%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV383+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 : n005.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 0.29s 1.62s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_81)
% Comments :
%------------------------------------------------------------------------------
fof(l19_l20,lemma,
! [X1,X2,X3] :
( ( ~ check_cpq(triple(X1,X2,X3))
| ~ ok(triple(X1,X2,X3)) )
=> ! [X4,X5,X6] :
( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
=> ( ~ ok(triple(X4,X5,X6))
| ~ check_cpq(triple(X4,X5,X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l19_l20) ).
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(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(l19_co,conjecture,
! [X1,X2,X3] :
( ~ check_cpq(triple(X1,X2,X3))
=> ! [X4,X5,X6] :
( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
=> ( ~ ok(triple(X4,X5,X6))
| ~ check_cpq(triple(X4,X5,X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l19_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/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_42,lemma,
! [X1,X2,X3] :
( ( ~ check_cpq(triple(X1,X2,X3))
| ~ ok(triple(X1,X2,X3)) )
=> ! [X4,X5,X6] :
( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
=> ( ~ ok(triple(X4,X5,X6))
| ~ check_cpq(triple(X4,X5,X6)) ) ) ),
inference(fof_simplification,[status(thm)],[l19_l20]) ).
fof(i_0_43,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_44,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_45,negated_conjecture,
~ ! [X1,X2,X3] :
( ~ check_cpq(triple(X1,X2,X3))
=> ! [X4,X5,X6] :
( succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
=> ( ~ ok(triple(X4,X5,X6))
| ~ check_cpq(triple(X4,X5,X6)) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l19_co])]) ).
fof(i_0_46,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_47,plain,
! [X1,X2] : ~ ok(triple(X1,X2,bad)),
inference(fof_simplification,[status(thm)],[ax40]) ).
fof(i_0_48,plain,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> X3 = bad ),
inference(fof_simplification,[status(thm)],[ax41]) ).
fof(i_0_49,plain,
! [X192,X193] :
( ~ succ_cpq(X192,X193)
| succ_cpq(X192,removemin_cpq_eff(X193)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax35])]) ).
fof(i_0_50,plain,
! [X247] : removemin_cpq_eff(X247) = remove_cpq(findmin_cpq_eff(X247),findmin_cpq_res(X247)),
inference(variable_rename,[status(thm)],[ax52]) ).
fof(i_0_51,plain,
! [X1,X2] : ~ pair_in_list(create_slb,X1,X2),
inference(fof_simplification,[status(thm)],[ax22]) ).
fof(i_0_52,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_53,plain,
! [X1] : ~ contains_slb(create_slb,X1),
inference(fof_simplification,[status(thm)],[ax20]) ).
fof(i_0_54,lemma,
! [X249,X250,X251,X252,X253,X254] :
( ( check_cpq(triple(X249,X250,X251))
| ~ succ_cpq(triple(X249,X250,X251),triple(X252,X253,X254))
| ~ ok(triple(X252,X253,X254))
| ~ check_cpq(triple(X252,X253,X254)) )
& ( ok(triple(X249,X250,X251))
| ~ succ_cpq(triple(X249,X250,X251),triple(X252,X253,X254))
| ~ ok(triple(X252,X253,X254))
| ~ check_cpq(triple(X252,X253,X254)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_42])])])]) ).
fof(i_0_55,plain,
! [X196,X197,X198,X199,X200] :
( ( ~ check_cpq(triple(X196,insert_slb(X197,pair(X199,X200)),X198))
| check_cpq(triple(X196,X197,X198))
| ~ less_than(X200,X199) )
& ( ~ check_cpq(triple(X196,X197,X198))
| check_cpq(triple(X196,insert_slb(X197,pair(X199,X200)),X198))
| ~ less_than(X200,X199) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])]) ).
fof(i_0_56,plain,
! [X201,X202,X203,X204,X205] :
( ~ strictly_less_than(X204,X205)
| ~ check_cpq(triple(X201,insert_slb(X202,pair(X204,X205)),X203)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_43])]) ).
