%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV417+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 : n004.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 05:22:07 PM UTC 2026
% Result : Theorem 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 3 unt; 0 def)
% Number of atoms : 46 ( 7 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 47 ( 18 ~; 14 |; 8 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 33 ( 0 sgn 21 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co4,conjecture,
! [X1,X2,X3] :
( pi_find_min(triple(X1,X2,X3))
=> ( phi(findmin_cpq_eff(triple(X1,X2,X3)))
=> ? [X4] :
( pi_sharp_find_min(i(triple(X1,X2,X3)),X4)
& findmin_cpq_res(triple(X1,X2,X3)) = findmin_pq_res(i(triple(X1,X2,X3)),X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co4) ).
fof(ax14,axiom,
! [X1,X2] :
( ( contains_pq(X1,X2)
& issmallestelement_pq(X1,X2) )
=> findmin_pq_res(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+1.ax',ax14) ).
fof(ax58,axiom,
! [X1,X2] :
( pi_sharp_find_min(X1,X2)
<=> ( contains_pq(X1,X2)
& issmallestelement_pq(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+4.ax',ax58) ).
fof(main4_l7,lemma,
! [X1,X2,X3] :
( phi(findmin_cpq_eff(triple(X1,X2,X3)))
=> pi_sharp_find_min(i(triple(X1,X2,X3)),findmin_cpq_res(triple(X1,X2,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main4_l7) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( pi_find_min(triple(X1,X2,X3))
=> ( phi(findmin_cpq_eff(triple(X1,X2,X3)))
=> ? [X4] :
( pi_sharp_find_min(i(triple(X1,X2,X3)),X4)
& findmin_cpq_res(triple(X1,X2,X3)) = findmin_pq_res(i(triple(X1,X2,X3)),X4) ) ) ),
inference(assume_negation,[status(cth)],[co4]) ).
fof(c_0_5,negated_conjecture,
! [X350] :
( pi_find_min(triple(esk5_0,esk6_0,esk7_0))
& phi(findmin_cpq_eff(triple(esk5_0,esk6_0,esk7_0)))
& ( ~ pi_sharp_find_min(i(triple(esk5_0,esk6_0,esk7_0)),X350)
| findmin_cpq_res(triple(esk5_0,esk6_0,esk7_0)) != findmin_pq_res(i(triple(esk5_0,esk6_0,esk7_0)),X350) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X204,X205] :
( ~ contains_pq(X204,X205)
| ~ issmallestelement_pq(X204,X205)
| findmin_pq_res(X204,X205) = X205 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax14])]) ).
fof(c_0_7,plain,
! [X328,X329] :
( ( contains_pq(X328,X329)
| ~ pi_sharp_find_min(X328,X329) )
& ( issmallestelement_pq(X328,X329)
| ~ pi_sharp_find_min(X328,X329) )
& ( ~ contains_pq(X328,X329)
| ~ issmallestelement_pq(X328,X329)
| pi_sharp_find_min(X328,X329) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax58])])]) ).
cnf(c_0_8,negated_conjecture,
( ~ pi_sharp_find_min(i(triple(esk5_0,esk6_0,esk7_0)),X1)
| findmin_cpq_res(triple(esk5_0,esk6_0,esk7_0)) != findmin_pq_res(i(triple(esk5_0,esk6_0,esk7_0)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( findmin_pq_res(X1,X2) = X2
| ~ contains_pq(X1,X2)
| ~ issmallestelement_pq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( contains_pq(X1,X2)
| ~ pi_sharp_find_min(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( issmallestelement_pq(X1,X2)
| ~ pi_sharp_find_min(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,lemma,
! [X344,X345,X346] :
( ~ phi(findmin_cpq_eff(triple(X344,X345,X346)))
| pi_sharp_find_min(i(triple(X344,X345,X346)),findmin_cpq_res(triple(X344,X345,X346))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[main4_l7])]) ).
cnf(c_0_13,negated_conjecture,
~ pi_sharp_find_min(i(triple(esk5_0,esk6_0,esk7_0)),findmin_cpq_res(triple(esk5_0,esk6_0,esk7_0))),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9])]),c_0_10]),c_0_11]) ).
cnf(c_0_14,lemma,
( pi_sharp_find_min(i(triple(X1,X2,X3)),findmin_cpq_res(triple(X1,X2,X3)))
| ~ phi(findmin_cpq_eff(triple(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
phi(findmin_cpq_eff(triple(esk5_0,esk6_0,esk7_0))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV417+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 : n004.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 05:08:02 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 : 1.376s
%------------------------------------------------------------------------------