%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV380+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 : n028.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 8.14s 5.76s
% Output : CNFRefutation 8.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 66 ( 20 unt; 0 def)
% Number of atoms : 144 ( 58 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 124 ( 46 ~; 53 |; 11 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 138 ( 25 sgn 85 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l16_co,conjecture,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> ~ ok(removemin_cpq_eff(triple(X1,X2,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l16_co) ).
fof(ax41,axiom,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> X3 = bad ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax41) ).
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(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(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(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(totality,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
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(ax40,axiom,
! [X1,X2] :
( ok(triple(X1,X2,bad))
<=> ~ $true ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax40) ).
fof(l16_l14,lemma,
! [X1,X2,X3,X4] :
( ~ ok(triple(X1,X2,X3))
=> ~ ok(remove_cpq(triple(X1,X2,X3),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l16_l14) ).
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(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(ax50,axiom,
! [X1,X2] : findmin_cpq_res(triple(X1,create_slb,X2)) = bottom,
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax50) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> ~ ok(removemin_cpq_eff(triple(X1,X2,X3))) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l16_co])]) ).
fof(c_0_14,plain,
! [X1,X2,X3] :
( ~ ok(triple(X1,X2,X3))
=> X3 = bad ),
inference(fof_simplification,[status(thm)],[ax41]) ).
fof(c_0_15,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(c_0_16,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(c_0_17,negated_conjecture,
( ~ ok(triple(esk1_0,esk2_0,esk3_0))
& ok(removemin_cpq_eff(triple(esk1_0,esk2_0,esk3_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_18,plain,
! [X241] : removemin_cpq_eff(X241) = remove_cpq(findmin_cpq_eff(X241),findmin_cpq_res(X241)),
inference(variable_rename,[status(thm)],[ax52]) ).
fof(c_0_19,plain,
! [X206,X207,X208] :
( ok(triple(X206,X207,X208))
| X208 = bad ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])]) ).
fof(c_0_20,plain,
! [X230,X231,X232] :
( X231 = create_slb
| ~ contains_slb(X231,findmin_pqp_res(X230))
| ~ strictly_less_than(findmin_pqp_res(X230),lookup_slb(X231,findmin_pqp_res(X230)))
| findmin_cpq_eff(triple(X230,X231,X232)) = triple(X230,update_slb(X231,findmin_pqp_res(X230)),bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax48])])]) ).
fof(c_0_21,plain,
! [X227,X228,X229] :
( X228 = create_slb
| contains_slb(X228,findmin_pqp_res(X227))
| findmin_cpq_eff(triple(X227,X228,X229)) = triple(X227,update_slb(X228,findmin_pqp_res(X227)),bad) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_15])])]) ).
fof(c_0_22,plain,
! [X136,X137] :
( ( less_than(X136,X137)
| ~ strictly_less_than(X136,X137) )
& ( ~ less_than(X137,X136)
| ~ strictly_less_than(X136,X137) )
& ( ~ less_than(X136,X137)
| less_than(X137,X136)
| strictly_less_than(X136,X137) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_23,plain,
! [X133,X134] :
( less_than(X133,X134)
| less_than(X134,X133) ),
inference(variable_rename,[status(thm)],[totality]) ).
cnf(c_0_24,negated_conjecture,
ok(removemin_cpq_eff(triple(esk1_0,esk2_0,esk3_0))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
removemin_cpq_eff(X1) = remove_cpq(findmin_cpq_eff(X1),findmin_cpq_res(X1)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
~ ok(triple(esk1_0,esk2_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
( ok(triple(X1,X2,X3))
| X3 = bad ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,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)],[c_0_20]) ).
cnf(c_0_29,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)],[c_0_21]) ).
cnf(c_0_30,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,negated_conjecture,
ok(remove_cpq(findmin_cpq_eff(triple(esk1_0,esk2_0,esk3_0)),findmin_cpq_res(triple(esk1_0,esk2_0,esk3_0)))),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,negated_conjecture,
esk3_0 = bad,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_34,plain,
! [X238,X239,X240] :
( X239 = create_slb
| findmin_cpq_res(triple(X238,X239,X240)) = findmin_pqp_res(X238) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax51])])]) ).
cnf(c_0_35,plain,
( findmin_cpq_eff(triple(X1,X2,X3)) = triple(X1,update_slb(X2,findmin_pqp_res(X1)),bad)
| X2 = create_slb
| ~ strictly_less_than(findmin_pqp_res(X1),lookup_slb(X2,findmin_pqp_res(X1))) ),
inference(csr,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(csr,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_37,plain,
! [X1,X2] : ~ ok(triple(X1,X2,bad)),
inference(fof_simplification,[status(thm)],[ax40]) ).
cnf(c_0_38,negated_conjecture,
ok(remove_cpq(findmin_cpq_eff(triple(esk1_0,esk2_0,bad)),findmin_cpq_res(triple(esk1_0,esk2_0,bad)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_33]) ).
cnf(c_0_39,plain,
( X1 = create_slb
| findmin_cpq_res(triple(X2,X1,X3)) = findmin_pqp_res(X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,plain,
( findmin_cpq_eff(triple(X1,X2,X3)) = triple(X1,update_slb(X2,findmin_pqp_res(X1)),bad)
| X2 = create_slb
| less_than(lookup_slb(X2,findmin_pqp_res(X1)),findmin_pqp_res(X1)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_41,lemma,
! [X1,X2,X3,X4] :
( ~ ok(triple(X1,X2,X3))
=> ~ ok(remove_cpq(triple(X1,X2,X3),X4)) ),
inference(fof_simplification,[status(thm)],[l16_l14]) ).