fof(i_0_57,plain,
! [X239,X240,X241] :
( X240 = create_slb
| ~ contains_slb(X240,findmin_pqp_res(X239))
| ~ less_than(lookup_slb(X240,findmin_pqp_res(X239)),findmin_pqp_res(X239))
| findmin_cpq_eff(triple(X239,X240,X241)) = triple(X239,update_slb(X240,findmin_pqp_res(X239)),X241) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax49])])]) ).
fof(i_0_58,plain,
! [X236,X237,X238] :
( X237 = create_slb
| ~ contains_slb(X237,findmin_pqp_res(X236))
| ~ strictly_less_than(findmin_pqp_res(X236),lookup_slb(X237,findmin_pqp_res(X236)))
| findmin_cpq_eff(triple(X236,X237,X238)) = triple(X236,update_slb(X237,findmin_pqp_res(X236)),bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax48])])]) ).
fof(i_0_59,plain,
! [X223,X224,X225,X226] :
( ~ contains_slb(X224,X226)
| ~ less_than(lookup_slb(X224,X226),X226)
| remove_cpq(triple(X223,X224,X225),X226) = triple(remove_pqp(X223,X226),remove_slb(X224,X226),X225) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])]) ).
fof(i_0_60,plain,
! [X227,X228,X229,X230] :
( ~ contains_slb(X228,X230)
| ~ strictly_less_than(X230,lookup_slb(X228,X230))
| remove_cpq(triple(X227,X228,X229),X230) = triple(remove_pqp(X227,X230),remove_slb(X228,X230),bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).
fof(i_0_61,plain,
! [X215,X216,X217,X218] : insert_cpq(triple(X215,X216,X217),X218) = triple(insert_pqp(X215,X218),insert_slb(X216,pair(X218,bottom)),X217),
inference(variable_rename,[status(thm)],[ax42]) ).
fof(i_0_62,plain,
! [X155,X156,X157,X158,X159] :
( ( X156 = X157
| pair_in_list(X155,X157,X159)
| ~ pair_in_list(insert_slb(X155,pair(X156,X158)),X157,X159) )
& ( X158 = X159
| pair_in_list(X155,X157,X159)
| ~ pair_in_list(insert_slb(X155,pair(X156,X158)),X157,X159) )
& ( ~ pair_in_list(X155,X157,X159)
| pair_in_list(insert_slb(X155,pair(X156,X158)),X157,X159) )
& ( X156 != X157
| X158 != X159
| pair_in_list(insert_slb(X155,pair(X156,X158)),X157,X159) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])]) ).
fof(i_0_63,plain,
! [X233,X234,X235] :
( X234 = create_slb
| contains_slb(X234,findmin_pqp_res(X233))
| findmin_cpq_eff(triple(X233,X234,X235)) = triple(X233,update_slb(X234,findmin_pqp_res(X233)),bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[i_0_44])])]) ).
fof(i_0_64,negated_conjecture,
( ~ check_cpq(triple(esk1_0,esk2_0,esk3_0))
& succ_cpq(triple(esk1_0,esk2_0,esk3_0),triple(esk4_0,esk5_0,esk6_0))
& ok(triple(esk4_0,esk5_0,esk6_0))
& check_cpq(triple(esk4_0,esk5_0,esk6_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_45])])]) ).
fof(i_0_65,plain,
! [X206,X207,X208,X209] :
( ( ~ contains_cpq(triple(X206,X207,X208),X209)
| contains_slb(X207,X209) )
& ( ~ contains_slb(X207,X209)
| contains_cpq(triple(X206,X207,X208),X209) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax39])]) ).
fof(i_0_66,plain,
! [X219,X220,X221,X222] :
( contains_slb(X220,X222)
| remove_cpq(triple(X219,X220,X221),X222) = triple(X219,X220,bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_46])]) ).
fof(i_0_67,plain,
! [X163,X164,X165,X166] :
( X164 = X165
| ~ contains_slb(X163,X165)
| remove_slb(insert_slb(X163,pair(X164,X166)),X165) = insert_slb(remove_slb(X163,X165),pair(X164,X166)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax25])]) ).
