmin_pqp_res(X232)),bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax48])])]) ).
fof(i_0_62,negated_conjecture,
( ( ~ check_cpq(triple(esk1_0,esk2_0,esk3_0))
| ~ ok(triple(esk1_0,esk2_0,esk3_0)) )
& check_cpq(im_succ_cpq(triple(esk1_0,esk2_0,esk3_0)))
& ok(im_succ_cpq(triple(esk1_0,esk2_0,esk3_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_46])])]) ).
fof(i_0_63,plain,
! [X219,X220,X221,X222] :
( ~ contains_slb(X220,X222)
| ~ less_than(lookup_slb(X220,X222),X222)
| remove_cpq(triple(X219,X220,X221),X222) = triple(remove_pqp(X219,X222),remove_slb(X220,X222),X221) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])]) ).
fof(i_0_64,plain,
! [X223,X224,X225,X226] :
( ~ contains_slb(X224,X226)
| ~ strictly_less_than(X226,lookup_slb(X224,X226))
| remove_cpq(triple(X223,X224,X225),X226) = triple(remove_pqp(X223,X226),remove_slb(X224,X226),bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
fof(i_0_65,plain,
! [X211,X212,X213,X214] : insert_cpq(triple(X211,X212,X213),X214) = triple(insert_pqp(X211,X214),insert_slb(X212,pair(X214,bottom)),X213),
inference(variable_rename,[status(thm)],[ax42]) ).
fof(i_0_66,plain,
! [X151,X152,X153,X154,X155] :
( ( X152 = X153
| pair_in_list(X151,X153,X155)
| ~ pair_in_list(insert_slb(X151,pair(X152,X154)),X153,X155) )
& ( X154 = X155
| pair_in_list(X151,X153,X155)
| ~ pair_in_list(insert_slb(X151,pair(X152,X154)),X153,X155) )
& ( ~ pair_in_list(X151,X153,X155)
| pair_in_list(insert_slb(X151,pair(X152,X154)),X153,X155) )
& ( X152 != X153
| X154 != X155
| pair_in_list(insert_slb(X151,pair(X152,X154)),X153,X155) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
fof(i_0_67,plain,
! [X229,X230,X231] :
( X230 = create_slb
| contains_slb(X230,findmin_pqp_res(X229))
| findmin_cpq_eff(triple(X229,X230,X231)) = triple(X229,update_slb(X230,findmin_pqp_res(X229)),bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[i_0_47])])]) ).
fof(i_0_68,plain,
! [X202,X203,X204,X205] :
( ( ~ contains_cpq(triple(X202,X203,X204),X205)
| contains_slb(X203,X205) )
& ( ~ contains_slb(X203,X205)
| contains_cpq(triple(X202,X203,X204),X205) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax39])]) ).
fof(i_0_69,plain,
! [X215,X216,X217,X218] :
( contains_slb(X216,X218)
| remove_cpq(triple(X215,X216,X217),X218) = triple(X215,X216,bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_48])]) ).
fof(i_0_70,plain,
! [X159,X160,X161,X162] :
( X160 = X161
| ~ contains_slb(X159,X161)
| remove_slb(insert_slb(X159,pair(X160,X162)),X161) = insert_slb(remove_slb(X159,X161),pair(X160,X162)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])]) ).
fof(i_0_71,plain,
! [X171,X172,X173,X174] :
( ~ strictly_less_than(X174,X173)
| update_slb(insert_slb(X171,pair(X172,X174)),X173) = insert_slb(update_slb(X171,X173),pair(X172,X173)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax29])]) ).
fof(i_0_72,plain,
! [X175,X176,X177,X178] :
( ~ less_than(X177,X178)
| update_slb(insert_slb(X175,pair(X176,X178)),X177) = insert_slb(update_slb(X175,X177),pair(X176,X178)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax30])]) ).
fof(i_0_73,plain,
! [X206,X207] : ~ ok(triple(X206,X207,bad)),
inference(variable_rename,[status(thm)],[i_0_49]) ).
