%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV381+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 : n007.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 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 15 unt; 0 def)
% Number of atoms : 103 ( 19 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 95 ( 38 ~; 37 |; 10 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 97 ( 8 sgn 60 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l17_l18,lemma,
! [X1,X2,X3] :
( ? [X4] :
( contains_cpq(triple(X1,X2,X3),X4)
& strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3))) )
=> ~ phi(findmin_cpq_eff(triple(X1,X2,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l17_l18) ).
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(l17_co,conjecture,
! [X1,X2,X3] :
( phi(findmin_cpq_eff(triple(X1,X2,X3)))
=> issmallestelement_pq(i(triple(X1,X2,X3)),findmin_cpq_res(triple(X1,X2,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l17_co) ).
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(totality,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(l17_li56,lemma,
! [X1,X2,X3,X4] :
( contains_cpq(triple(X1,X2,X3),X4)
<=> contains_pq(i(triple(X1,X2,X3)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l17_li56) ).
fof(ax10,axiom,
! [X1,X2] :
( issmallestelement_pq(X1,X2)
<=> ! [X3] :
( contains_pq(X1,X3)
=> less_than(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+1.ax',ax10) ).
fof(ax8,axiom,
! [X1] : ~ contains_pq(create_pq,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+1.ax',ax8) ).
fof(ax54,axiom,
! [X1,X2] : i(triple(X1,create_slb,X2)) = create_pq,
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+4.ax',ax54) ).
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_10,lemma,
! [X1,X2,X3] :
( ? [X4] :
( contains_cpq(triple(X1,X2,X3),X4)
& strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3))) )
=> ~ phi(findmin_cpq_eff(triple(X1,X2,X3))) ),
inference(fof_simplification,[status(thm)],[l17_l18]) ).
fof(c_0_11,lemma,
! [X352,X353,X354,X355] :
( ~ contains_cpq(triple(X352,X353,X354),X355)
| ~ strictly_less_than(X355,findmin_cpq_res(triple(X352,X353,X354)))
| ~ phi(findmin_cpq_eff(triple(X352,X353,X354))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_12,plain,
! [X316,X317,X318] :
( X317 = create_slb
| findmin_cpq_res(triple(X316,X317,X318)) = findmin_pqp_res(X316) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax51])])]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2,X3] :
( phi(findmin_cpq_eff(triple(X1,X2,X3)))
=> issmallestelement_pq(i(triple(X1,X2,X3)),findmin_cpq_res(triple(X1,X2,X3))) ),
inference(assume_negation,[status(cth)],[l17_co]) ).
fof(c_0_14,plain,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[stricly_smaller_definition]) ).
cnf(c_0_15,lemma,
( ~ contains_cpq(triple(X1,X2,X3),X4)
| ~ strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3)))
| ~ phi(findmin_cpq_eff(triple(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( X1 = create_slb
| findmin_cpq_res(triple(X2,X1,X3)) = findmin_pqp_res(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,negated_conjecture,
( phi(findmin_cpq_eff(triple(esk5_0,esk6_0,esk7_0)))
& ~ issmallestelement_pq(i(triple(esk5_0,esk6_0,esk7_0)),findmin_cpq_res(triple(esk5_0,esk6_0,esk7_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_18,plain,
! [X186,X187] :
( ( less_than(X186,X187)
| ~ strictly_less_than(X186,X187) )
& ( ~ less_than(X187,X186)
| ~ strictly_less_than(X186,X187) )
& ( ~ less_than(X186,X187)
| less_than(X187,X186)
| strictly_less_than(X186,X187) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_19,plain,
! [X183,X184] :
( less_than(X183,X184)
| less_than(X184,X183) ),
inference(variable_rename,[status(thm)],[totality]) ).