fof(i_0_68,plain,
! [X175,X176,X177,X178] :
( ~ strictly_less_than(X178,X177)
| update_slb(insert_slb(X175,pair(X176,X178)),X177) = insert_slb(update_slb(X175,X177),pair(X176,X177)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax29])]) ).
fof(i_0_69,plain,
! [X179,X180,X181,X182] :
( ~ less_than(X181,X182)
| update_slb(insert_slb(X179,pair(X180,X182)),X181) = insert_slb(update_slb(X179,X181),pair(X180,X182)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax30])]) ).
fof(i_0_70,plain,
! [X210,X211] : ~ ok(triple(X210,X211,bad)),
inference(variable_rename,[status(thm)],[i_0_47]) ).
fof(i_0_71,plain,
! [X149,X150,X151,X152] :
( ( ~ contains_slb(insert_slb(X149,pair(X150,X152)),X151)
| contains_slb(X149,X151)
| X150 = X151 )
& ( ~ contains_slb(X149,X151)
| contains_slb(insert_slb(X149,pair(X150,X152)),X151) )
& ( X150 != X151
| contains_slb(insert_slb(X149,pair(X150,X152)),X151) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax21])])]) ).
fof(i_0_72,plain,
! [X231,X232] : findmin_cpq_eff(triple(X231,create_slb,X232)) = triple(X231,create_slb,bad),
inference(variable_rename,[status(thm)],[ax46]) ).
fof(i_0_73,plain,
! [X170,X171,X172,X173] :
( X171 = X172
| ~ contains_slb(X170,X172)
| lookup_slb(insert_slb(X170,pair(X171,X173)),X172) = lookup_slb(X170,X172) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax27])]) ).
fof(i_0_74,plain,
! [X244,X245,X246] :
( X245 = create_slb
| findmin_cpq_res(triple(X244,X245,X246)) = findmin_pqp_res(X244) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax51])])]) ).
fof(i_0_75,plain,
! [X212,X213,X214] :
( ok(triple(X212,X213,X214))
| X214 = bad ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_48])]) ).
fof(i_0_76,plain,
! [X194,X195] : check_cpq(triple(X194,create_slb,X195)),
inference(variable_rename,[status(thm)],[ax36]) ).
fof(i_0_77,plain,
! [X242,X243] : findmin_cpq_res(triple(X242,create_slb,X243)) = bottom,
inference(variable_rename,[status(thm)],[ax50]) ).
fof(i_0_78,plain,
! [X167,X168,X169] : lookup_slb(insert_slb(X167,pair(X168,X169)),X168) = X169,
inference(variable_rename,[status(thm)],[ax26]) ).
fof(i_0_79,plain,
! [X160,X161,X162] : remove_slb(insert_slb(X160,pair(X161,X162)),X161) = X160,
inference(variable_rename,[status(thm)],[ax24]) ).
cnf(i_0_80,plain,
( succ_cpq(X1,removemin_cpq_eff(X2))
| ~ succ_cpq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_49]) ).
cnf(i_0_81,plain,
removemin_cpq_eff(X1) = remove_cpq(findmin_cpq_eff(X1),findmin_cpq_res(X1)),
inference(split_conjunct,[status(thm)],[i_0_50]) ).
fof(i_0_82,plain,
! [X153,X154] : ~ pair_in_list(create_slb,X153,X154),
inference(variable_rename,[status(thm)],[i_0_51]) ).
fof(i_0_83,plain,
! [X145,X146,X147] : isnonempty_slb(insert_slb(X145,pair(X146,X147))),
inference(variable_rename,[status(thm)],[ax19]) ).
fof(i_0_84,plain,
! [X187,X188,X189] :
( ~ succ_cpq(X187,X188)
| succ_cpq(X187,remove_cpq(X188,X189)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax33])]) ).