fof(i_0_74,plain,
! [X145,X146,X147,X148] :
( ( ~ contains_slb(insert_slb(X145,pair(X146,X148)),X147)
| contains_slb(X145,X147)
| X146 = X147 )
& ( ~ contains_slb(X145,X147)
| contains_slb(insert_slb(X145,pair(X146,X148)),X147) )
& ( X146 != X147
| contains_slb(insert_slb(X145,pair(X146,X148)),X147) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
fof(i_0_75,plain,
! [X227,X228] : findmin_cpq_eff(triple(X227,create_slb,X228)) = triple(X227,create_slb,bad),
inference(variable_rename,[status(thm)],[ax46]) ).
fof(i_0_76,plain,
! [X166,X167,X168,X169] :
( X167 = X168
| ~ contains_slb(X166,X168)
| lookup_slb(insert_slb(X166,pair(X167,X169)),X168) = lookup_slb(X166,X168) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])]) ).
fof(i_0_77,plain,
! [X240,X241,X242] :
( X241 = create_slb
| findmin_cpq_res(triple(X240,X241,X242)) = findmin_pqp_res(X240) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax51])])]) ).
fof(i_0_78,plain,
! [X208,X209,X210] :
( ok(triple(X208,X209,X210))
| X210 = bad ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_50])]) ).
fof(i_0_79,plain,
! [X190,X191] : check_cpq(triple(X190,create_slb,X191)),
inference(variable_rename,[status(thm)],[ax36]) ).
fof(i_0_80,plain,
! [X238,X239] : findmin_cpq_res(triple(X238,create_slb,X239)) = bottom,
inference(variable_rename,[status(thm)],[ax50]) ).
fof(i_0_81,plain,
! [X163,X164,X165] : lookup_slb(insert_slb(X163,pair(X164,X165)),X164) = X165,
inference(variable_rename,[status(thm)],[ax26]) ).
fof(i_0_82,plain,
! [X156,X157,X158] : remove_slb(insert_slb(X156,pair(X157,X158)),X157) = X156,
inference(variable_rename,[status(thm)],[ax24]) ).
cnf(i_0_83,plain,
( succ_cpq(X1,removemin_cpq_eff(X2))
| ~ succ_cpq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_51]) ).
cnf(i_0_84,plain,
removemin_cpq_eff(X1) = remove_cpq(findmin_cpq_eff(X1),findmin_cpq_res(X1)),
inference(split_conjunct,[status(thm)],[i_0_52]) ).
fof(i_0_85,plain,
! [X149,X150] : ~ pair_in_list(create_slb,X149,X150),
inference(variable_rename,[status(thm)],[i_0_53]) ).
fof(i_0_86,plain,
! [X141,X142,X143] : isnonempty_slb(insert_slb(X141,pair(X142,X143))),
inference(variable_rename,[status(thm)],[ax19]) ).
fof(i_0_87,plain,
! [X183,X184,X185] :
( ~ succ_cpq(X183,X184)
| succ_cpq(X183,remove_cpq(X184,X185)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax33])]) ).
fof(i_0_88,plain,
! [X180,X181,X182] :
( ~ succ_cpq(X180,X181)
| succ_cpq(X180,insert_cpq(X181,X182)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax32])]) ).
fof(i_0_89,plain,
! [X132,X133,X134] :
( ~ less_than(X132,X133)
| ~ less_than(X133,X134)
| less_than(X132,X134) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity])]) ).
fof(i_0_90,plain,
! [X138,X139] :
( ( less_than(X138,X139)
| ~ strictly_less_than(X138,X139) )
& ( ~ less_than(X139,X138)
| ~ strictly_less_than(X138,X139) )
& ( ~ less_than(X138,X139)
| less_than(X139,X138)
| strictly_less_than(X138,X139) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_54])])]) ).
fof(i_0_91,plain,
! [X186,X187] :
( ~ succ_cpq(X186,X187)
| succ_cpq(X186,findmin_cpq_eff(X187)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax34])]) ).