cnf(c_0_20,lemma,
( X1 = create_slb
| ~ phi(findmin_cpq_eff(triple(X2,X1,X3)))
| ~ contains_cpq(triple(X2,X1,X3),X4)
| ~ strictly_less_than(X4,findmin_pqp_res(X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
phi(findmin_cpq_eff(triple(esk5_0,esk6_0,esk7_0))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( esk6_0 = create_slb
| ~ contains_cpq(triple(esk5_0,esk6_0,esk7_0),X1)
| ~ strictly_less_than(X1,findmin_pqp_res(esk5_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(csr,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_26,lemma,
! [X348,X349,X350,X351] :
( ( ~ contains_cpq(triple(X348,X349,X350),X351)
| contains_pq(i(triple(X348,X349,X350)),X351) )
& ( ~ contains_pq(i(triple(X348,X349,X350)),X351)
| contains_cpq(triple(X348,X349,X350),X351) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l17_li56])]) ).
cnf(c_0_27,negated_conjecture,
( esk6_0 = create_slb
| less_than(findmin_pqp_res(esk5_0),X1)
| ~ contains_cpq(triple(esk5_0,esk6_0,esk7_0),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,lemma,
( contains_cpq(triple(X1,X2,X3),X4)
| ~ contains_pq(i(triple(X1,X2,X3)),X4) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_29,plain,
! [X195,X196,X197,X198,X199] :
( ( ~ issmallestelement_pq(X195,X196)
| ~ contains_pq(X195,X197)
| less_than(X196,X197) )
& ( contains_pq(X198,esk1_2(X198,X199))
| issmallestelement_pq(X198,X199) )
& ( ~ less_than(X199,esk1_2(X198,X199))
| issmallestelement_pq(X198,X199) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ax10])])])])])]) ).
fof(c_0_30,plain,
! [X1] : ~ contains_pq(create_pq,X1),
inference(fof_simplification,[status(thm)],[ax8]) ).
cnf(c_0_31,lemma,
( esk6_0 = create_slb
| less_than(findmin_pqp_res(esk5_0),X1)
| ~ contains_pq(i(triple(esk5_0,esk6_0,esk7_0)),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( contains_pq(X1,esk1_2(X1,X2))
| issmallestelement_pq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_33,negated_conjecture,
~ issmallestelement_pq(i(triple(esk5_0,esk6_0,esk7_0)),findmin_cpq_res(triple(esk5_0,esk6_0,esk7_0))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_34,plain,
! [X191] : ~ contains_pq(create_pq,X191),
inference(variable_rename,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
( issmallestelement_pq(X2,X1)
| ~ less_than(X1,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,lemma,
( esk6_0 = create_slb
| issmallestelement_pq(i(triple(esk5_0,esk6_0,esk7_0)),X1)
| less_than(findmin_pqp_res(esk5_0),esk1_2(i(triple(esk5_0,esk6_0,esk7_0)),X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( esk6_0 = create_slb
| ~ issmallestelement_pq(i(triple(esk5_0,esk6_0,esk7_0)),findmin_pqp_res(esk5_0)) ),
inference(spm,[status(thm)],[c_0_33,c_0_16]) ).
fof(c_0_38,plain,
! [X321,X322] : i(triple(X321,create_slb,X322)) = create_pq,
inference(variable_rename,[status(thm)],[ax54]) ).
fof(c_0_39,plain,
! [X314,X315] : findmin_cpq_res(triple(X314,create_slb,X315)) = bottom,
inference(variable_rename,[status(thm)],[ax50]) ).
cnf(c_0_40,plain,
~ contains_pq(create_pq,X1),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,lemma,
esk6_0 = create_slb,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_42,plain,
i(triple(X1,create_slb,X2)) = create_pq,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_43,plain,
findmin_cpq_res(triple(X1,create_slb,X2)) = bottom,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,plain,
issmallestelement_pq(create_pq,X1),
inference(spm,[status(thm)],[c_0_40,c_0_32]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_41]),c_0_42]),c_0_41]),c_0_43]),c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV381+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
% 0.15/0.33 % Computer : n007.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 05:04:09 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Theorem for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.372s
%------------------------------------------------------------------------------