fof(c_0_42,plain,
! [X204,X205] : ~ ok(triple(X204,X205,bad)),
inference(variable_rename,[status(thm)],[c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( esk2_0 = create_slb
| ok(remove_cpq(findmin_cpq_eff(triple(esk1_0,esk2_0,bad)),findmin_pqp_res(esk1_0))) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
( findmin_cpq_eff(triple(X1,X2,X3)) = findmin_cpq_eff(triple(X1,X2,X4))
| X2 = create_slb
| less_than(lookup_slb(X2,findmin_pqp_res(X1)),findmin_pqp_res(X1)) ),
inference(spm,[status(thm)],[c_0_40,c_0_40]) ).
fof(c_0_45,lemma,
! [X243,X244,X245,X246] :
( ok(triple(X243,X244,X245))
| ~ ok(remove_cpq(triple(X243,X244,X245),X246)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])]) ).
cnf(c_0_46,plain,
~ ok(triple(X1,X2,bad)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_47,negated_conjecture,
( esk2_0 = create_slb
| ok(remove_cpq(findmin_cpq_eff(triple(esk1_0,esk2_0,X1)),findmin_pqp_res(esk1_0)))
| less_than(lookup_slb(esk2_0,findmin_pqp_res(esk1_0)),findmin_pqp_res(esk1_0)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,lemma,
( ok(triple(X1,X2,X3))
| ~ ok(remove_cpq(triple(X1,X2,X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,plain,
( X1 = create_slb
| contains_slb(X1,findmin_pqp_res(X2))
| ~ ok(findmin_cpq_eff(triple(X2,X1,X3))) ),
inference(spm,[status(thm)],[c_0_46,c_0_29]) ).
fof(c_0_50,plain,
! [X233,X234,X235] :
( X234 = create_slb
| ~ contains_slb(X234,findmin_pqp_res(X233))
| ~ less_than(lookup_slb(X234,findmin_pqp_res(X233)),findmin_pqp_res(X233))
| findmin_cpq_eff(triple(X233,X234,X235)) = triple(X233,update_slb(X234,findmin_pqp_res(X233)),X235) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax49])])]) ).
cnf(c_0_51,negated_conjecture,
( esk2_0 = create_slb
| ok(remove_cpq(triple(esk1_0,update_slb(esk2_0,findmin_pqp_res(esk1_0)),bad),findmin_pqp_res(esk1_0)))
| less_than(lookup_slb(esk2_0,findmin_pqp_res(esk1_0)),findmin_pqp_res(esk1_0)) ),
inference(spm,[status(thm)],[c_0_47,c_0_40]) ).
cnf(c_0_52,lemma,
( X1 = create_slb
| contains_slb(X1,findmin_pqp_res(X2))
| ~ ok(remove_cpq(findmin_cpq_eff(triple(X2,X1,X3)),X4)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_29]),c_0_49]) ).
cnf(c_0_53,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)],[c_0_50]) ).
cnf(c_0_54,lemma,
( esk2_0 = create_slb
| less_than(lookup_slb(esk2_0,findmin_pqp_res(esk1_0)),findmin_pqp_res(esk1_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_51]),c_0_46]) ).
cnf(c_0_55,negated_conjecture,
( esk2_0 = create_slb
| contains_slb(esk2_0,findmin_pqp_res(esk1_0)) ),
inference(spm,[status(thm)],[c_0_52,c_0_38]) ).
cnf(c_0_56,lemma,
( triple(esk1_0,update_slb(esk2_0,findmin_pqp_res(esk1_0)),X1) = findmin_cpq_eff(triple(esk1_0,esk2_0,X1))
| esk2_0 = create_slb ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_57,lemma,
( esk2_0 = create_slb
| ok(findmin_cpq_eff(triple(esk1_0,esk2_0,X1)))
| ~ ok(remove_cpq(findmin_cpq_eff(triple(esk1_0,esk2_0,X1)),X2)) ),
inference(spm,[status(thm)],[c_0_48,c_0_56]) ).
cnf(c_0_58,lemma,
( esk2_0 = create_slb
| ~ ok(findmin_cpq_eff(triple(esk1_0,esk2_0,bad))) ),
inference(spm,[status(thm)],[c_0_46,c_0_56]) ).
fof(c_0_59,plain,
! [X225,X226] : findmin_cpq_eff(triple(X225,create_slb,X226)) = triple(X225,create_slb,bad),
inference(variable_rename,[status(thm)],[ax46]) ).
fof(c_0_60,plain,
! [X236,X237] : findmin_cpq_res(triple(X236,create_slb,X237)) = bottom,
inference(variable_rename,[status(thm)],[ax50]) ).
cnf(c_0_61,negated_conjecture,
esk2_0 = create_slb,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_38]),c_0_58]) ).
cnf(c_0_62,plain,
findmin_cpq_eff(triple(X1,create_slb,X2)) = triple(X1,create_slb,bad),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_63,plain,
findmin_cpq_res(triple(X1,create_slb,X2)) = bottom,
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_64,negated_conjecture,
ok(remove_cpq(triple(esk1_0,create_slb,bad),bottom)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_61]),c_0_62]),c_0_61]),c_0_63]) ).
cnf(c_0_65,lemma,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_64]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV380+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 : n028.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 05:05:01 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 8.14/5.76 % Version : CSE_E---1.7
% 8.14/5.76 % Problem : theBenchmark.p
% 8.14/5.76 % SZS status Theorem for theBenchmark.p
% 8.14/5.76 % SZS output start CNFRefutation
% See solution above
% 8.14/5.79 % Total time : 4.372s
%------------------------------------------------------------------------------