fof(i_0_92,plain,
! [X135,X136] :
( less_than(X135,X136)
| less_than(X136,X135) ),
inference(variable_rename,[status(thm)],[totality]) ).
fof(i_0_93,plain,
! [X144] : ~ contains_slb(create_slb,X144),
inference(variable_rename,[status(thm)],[i_0_55]) ).
fof(i_0_94,plain,
! [X179] : succ_cpq(X179,X179),
inference(variable_rename,[status(thm)],[ax31]) ).
fof(i_0_95,plain,
! [X137] : less_than(X137,X137),
inference(variable_rename,[status(thm)],[reflexivity]) ).
fof(i_0_96,plain,
! [X140] : less_than(bottom,X140),
inference(variable_rename,[status(thm)],[bottom_smallest]) ).
fof(i_0_97,plain,
! [X170] : update_slb(create_slb,X170) = create_slb,
inference(variable_rename,[status(thm)],[ax28]) ).
fof(i_0_98,plain,
~ isnonempty_slb(create_slb),
inference(fof_simplification,[status(thm)],[ax18]) ).
cnf(i_0_99,lemma,
( check_cpq(triple(X1,X2,X3))
| ~ check_cpq(im_succ_cpq(triple(X1,X2,X3)))
| ~ ok(im_succ_cpq(triple(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_100,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_57]),
[final] ).
cnf(i_0_101,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_57]),
[final] ).
cnf(i_0_102,lemma,
( ok(triple(X1,X2,X3))
| ~ ok(im_succ_cpq(triple(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_103,plain,
( ~ strictly_less_than(X1,X2)
| ~ check_cpq(triple(X3,insert_slb(X4,pair(X1,X2)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_104,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_60]),
[final] ).
cnf(i_0_105,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_61]),
[final] ).
cnf(i_0_106,negated_conjecture,
( ~ check_cpq(triple(esk1_0,esk2_0,esk3_0))
| ~ ok(triple(esk1_0,esk2_0,esk3_0)) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_107,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_63]),
[final] ).
cnf(i_0_108,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_64]),
[final] ).
cnf(i_0_109,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_65]),
[final] ).
cnf(i_0_110,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_66]),
[final] ).
cnf(i_0_111,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_66]),
[final] ).
cnf(i_0_112,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_67]),
[final] ).
cnf(i_0_113,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_66]),
[final] ).
cnf(i_0_114,negated_conjecture,
ok(im_succ_cpq(triple(esk1_0,esk2_0,esk3_0))),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_115,negated_conjecture,
check_cpq(im_succ_cpq(triple(esk1_0,esk2_0,esk3_0))),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_116,plain,
( contains_slb(X2,X4)
| ~ contains_cpq(triple(X1,X2,X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_117,plain,
( contains_slb(X1,X2)
| remove_cpq(triple(X3,X1,X4),X2) = triple(X3,X1,bad) ),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_118,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_70]),
[final] ).
cnf(i_0_119,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_71]),
[final] ).
cnf(i_0_120,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_72]),
[final] ).
cnf(i_0_121,plain,
~ ok(triple(X1,X2,bad)),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_122,plain,
( contains_slb(X1,X4)
| X2 = X4
| ~ contains_slb(insert_slb(X1,pair(X2,X3)),X4) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_123,plain,
findmin_cpq_eff(triple(X1,create_slb,X2)) = triple(X1,create_slb,bad),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_124,plain,
( contains_cpq(triple(X3,X1,X4),X2)
| ~ contains_slb(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_125,plain,
( pair_in_list(insert_slb(X5,pair(X1,X3)),X2,X4)
| X1 != X2
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_126,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_76]),
[final] ).