fof(i_0_85,plain,
! [X184,X185,X186] :
( ~ succ_cpq(X184,X185)
| succ_cpq(X184,insert_cpq(X185,X186)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax32])]) ).
fof(i_0_86,plain,
! [X136,X137,X138] :
( ~ less_than(X136,X137)
| ~ less_than(X137,X138)
| less_than(X136,X138) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity])]) ).
fof(i_0_87,plain,
! [X142,X143] :
( ( less_than(X142,X143)
| ~ strictly_less_than(X142,X143) )
& ( ~ less_than(X143,X142)
| ~ strictly_less_than(X142,X143) )
& ( ~ less_than(X142,X143)
| less_than(X143,X142)
| strictly_less_than(X142,X143) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_52])])]) ).
fof(i_0_88,plain,
! [X190,X191] :
( ~ succ_cpq(X190,X191)
| succ_cpq(X190,findmin_cpq_eff(X191)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax34])]) ).
fof(i_0_89,plain,
! [X139,X140] :
( less_than(X139,X140)
| less_than(X140,X139) ),
inference(variable_rename,[status(thm)],[totality]) ).
fof(i_0_90,plain,
! [X148] : ~ contains_slb(create_slb,X148),
inference(variable_rename,[status(thm)],[i_0_53]) ).
fof(i_0_91,plain,
! [X183] : succ_cpq(X183,X183),
inference(variable_rename,[status(thm)],[ax31]) ).
fof(i_0_92,plain,
! [X141] : less_than(X141,X141),
inference(variable_rename,[status(thm)],[reflexivity]) ).
fof(i_0_93,plain,
! [X144] : less_than(bottom,X144),
inference(variable_rename,[status(thm)],[bottom_smallest]) ).
fof(i_0_94,plain,
! [X174] : update_slb(create_slb,X174) = create_slb,
inference(variable_rename,[status(thm)],[ax28]) ).
fof(i_0_95,plain,
~ isnonempty_slb(create_slb),
inference(fof_simplification,[status(thm)],[ax18]) ).
cnf(i_0_96,lemma,
( ok(triple(X1,X2,X3))
| ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
| ~ ok(triple(X4,X5,X6))
| ~ check_cpq(triple(X4,X5,X6)) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_97,lemma,
( check_cpq(triple(X1,X2,X3))
| ~ succ_cpq(triple(X1,X2,X3),triple(X4,X5,X6))
| ~ ok(triple(X4,X5,X6))
| ~ check_cpq(triple(X4,X5,X6)) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_98,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_55]),
[final] ).
cnf(i_0_99,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_55]),
[final] ).
cnf(i_0_100,plain,
( ~ strictly_less_than(X1,X2)
| ~ check_cpq(triple(X3,insert_slb(X4,pair(X1,X2)),X5)) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_101,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_57]),
[final] ).
cnf(i_0_102,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_58]),
[final] ).
cnf(i_0_103,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_59]),
[final] ).
cnf(i_0_104,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_60]),
[final] ).
cnf(i_0_105,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_61]),
[final] ).
cnf(i_0_106,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_62]),
[final] ).
cnf(i_0_107,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_62]),
[final] ).
cnf(i_0_108,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_63]),
[final] ).
cnf(i_0_109,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_62]),
[final] ).
cnf(i_0_110,negated_conjecture,
succ_cpq(triple(esk1_0,esk2_0,esk3_0),triple(esk4_0,esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_111,plain,
( contains_slb(X2,X4)
| ~ contains_cpq(triple(X1,X2,X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_112,plain,
( contains_slb(X1,X2)
| remove_cpq(triple(X3,X1,X4),X2) = triple(X3,X1,bad) ),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_113,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_67]),
[final] ).
cnf(i_0_114,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_68]),
[final] ).
cnf(i_0_115,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_69]),
[final] ).
