%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT056+1 : TPTP v9.2.1. Released v2.4.0.
% 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 : n011.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 04:48:22 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 64 ( 17 unt; 0 def)
% Number of atoms : 202 ( 36 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 202 ( 64 ~; 79 |; 44 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(lemma_9,conjecture,
! [X1,X5,X6,X7] :
( ( organization(X1)
& has_endowment(X1)
& age(X1,X5) = zero
& smaller_or_equal(age(X1,X6),eta)
& greater(age(X1,X7),eta)
& greater_or_equal(eta,sigma)
& greater(sigma,zero) )
=> ( greater(hazard_of_mortality(X1,X7),hazard_of_mortality(X1,X6))
& hazard_of_mortality(X1,X6) = hazard_of_mortality(X1,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_9) ).
fof(meaning_postulate_greater_transitive,axiom,
! [X1,X2,X3] :
( ( greater(X1,X2)
& greater(X2,X3) )
=> greater(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT001+0.ax',meaning_postulate_greater_transitive) ).
fof(definition_greater_or_equal,axiom,
! [X1,X2] :
( greater_or_equal(X1,X2)
<=> ( greater(X1,X2)
| X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT001+0.ax',definition_greater_or_equal) ).
fof(definition_1,axiom,
! [X1] :
( has_endowment(X1)
<=> ! [X4] :
( organization(X1)
& ( smaller_or_equal(age(X1,X4),eta)
=> has_immunity(X1,X4) )
& ( greater(age(X1,X4),eta)
=> ~ has_immunity(X1,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_1) ).
fof(definition_smaller,axiom,
! [X1,X2] :
( smaller(X1,X2)
<=> greater(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT001+0.ax',definition_smaller) ).
fof(definition_smaller_or_equal,axiom,
! [X1,X2] :
( smaller_or_equal(X1,X2)
<=> ( smaller(X1,X2)
| X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT001+0.ax',definition_smaller_or_equal) ).
fof(assumption_3,axiom,
! [X1,X5,X4] :
( ( organization(X1)
& has_immunity(X1,X5)
& ~ has_immunity(X1,X4) )
=> greater(hazard_of_mortality(X1,X4),hazard_of_mortality(X1,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_3) ).
fof(assumption_2,axiom,
! [X1,X5,X4] :
( ( organization(X1)
& has_immunity(X1,X5)
& has_immunity(X1,X4) )
=> hazard_of_mortality(X1,X5) = hazard_of_mortality(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_2) ).
fof(meaning_postulate_greater_comparable,axiom,
! [X1,X2] :
( smaller(X1,X2)
| X1 = X2
| greater(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT001+0.ax',meaning_postulate_greater_comparable) ).
fof(meaning_postulate_greater_strict,axiom,
! [X1,X2] :
~ ( greater(X1,X2)
& greater(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT001+0.ax',meaning_postulate_greater_strict) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X5,X6,X7] :
( ( organization(X1)
& has_endowment(X1)
& age(X1,X5) = zero
& smaller_or_equal(age(X1,X6),eta)
& greater(age(X1,X7),eta)
& greater_or_equal(eta,sigma)
& greater(sigma,zero) )
=> ( greater(hazard_of_mortality(X1,X7),hazard_of_mortality(X1,X6))
& hazard_of_mortality(X1,X6) = hazard_of_mortality(X1,X5) ) ),
inference(assume_negation,[status(cth)],[lemma_9]) ).
fof(c_0_11,plain,
! [X41,X42,X43] :
( ~ greater(X41,X42)
| ~ greater(X42,X43)
| greater(X41,X43) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[meaning_postulate_greater_transitive])]) ).
fof(c_0_12,negated_conjecture,
( organization(esk3_0)
& has_endowment(esk3_0)
& age(esk3_0,esk4_0) = zero
& smaller_or_equal(age(esk3_0,esk5_0),eta)
& greater(age(esk3_0,esk6_0),eta)
& greater_or_equal(eta,sigma)
& greater(sigma,zero)
& ( ~ greater(hazard_of_mortality(esk3_0,esk6_0),hazard_of_mortality(esk3_0,esk5_0))
| hazard_of_mortality(esk3_0,esk5_0) != hazard_of_mortality(esk3_0,esk4_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_13,plain,
! [X35,X36] :
( ( ~ greater_or_equal(X35,X36)
| greater(X35,X36)
| X35 = X36 )
& ( ~ greater(X35,X36)
| greater_or_equal(X35,X36) )
& ( X35 != X36
| greater_or_equal(X35,X36) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[definition_greater_or_equal])])]) ).