cnf(i_0_127,plain,
( X1 = create_slb
| findmin_cpq_res(triple(X2,X1,X3)) = findmin_pqp_res(X2) ),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_128,plain,
( contains_slb(insert_slb(X1,pair(X3,X4)),X2)
| ~ contains_slb(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_129,plain,
( ok(triple(X1,X2,X3))
| X3 = bad ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_130,plain,
check_cpq(triple(X1,create_slb,X2)),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_131,plain,
findmin_cpq_res(triple(X1,create_slb,X2)) = bottom,
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_132,plain,
( contains_slb(insert_slb(X3,pair(X1,X4)),X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_133,plain,
lookup_slb(insert_slb(X1,pair(X2,X3)),X2) = X3,
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_134,plain,
remove_slb(insert_slb(X1,pair(X2,X3)),X2) = X1,
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_135,plain,
( succ_cpq(X1,remove_cpq(findmin_cpq_eff(X2),findmin_cpq_res(X2)))
| ~ succ_cpq(X1,X2) ),
inference(rw,[status(thm)],[i_0_83,c_0_84]),
[final] ).
cnf(i_0_136,plain,
~ pair_in_list(create_slb,X1,X2),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_137,plain,
isnonempty_slb(insert_slb(X1,pair(X2,X3))),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_138,plain,
( succ_cpq(X1,remove_cpq(X2,X3))
| ~ succ_cpq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_139,plain,
( succ_cpq(X1,insert_cpq(X2,X3))
| ~ succ_cpq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_140,plain,
( less_than(X1,X3)
| ~ less_than(X1,X2)
| ~ less_than(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_141,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_142,plain,
( ~ less_than(X1,X2)
| ~ strictly_less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_143,plain,
( succ_cpq(X1,findmin_cpq_eff(X2))
| ~ succ_cpq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_144,plain,
( less_than(X1,X2)
| ~ strictly_less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_145,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_92]),
[final] ).
cnf(i_0_146,plain,
~ contains_slb(create_slb,X1),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_147,plain,
succ_cpq(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_94]),
[final] ).
cnf(i_0_148,plain,
less_than(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_149,plain,
less_than(bottom,X1),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_150,plain,
update_slb(create_slb,X1) = create_slb,
inference(split_conjunct,[status(thm)],[i_0_97]),
[final] ).
cnf(i_0_151,plain,
~ isnonempty_slb(create_slb),
inference(split_conjunct,[status(thm)],[i_0_98]),
[final] ).
cnf(i_0_152,axiom,
X1 = X1 ).
cnf(i_0_153,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_154,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_155,axiom,
( X1 != X2
| triple(X1,X3,X4) = triple(X2,X3,X4) ) ).
cnf(i_0_156,axiom,
( X1 != X2
| triple(X3,X1,X4) = triple(X3,X2,X4) ) ).
cnf(i_0_157,axiom,
( X1 != X2
| triple(X3,X4,X1) = triple(X3,X4,X2) ) ).
cnf(i_0_158,axiom,
( X1 != X2
| remove_slb(X1,X3) = remove_slb(X2,X3) ) ).
cnf(i_0_159,axiom,
( X1 != X2
| remove_slb(X3,X1) = remove_slb(X3,X2) ) ).
cnf(i_0_160,axiom,
( X1 != X2
| insert_cpq(X1,X3) = insert_cpq(X2,X3) ) ).
cnf(i_0_161,axiom,
( X1 != X2
| insert_cpq(X3,X1) = insert_cpq(X3,X2) ) ).
cnf(i_0_162,axiom,
( X1 != X2
| findmin_cpq_res(X1) = findmin_cpq_res(X2) ) ).
cnf(i_0_163,axiom,
( X1 != X2
| insert_slb(X1,X3) = insert_slb(X2,X3) ) ).
cnf(i_0_164,axiom,
( X1 != X2
| insert_slb(X3,X1) = insert_slb(X3,X2) ) ).
cnf(i_0_165,axiom,
( X1 != X2
| findmin_cpq_eff(X1) = findmin_cpq_eff(X2) ) ).
cnf(i_0_166,axiom,
( X1 != X2
| update_slb(X1,X3) = update_slb(X2,X3) ) ).
cnf(i_0_167,axiom,
( X1 != X2
| update_slb(X3,X1) = update_slb(X3,X2) ) ).
cnf(i_0_168,axiom,
( X1 != X2
| findmin_pqp_res(X1) = findmin_pqp_res(X2) ) ).