cnf(i_0_116,plain,
~ ok(triple(X1,X2,bad)),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_117,plain,
( contains_slb(X1,X4)
| X2 = X4
| ~ contains_slb(insert_slb(X1,pair(X2,X3)),X4) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_118,negated_conjecture,
~ check_cpq(triple(esk1_0,esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_119,plain,
findmin_cpq_eff(triple(X1,create_slb,X2)) = triple(X1,create_slb,bad),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_120,plain,
( contains_cpq(triple(X3,X1,X4),X2)
| ~ contains_slb(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_121,plain,
( pair_in_list(insert_slb(X5,pair(X1,X3)),X2,X4)
| X1 != X2
| X3 != X4 ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_122,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_73]),
[final] ).
cnf(i_0_123,plain,
( X1 = create_slb
| findmin_cpq_res(triple(X2,X1,X3)) = findmin_pqp_res(X2) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_124,plain,
( contains_slb(insert_slb(X1,pair(X3,X4)),X2)
| ~ contains_slb(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_125,plain,
( ok(triple(X1,X2,X3))
| X3 = bad ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_126,plain,
check_cpq(triple(X1,create_slb,X2)),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_127,plain,
findmin_cpq_res(triple(X1,create_slb,X2)) = bottom,
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_128,negated_conjecture,
ok(triple(esk4_0,esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_129,negated_conjecture,
check_cpq(triple(esk4_0,esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_130,plain,
( contains_slb(insert_slb(X3,pair(X1,X4)),X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_131,plain,
lookup_slb(insert_slb(X1,pair(X2,X3)),X2) = X3,
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_132,plain,
remove_slb(insert_slb(X1,pair(X2,X3)),X2) = X1,
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_133,plain,
( succ_cpq(X1,remove_cpq(findmin_cpq_eff(X2),findmin_cpq_res(X2)))
| ~ succ_cpq(X1,X2) ),
inference(rw,[status(thm)],[i_0_80,c_0_81]),
[final] ).
cnf(i_0_134,plain,
~ pair_in_list(create_slb,X1,X2),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_135,plain,
isnonempty_slb(insert_slb(X1,pair(X2,X3))),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_136,plain,
( succ_cpq(X1,remove_cpq(X2,X3))
| ~ succ_cpq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_137,plain,
( succ_cpq(X1,insert_cpq(X2,X3))
| ~ succ_cpq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_138,plain,
( less_than(X1,X3)
| ~ less_than(X1,X2)
| ~ less_than(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_139,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_140,plain,
( ~ less_than(X1,X2)
| ~ strictly_less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_141,plain,
( succ_cpq(X1,findmin_cpq_eff(X2))
| ~ succ_cpq(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_142,plain,
( less_than(X1,X2)
| ~ strictly_less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_143,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_144,plain,
~ contains_slb(create_slb,X1),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_145,plain,
succ_cpq(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_146,plain,
less_than(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_92]),
[final] ).
cnf(i_0_147,plain,
less_than(bottom,X1),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_148,plain,
update_slb(create_slb,X1) = create_slb,
inference(split_conjunct,[status(thm)],[i_0_94]),
[final] ).
cnf(i_0_149,plain,
~ isnonempty_slb(create_slb),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_150,axiom,
X1 = X1 ).
cnf(i_0_151,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_152,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_153,axiom,
( X1 != X2
| triple(X1,X3,X4) = triple(X2,X3,X4) ) ).
cnf(i_0_154,axiom,
( X1 != X2
| triple(X3,X1,X4) = triple(X3,X2,X4) ) ).
cnf(i_0_155,axiom,
( X1 != X2
| triple(X3,X4,X1) = triple(X3,X4,X2) ) ).
cnf(i_0_156,axiom,
( X1 != X2
| remove_slb(X1,X3) = remove_slb(X2,X3) ) ).
cnf(i_0_157,axiom,
( X1 != X2
| remove_slb(X3,X1) = remove_slb(X3,X2) ) ).
cnf(i_0_158,axiom,
( X1 != X2
| insert_cpq(X1,X3) = insert_cpq(X2,X3) ) ).
cnf(i_0_159,axiom,
( X1 != X2
| insert_cpq(X3,X1) = insert_cpq(X3,X2) ) ).