cnf(c_0_14,plain,
( greater(X1,X3)
| ~ greater(X1,X2)
| ~ greater(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
greater(sigma,zero),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( greater(X1,X2)
| X1 = X2
| ~ greater_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
greater_or_equal(eta,sigma),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,plain,
! [X1] :
( has_endowment(X1)
<=> ! [X4] :
( organization(X1)
& ( smaller_or_equal(age(X1,X4),eta)
=> has_immunity(X1,X4) )
& ( greater(age(X1,X4),eta)
=> ~ has_immunity(X1,X4) ) ) ),
inference(fof_simplification,[status(thm)],[definition_1]) ).
fof(c_0_19,plain,
! [X37,X38] :
( ( ~ smaller(X37,X38)
| greater(X38,X37) )
& ( ~ greater(X38,X37)
| smaller(X37,X38) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[definition_smaller])]) ).
cnf(c_0_20,negated_conjecture,
( greater(X1,zero)
| ~ greater(X1,sigma) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( sigma = eta
| greater(eta,sigma) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_22,plain,
! [X46,X47,X48,X49] :
( ( organization(X46)
| ~ has_endowment(X46) )
& ( ~ smaller_or_equal(age(X46,X47),eta)
| has_immunity(X46,X47)
| ~ has_endowment(X46) )
& ( ~ greater(age(X46,X48),eta)
| ~ has_immunity(X46,X48)
| ~ has_endowment(X46) )
& ( greater(age(X49,esk2_1(X49)),eta)
| smaller_or_equal(age(X49,esk1_1(X49)),eta)
| ~ organization(X49)
| has_endowment(X49) )
& ( has_immunity(X49,esk2_1(X49))
| smaller_or_equal(age(X49,esk1_1(X49)),eta)
| ~ organization(X49)
| has_endowment(X49) )
& ( greater(age(X49,esk2_1(X49)),eta)
| ~ has_immunity(X49,esk1_1(X49))
| ~ organization(X49)
| has_endowment(X49) )
& ( has_immunity(X49,esk2_1(X49))
| ~ has_immunity(X49,esk1_1(X49))
| ~ organization(X49)
| has_endowment(X49) ) ),
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)],[c_0_18])])])])])]) ).
fof(c_0_23,plain,
! [X33,X34] :
( ( ~ smaller_or_equal(X33,X34)
| smaller(X33,X34)
| X33 = X34 )
& ( ~ smaller(X33,X34)
| smaller_or_equal(X33,X34) )
& ( X33 != X34
| smaller_or_equal(X33,X34) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[definition_smaller_or_equal])])]) ).
cnf(c_0_24,plain,
( smaller(X2,X1)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( sigma = eta
| greater(eta,zero) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_26,plain,
! [X1,X5,X4] :
( ( organization(X1)
& has_immunity(X1,X5)
& ~ has_immunity(X1,X4) )
=> greater(hazard_of_mortality(X1,X4),hazard_of_mortality(X1,X5)) ),
inference(fof_simplification,[status(thm)],[assumption_3]) ).
fof(c_0_27,plain,
! [X52,X53,X54] :
( ~ organization(X52)
| ~ has_immunity(X52,X53)
| ~ has_immunity(X52,X54)
| hazard_of_mortality(X52,X53) = hazard_of_mortality(X52,X54) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[assumption_2])]) ).
cnf(c_0_28,plain,
( has_immunity(X1,X2)
| ~ smaller_or_equal(age(X1,X2),eta)
| ~ has_endowment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
smaller_or_equal(age(esk3_0,esk5_0),eta),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,negated_conjecture,
has_endowment(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_31,negated_conjecture,
age(esk3_0,esk4_0) = zero,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_32,plain,
( smaller_or_equal(X1,X2)
| ~ smaller(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,negated_conjecture,
( sigma = eta
| smaller(zero,eta) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_34,plain,
! [X55,X56,X57] :
( ~ organization(X55)
| ~ has_immunity(X55,X56)
| has_immunity(X55,X57)
| greater(hazard_of_mortality(X55,X57),hazard_of_mortality(X55,X56)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])]) ).