cnf(i_0_169,axiom,
( X1 != X2
| lookup_slb(X1,X3) = lookup_slb(X2,X3) ) ).
cnf(i_0_170,axiom,
( X1 != X2
| lookup_slb(X3,X1) = lookup_slb(X3,X2) ) ).
cnf(i_0_171,axiom,
( X1 != X2
| remove_cpq(X1,X3) = remove_cpq(X2,X3) ) ).
cnf(i_0_172,axiom,
( X1 != X2
| remove_cpq(X3,X1) = remove_cpq(X3,X2) ) ).
cnf(i_0_173,axiom,
( X1 != X2
| ~ check_cpq(X1)
| check_cpq(X2) ) ).
cnf(i_0_174,axiom,
( X1 != X2
| ~ ok(X1)
| ok(X2) ) ).
cnf(i_0_175,axiom,
( X1 != X2
| ~ less_than(X1,X3)
| less_than(X2,X3) ) ).
cnf(i_0_176,axiom,
( X1 != X2
| ~ less_than(X3,X1)
| less_than(X3,X2) ) ).
cnf(i_0_177,axiom,
( X1 != X2
| ~ strictly_less_than(X1,X3)
| strictly_less_than(X2,X3) ) ).
cnf(i_0_178,axiom,
( X1 != X2
| ~ strictly_less_than(X3,X1)
| strictly_less_than(X3,X2) ) ).
cnf(i_0_179,axiom,
( X1 != X2
| ~ contains_slb(X1,X3)
| contains_slb(X2,X3) ) ).
cnf(i_0_180,axiom,
( X1 != X2
| ~ contains_slb(X3,X1)
| contains_slb(X3,X2) ) ).
cnf(i_0_181,axiom,
( X1 != X2
| ~ pair_in_list(X1,X3,X4)
| pair_in_list(X2,X3,X4) ) ).
cnf(i_0_182,axiom,
( X1 != X2
| ~ pair_in_list(X3,X1,X4)
| pair_in_list(X3,X2,X4) ) ).
cnf(i_0_183,axiom,
( X1 != X2
| ~ pair_in_list(X3,X4,X1)
| pair_in_list(X3,X4,X2) ) ).
cnf(i_0_184,axiom,
( X1 != X2
| ~ contains_cpq(X1,X3)
| contains_cpq(X2,X3) ) ).
cnf(i_0_185,axiom,
( X1 != X2
| ~ contains_cpq(X3,X1)
| contains_cpq(X3,X2) ) ).
cnf(i_0_186,axiom,
( X1 != X2
| ~ succ_cpq(X1,X3)
| succ_cpq(X2,X3) ) ).
cnf(i_0_187,axiom,
( X1 != X2
| ~ succ_cpq(X3,X1)
| succ_cpq(X3,X2) ) ).
cnf(i_0_188,axiom,
( X1 != X2
| ~ isnonempty_slb(X1)
| isnonempty_slb(X2) ) ).
cnf(i_0_152_001,axiom,
X1 = X1 ).
cnf(i_0_153_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_154_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_155_004,axiom,
( X1 != X2
| triple(X1,X3,X4) = triple(X2,X3,X4) ) ).
cnf(i_0_156_005,axiom,
( X1 != X2
| triple(X3,X1,X4) = triple(X3,X2,X4) ) ).
cnf(i_0_157_006,axiom,
( X1 != X2
| triple(X3,X4,X1) = triple(X3,X4,X2) ) ).
cnf(i_0_158_007,axiom,
( X1 != X2
| remove_slb(X1,X3) = remove_slb(X2,X3) ) ).
cnf(i_0_159_008,axiom,
( X1 != X2
| remove_slb(X3,X1) = remove_slb(X3,X2) ) ).
cnf(i_0_160_009,axiom,
( X1 != X2
| insert_cpq(X1,X3) = insert_cpq(X2,X3) ) ).
cnf(i_0_161_010,axiom,
( X1 != X2
| insert_cpq(X3,X1) = insert_cpq(X3,X2) ) ).