cnf(i_0_160,axiom,
( X1 != X2
| findmin_cpq_res(X1) = findmin_cpq_res(X2) ) ).
cnf(i_0_161,axiom,
( X1 != X2
| insert_slb(X1,X3) = insert_slb(X2,X3) ) ).
cnf(i_0_162,axiom,
( X1 != X2
| insert_slb(X3,X1) = insert_slb(X3,X2) ) ).
cnf(i_0_163,axiom,
( X1 != X2
| findmin_cpq_eff(X1) = findmin_cpq_eff(X2) ) ).
cnf(i_0_164,axiom,
( X1 != X2
| update_slb(X1,X3) = update_slb(X2,X3) ) ).
cnf(i_0_165,axiom,
( X1 != X2
| update_slb(X3,X1) = update_slb(X3,X2) ) ).
cnf(i_0_166,axiom,
( X1 != X2
| findmin_pqp_res(X1) = findmin_pqp_res(X2) ) ).
cnf(i_0_167,axiom,
( X1 != X2
| lookup_slb(X1,X3) = lookup_slb(X2,X3) ) ).
cnf(i_0_168,axiom,
( X1 != X2
| lookup_slb(X3,X1) = lookup_slb(X3,X2) ) ).
cnf(i_0_169,axiom,
( X1 != X2
| remove_cpq(X1,X3) = remove_cpq(X2,X3) ) ).
cnf(i_0_170,axiom,
( X1 != X2
| remove_cpq(X3,X1) = remove_cpq(X3,X2) ) ).
cnf(i_0_171,axiom,
( X1 != X2
| ~ ok(X1)
| ok(X2) ) ).
cnf(i_0_172,axiom,
( X1 != X2
| ~ succ_cpq(X1,X3)
| succ_cpq(X2,X3) ) ).
cnf(i_0_173,axiom,
( X1 != X2
| ~ succ_cpq(X3,X1)
| succ_cpq(X3,X2) ) ).
cnf(i_0_174,axiom,
( X1 != X2
| ~ check_cpq(X1)
| check_cpq(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
| ~ isnonempty_slb(X1)
| isnonempty_slb(X2) ) ).
cnf(i_0_150_001,axiom,
X1 = X1 ).
cnf(i_0_151_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_152_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_153_004,axiom,
( X1 != X2
| triple(X1,X3,X4) = triple(X2,X3,X4) ) ).
cnf(i_0_154_005,axiom,
( X1 != X2
| triple(X3,X1,X4) = triple(X3,X2,X4) ) ).
cnf(i_0_155_006,axiom,
( X1 != X2
| triple(X3,X4,X1) = triple(X3,X4,X2) ) ).
cnf(i_0_156_007,axiom,
( X1 != X2
| remove_slb(X1,X3) = remove_slb(X2,X3) ) ).
cnf(i_0_157_008,axiom,
( X1 != X2
| remove_slb(X3,X1) = remove_slb(X3,X2) ) ).
cnf(i_0_158_009,axiom,
( X1 != X2
| insert_cpq(X1,X3) = insert_cpq(X2,X3) ) ).
cnf(i_0_159_010,axiom,
( X1 != X2
| insert_cpq(X3,X1) = insert_cpq(X3,X2) ) ).
cnf(i_0_160_011,axiom,
( X1 != X2
| findmin_cpq_res(X1) = findmin_cpq_res(X2) ) ).
cnf(i_0_161_012,axiom,
( X1 != X2
| insert_slb(X1,X3) = insert_slb(X2,X3) ) ).
cnf(i_0_162_013,axiom,
( X1 != X2
| insert_slb(X3,X1) = insert_slb(X3,X2) ) ).
cnf(i_0_163_014,axiom,
( X1 != X2
| findmin_cpq_eff(X1) = findmin_cpq_eff(X2) ) ).
cnf(i_0_164_015,axiom,
( X1 != X2
| update_slb(X1,X3) = update_slb(X2,X3) ) ).