fof(c_0_35,plain,
! [X44,X45] :
( smaller(X44,X45)
| X44 = X45
| greater(X44,X45) ),
inference(variable_rename,[status(thm)],[meaning_postulate_greater_comparable]) ).
cnf(c_0_36,plain,
( hazard_of_mortality(X1,X2) = hazard_of_mortality(X1,X3)
| ~ organization(X1)
| ~ has_immunity(X1,X2)
| ~ has_immunity(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,negated_conjecture,
has_immunity(esk3_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_38,negated_conjecture,
organization(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_39,negated_conjecture,
( has_immunity(esk3_0,esk4_0)
| ~ smaller_or_equal(zero,eta) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_31]),c_0_30])]) ).
cnf(c_0_40,negated_conjecture,
( sigma = eta
| smaller_or_equal(zero,eta) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_41,plain,
( has_immunity(X1,X3)
| greater(hazard_of_mortality(X1,X3),hazard_of_mortality(X1,X2))
| ~ organization(X1)
| ~ has_immunity(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
( ~ greater(age(X1,X2),eta)
| ~ has_immunity(X1,X2)
| ~ has_endowment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_43,negated_conjecture,
greater(age(esk3_0,esk6_0),eta),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_44,plain,
( smaller(X1,X2)
| X1 = X2
| greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
fof(c_0_45,plain,
! [X39,X40] :
( ~ greater(X39,X40)
| ~ greater(X40,X39) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[meaning_postulate_greater_strict])]) ).
cnf(c_0_46,negated_conjecture,
( hazard_of_mortality(esk3_0,X1) = hazard_of_mortality(esk3_0,esk5_0)
| ~ has_immunity(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_47,negated_conjecture,
( sigma = eta
| has_immunity(esk3_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,negated_conjecture,
( ~ greater(hazard_of_mortality(esk3_0,esk6_0),hazard_of_mortality(esk3_0,esk5_0))
| hazard_of_mortality(esk3_0,esk5_0) != hazard_of_mortality(esk3_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_49,negated_conjecture,
( has_immunity(esk3_0,X1)
| greater(hazard_of_mortality(esk3_0,X1),hazard_of_mortality(esk3_0,esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_37]),c_0_38])]) ).
cnf(c_0_50,negated_conjecture,
~ has_immunity(esk3_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_30])]) ).
cnf(c_0_51,plain,
( X1 = X2
| greater(X1,X2)
| smaller_or_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_44]) ).
cnf(c_0_52,plain,
( ~ greater(X1,X2)
| ~ greater(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( hazard_of_mortality(esk3_0,esk4_0) = hazard_of_mortality(esk3_0,esk5_0)
| sigma = eta ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,negated_conjecture,
hazard_of_mortality(esk3_0,esk4_0) != hazard_of_mortality(esk3_0,esk5_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_55,negated_conjecture,
( zero = eta
| has_immunity(esk3_0,esk4_0)
| greater(zero,eta) ),
inference(spm,[status(thm)],[c_0_39,c_0_51]) ).
cnf(c_0_56,negated_conjecture,
~ greater(zero,sigma),
inference(spm,[status(thm)],[c_0_52,c_0_15]) ).
cnf(c_0_57,negated_conjecture,
sigma = eta,
inference(sr,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,negated_conjecture,
( hazard_of_mortality(esk3_0,esk4_0) = hazard_of_mortality(esk3_0,esk5_0)
| zero = eta
| greater(zero,eta) ),
inference(spm,[status(thm)],[c_0_46,c_0_55]) ).
cnf(c_0_59,negated_conjecture,
~ greater(zero,eta),
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,negated_conjecture,
zero = eta,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_58,c_0_54]),c_0_59]) ).
cnf(c_0_61,negated_conjecture,
greater(eta,zero),
inference(rw,[status(thm)],[c_0_15,c_0_57]) ).
cnf(c_0_62,negated_conjecture,
~ greater(eta,eta),
inference(rw,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_63,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_60]),c_0_62]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT056+1 : TPTP v9.2.1. Released v2.4.0.
% 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
% 0.16/0.33 % Computer : n011.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 23:30:02 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------