cnf(i_0_162_011,axiom,
( X1 != X2
| findmin_cpq_res(X1) = findmin_cpq_res(X2) ) ).
cnf(i_0_163_012,axiom,
( X1 != X2
| insert_slb(X1,X3) = insert_slb(X2,X3) ) ).
cnf(i_0_164_013,axiom,
( X1 != X2
| insert_slb(X3,X1) = insert_slb(X3,X2) ) ).
cnf(i_0_165_014,axiom,
( X1 != X2
| findmin_cpq_eff(X1) = findmin_cpq_eff(X2) ) ).
cnf(i_0_166_015,axiom,
( X1 != X2
| update_slb(X1,X3) = update_slb(X2,X3) ) ).
cnf(i_0_167_016,axiom,
( X1 != X2
| update_slb(X3,X1) = update_slb(X3,X2) ) ).
cnf(i_0_168_017,axiom,
( X1 != X2
| findmin_pqp_res(X1) = findmin_pqp_res(X2) ) ).
cnf(i_0_169_018,axiom,
( X1 != X2
| lookup_slb(X1,X3) = lookup_slb(X2,X3) ) ).
cnf(i_0_170_019,axiom,
( X1 != X2
| lookup_slb(X3,X1) = lookup_slb(X3,X2) ) ).
cnf(i_0_171_020,axiom,
( X1 != X2
| remove_cpq(X1,X3) = remove_cpq(X2,X3) ) ).
cnf(i_0_172_021,axiom,
( X1 != X2
| remove_cpq(X3,X1) = remove_cpq(X3,X2) ) ).
cnf(i_0_173_022,axiom,
( X1 != X2
| ~ check_cpq(X1)
| check_cpq(X2) ) ).
cnf(i_0_174_023,axiom,
( X1 != X2
| ~ ok(X1)
| ok(X2) ) ).
cnf(i_0_175_024,axiom,
( X1 != X2
| ~ less_than(X1,X3)
| less_than(X2,X3) ) ).
cnf(i_0_176_025,axiom,
( X1 != X2
| ~ less_than(X3,X1)
| less_than(X3,X2) ) ).
cnf(i_0_177_026,axiom,
( X1 != X2
| ~ strictly_less_than(X1,X3)
| strictly_less_than(X2,X3) ) ).
cnf(i_0_178_027,axiom,
( X1 != X2
| ~ strictly_less_than(X3,X1)
| strictly_less_than(X3,X2) ) ).
cnf(i_0_179_028,axiom,
( X1 != X2
| ~ contains_slb(X1,X3)
| contains_slb(X2,X3) ) ).
cnf(i_0_180_029,axiom,
( X1 != X2
| ~ contains_slb(X3,X1)
| contains_slb(X3,X2) ) ).
cnf(i_0_181_030,axiom,
( X1 != X2
| ~ pair_in_list(X1,X3,X4)
| pair_in_list(X2,X3,X4) ) ).
cnf(i_0_182_031,axiom,
( X1 != X2
| ~ pair_in_list(X3,X1,X4)
| pair_in_list(X3,X2,X4) ) ).
cnf(i_0_183_032,axiom,
( X1 != X2
| ~ pair_in_list(X3,X4,X1)
| pair_in_list(X3,X4,X2) ) ).
cnf(i_0_184_033,axiom,
( X1 != X2
| ~ contains_cpq(X1,X3)
| contains_cpq(X2,X3) ) ).
cnf(i_0_185_034,axiom,
( X1 != X2
| ~ contains_cpq(X3,X1)
| contains_cpq(X3,X2) ) ).
cnf(i_0_186_035,axiom,
( X1 != X2
| ~ succ_cpq(X1,X3)
| succ_cpq(X2,X3) ) ).
cnf(i_0_187_036,axiom,
( X1 != X2
| ~ succ_cpq(X3,X1)
| succ_cpq(X3,X2) ) ).
cnf(i_0_188_037,axiom,
( X1 != X2
| ~ isnonempty_slb(X1)
| isnonempty_slb(X2) ) ).