cnf(i_0_165_016,axiom,
( X1 != X2
| update_slb(X3,X1) = update_slb(X3,X2) ) ).
cnf(i_0_166_017,axiom,
( X1 != X2
| findmin_pqp_res(X1) = findmin_pqp_res(X2) ) ).
cnf(i_0_167_018,axiom,
( X1 != X2
| lookup_slb(X1,X3) = lookup_slb(X2,X3) ) ).
cnf(i_0_168_019,axiom,
( X1 != X2
| lookup_slb(X3,X1) = lookup_slb(X3,X2) ) ).
cnf(i_0_169_020,axiom,
( X1 != X2
| remove_cpq(X1,X3) = remove_cpq(X2,X3) ) ).
cnf(i_0_170_021,axiom,
( X1 != X2
| remove_cpq(X3,X1) = remove_cpq(X3,X2) ) ).
cnf(i_0_171_022,axiom,
( X1 != X2
| ~ ok(X1)
| ok(X2) ) ).
cnf(i_0_172_023,axiom,
( X1 != X2
| ~ succ_cpq(X1,X3)
| succ_cpq(X2,X3) ) ).
cnf(i_0_173_024,axiom,
( X1 != X2
| ~ succ_cpq(X3,X1)
| succ_cpq(X3,X2) ) ).
cnf(i_0_174_025,axiom,
( X1 != X2
| ~ check_cpq(X1)
| check_cpq(X2) ) ).
cnf(i_0_175_026,axiom,
( X1 != X2
| ~ less_than(X1,X3)
| less_than(X2,X3) ) ).
cnf(i_0_176_027,axiom,
( X1 != X2
| ~ less_than(X3,X1)
| less_than(X3,X2) ) ).
cnf(i_0_177_028,axiom,
( X1 != X2
| ~ strictly_less_than(X1,X3)
| strictly_less_than(X2,X3) ) ).
cnf(i_0_178_029,axiom,
( X1 != X2
| ~ strictly_less_than(X3,X1)
| strictly_less_than(X3,X2) ) ).
cnf(i_0_179_030,axiom,
( X1 != X2
| ~ contains_slb(X1,X3)
| contains_slb(X2,X3) ) ).
cnf(i_0_180_031,axiom,
( X1 != X2
| ~ contains_slb(X3,X1)
| contains_slb(X3,X2) ) ).
cnf(i_0_181_032,axiom,
( X1 != X2
| ~ pair_in_list(X1,X3,X4)
| pair_in_list(X2,X3,X4) ) ).
cnf(i_0_182_033,axiom,
( X1 != X2
| ~ pair_in_list(X3,X1,X4)
| pair_in_list(X3,X2,X4) ) ).
cnf(i_0_183_034,axiom,
( X1 != X2
| ~ pair_in_list(X3,X4,X1)
| pair_in_list(X3,X4,X2) ) ).
cnf(i_0_184_035,axiom,
( X1 != X2
| ~ contains_cpq(X1,X3)
| contains_cpq(X2,X3) ) ).
cnf(i_0_185_036,axiom,
( X1 != X2
| ~ contains_cpq(X3,X1)
| contains_cpq(X3,X2) ) ).
cnf(i_0_186_037,axiom,
( X1 != X2
| ~ isnonempty_slb(X1)
| isnonempty_slb(X2) ) ).
cnf(i_0_187,plain,
contains_slb(insert_slb(X1,pair(X2,X3)),X2),
inference(equality_inference,[],[130]) ).
cnf(i_0_188,plain,
$false,
inference(scs_inference,[],[i_0_118,i_0_110,i_0_128,i_0_129,i_0_97]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV383+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.17/0.34 % Computer : n005.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 05:04:30 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 0.29/1.62 % Version : CSE_E---1.7
% 0.29/1.62 % Problem : theBenchmark.p
% 0.29/1.62 % SZS status Theorem for theBenchmark.p
% 0.29/1.62 % SZS output start CNFRefutation
% See solution above
% 0.29/1.64 % Total time : 1.271s
%------------------------------------------------------------------------------