cnf(i_0_189,plain,
contains_slb(insert_slb(X1,pair(X2,X3)),X2),
inference(equality_inference,[],[132]) ).
cnf(i_0_190,plain,
ok(triple(esk1_0,esk2_0,esk3_0)),
inference(scs_inference,[],[i_0_114,i_0_102]) ).
cnf(i_0_191,plain,
( ~ ok(im_succ_cpq(triple(X1,X2,X3)))
| ok(triple(X1,X2,X3)) ),
inference(rename_variables,[],[i_0_102]) ).
cnf(i_0_192,plain,
create_slb = update_slb(create_slb,X1),
inference(scs_inference,[],[i_0_114,i_0_150,i_0_102,i_0_153]) ).
cnf(i_0_193,plain,
check_cpq(triple(esk1_0,esk2_0,esk3_0)),
inference(scs_inference,[],[i_0_114,i_0_115,i_0_150,i_0_102,i_0_153,i_0_99]) ).
cnf(i_0_194,plain,
( ~ check_cpq(im_succ_cpq(triple(X1,X2,X3)))
| ~ ok(im_succ_cpq(triple(X1,X2,X3)))
| check_cpq(triple(X1,X2,X3)) ),
inference(rename_variables,[],[i_0_99]) ).
cnf(i_0_195,plain,
im_succ_cpq(triple(esk1_0,esk2_0,esk3_0)) != triple(X1,X2,bad),
inference(scs_inference,[],[i_0_114,i_0_115,i_0_150,i_0_121,i_0_102,i_0_153,i_0_99,i_0_174]) ).
cnf(i_0_196,plain,
im_succ_cpq(triple(esk1_0,esk2_0,esk3_0)) != findmin_cpq_eff(triple(X1,create_slb,X2)),
inference(scs_inference,[],[i_0_114,i_0_115,i_0_150,i_0_121,i_0_123,i_0_102,i_0_153,i_0_99,i_0_174,i_0_154]) ).
cnf(i_0_197,plain,
findmin_cpq_eff(triple(X1,create_slb,X2)) = triple(X1,create_slb,bad),
inference(rename_variables,[],[i_0_123]) ).
cnf(i_0_198,plain,
~ contains_slb(update_slb(create_slb,X1),X2),
inference(scs_inference,[],[i_0_114,i_0_115,i_0_150,i_0_121,i_0_123,i_0_146,i_0_102,i_0_153,i_0_99,i_0_174,i_0_154,i_0_179]) ).
cnf(i_0_199,plain,
~ pair_in_list(update_slb(create_slb,X1),X2,X3),
inference(scs_inference,[],[i_0_114,i_0_115,i_0_150,i_0_121,i_0_123,i_0_136,i_0_146,i_0_102,i_0_153,i_0_99,i_0_174,i_0_154,i_0_179,i_0_181]) ).
cnf(i_0_200,plain,
insert_slb(X1,pair(X2,X3)) != create_slb,
inference(scs_inference,[],[i_0_114,i_0_115,i_0_150,i_0_121,i_0_123,i_0_136,i_0_146,i_0_151,i_0_137,i_0_102,i_0_153,i_0_99,i_0_174,i_0_154,i_0_179,i_0_181,i_0_188]) ).
cnf(i_0_201,plain,
$false,
inference(scs_inference,[],[i_0_114,i_0_115,i_0_150,i_0_121,i_0_123,i_0_136,i_0_146,i_0_151,i_0_137,i_0_102,i_0_153,i_0_99,i_0_174,i_0_154,i_0_179,i_0_181,i_0_188,i_0_106]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV385+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n002.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 05:04:46 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 0.25/1.61 % Version : CSE_E---1.7
% 0.25/1.61 % Problem : theBenchmark.p
% 0.25/1.61 % SZS status Theorem for theBenchmark.p
% 0.25/1.61 % SZS output start CNFRefutation
% See solution above
% 0.25/1.67 % Total time : 1.271s
%------------------------------------------------------------------------------