%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT058+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 : n001.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 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 11 unt; 0 def)
% Number of atoms : 148 ( 26 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 147 ( 42 ~; 56 |; 32 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 30 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(lemma_10,conjecture,
! [X1] :
( ( organization(X1)
& ? [X5] : age(X1,X5) = zero
& greater_or_equal(sigma,zero)
& greater_or_equal(tau,zero) )
=> ~ ( fragile_position(X1)
& robust_position(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_10) ).
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_3,axiom,
! [X1] :
( fragile_position(X1)
<=> ! [X4] :
( ( smaller_or_equal(age(X1,X4),sigma)
=> positional_advantage(X1,X4) )
& ( greater(age(X1,X4),sigma)
=> ~ positional_advantage(X1,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_3) ).
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(definition_4,axiom,
! [X1] :
( robust_position(X1)
<=> ! [X4] :
( ( smaller_or_equal(age(X1,X4),tau)
=> ~ positional_advantage(X1,X4) )
& ( greater(age(X1,X4),tau)
=> positional_advantage(X1,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_4) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ( organization(X1)
& ? [X5] : age(X1,X5) = zero
& greater_or_equal(sigma,zero)
& greater_or_equal(tau,zero) )
=> ~ ( fragile_position(X1)
& robust_position(X1) ) ),
inference(assume_negation,[status(cth)],[lemma_10]) ).
fof(c_0_7,plain,
! [X27,X28] :
( ( ~ greater_or_equal(X27,X28)
| greater(X27,X28)
| X27 = X28 )
& ( ~ greater(X27,X28)
| greater_or_equal(X27,X28) )
& ( X27 != X28
| greater_or_equal(X27,X28) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[definition_greater_or_equal])])]) ).
fof(c_0_8,negated_conjecture,
( organization(esk5_0)
& age(esk5_0,esk6_0) = zero
& greater_or_equal(sigma,zero)
& greater_or_equal(tau,zero)
& fragile_position(esk5_0)
& robust_position(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_9,plain,
! [X1] :
( fragile_position(X1)
<=> ! [X4] :
( ( smaller_or_equal(age(X1,X4),sigma)
=> positional_advantage(X1,X4) )
& ( greater(age(X1,X4),sigma)
=> ~ positional_advantage(X1,X4) ) ) ),
inference(fof_simplification,[status(thm)],[definition_3]) ).
fof(c_0_10,plain,
! [X29,X30] :
( ( ~ smaller(X29,X30)
| greater(X30,X29) )
& ( ~ greater(X30,X29)
| smaller(X29,X30) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[definition_smaller])]) ).
cnf(c_0_11,plain,
( greater(X1,X2)
| X1 = X2
| ~ greater_or_equal(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
greater_or_equal(sigma,zero),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X38,X39,X40,X41] :
( ( ~ smaller_or_equal(age(X38,X39),sigma)
| positional_advantage(X38,X39)
| ~ fragile_position(X38) )
& ( ~ greater(age(X38,X40),sigma)
| ~ positional_advantage(X38,X40)
| ~ fragile_position(X38) )
& ( greater(age(X41,esk2_1(X41)),sigma)
| smaller_or_equal(age(X41,esk1_1(X41)),sigma)
| fragile_position(X41) )
& ( positional_advantage(X41,esk2_1(X41))
| smaller_or_equal(age(X41,esk1_1(X41)),sigma)
| fragile_position(X41) )
& ( greater(age(X41,esk2_1(X41)),sigma)
| ~ positional_advantage(X41,esk1_1(X41))
| fragile_position(X41) )
& ( positional_advantage(X41,esk2_1(X41))
| ~ positional_advantage(X41,esk1_1(X41))
| fragile_position(X41) ) ),
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_9])])])])])]) ).
fof(c_0_14,plain,
! [X25,X26] :
( ( ~ smaller_or_equal(X25,X26)
| smaller(X25,X26)
| X25 = X26 )
& ( ~ smaller(X25,X26)
| smaller_or_equal(X25,X26) )
& ( X25 != X26
| smaller_or_equal(X25,X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[definition_smaller_or_equal])])]) ).
cnf(c_0_15,plain,
( smaller(X2,X1)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( zero = sigma
| greater(sigma,zero) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_17,plain,
! [X1] :
( robust_position(X1)
<=> ! [X4] :
( ( smaller_or_equal(age(X1,X4),tau)
=> ~ positional_advantage(X1,X4) )
& ( greater(age(X1,X4),tau)
=> positional_advantage(X1,X4) ) ) ),
inference(fof_simplification,[status(thm)],[definition_4]) ).
cnf(c_0_18,plain,
( positional_advantage(X1,X2)
| ~ smaller_or_equal(age(X1,X2),sigma)
| ~ fragile_position(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
age(esk5_0,esk6_0) = zero,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
fragile_position(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,plain,
( smaller_or_equal(X1,X2)
| ~ smaller(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
( zero = sigma
| smaller(zero,sigma) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,negated_conjecture,
greater_or_equal(tau,zero),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_24,plain,
! [X44,X45,X46,X47] :
( ( ~ smaller_or_equal(age(X44,X45),tau)
| ~ positional_advantage(X44,X45)
| ~ robust_position(X44) )
& ( ~ greater(age(X44,X46),tau)
| positional_advantage(X44,X46)
| ~ robust_position(X44) )
& ( greater(age(X47,esk4_1(X47)),tau)
| smaller_or_equal(age(X47,esk3_1(X47)),tau)
| robust_position(X47) )
& ( ~ positional_advantage(X47,esk4_1(X47))
| smaller_or_equal(age(X47,esk3_1(X47)),tau)
| robust_position(X47) )
& ( greater(age(X47,esk4_1(X47)),tau)
| positional_advantage(X47,esk3_1(X47))
| robust_position(X47) )
& ( ~ positional_advantage(X47,esk4_1(X47))
| positional_advantage(X47,esk3_1(X47))
| robust_position(X47) ) ),
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_17])])])])])]) ).
cnf(c_0_25,negated_conjecture,
( positional_advantage(esk5_0,esk6_0)
| ~ smaller_or_equal(zero,sigma) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_26,negated_conjecture,
( zero = sigma
| smaller_or_equal(zero,sigma) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
( zero = tau
| greater(tau,zero) ),
inference(spm,[status(thm)],[c_0_11,c_0_23]) ).
cnf(c_0_28,plain,
( ~ smaller_or_equal(age(X1,X2),tau)
| ~ positional_advantage(X1,X2)
| ~ robust_position(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( zero = sigma
| positional_advantage(esk5_0,esk6_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
robust_position(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_31,negated_conjecture,
( zero = tau
| smaller(zero,tau) ),
inference(spm,[status(thm)],[c_0_15,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
( zero = sigma
| ~ smaller_or_equal(zero,tau) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_19])]) ).
cnf(c_0_33,negated_conjecture,
( zero = tau
| smaller_or_equal(zero,tau) ),
inference(spm,[status(thm)],[c_0_21,c_0_31]) ).
cnf(c_0_34,plain,
( smaller_or_equal(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_35,negated_conjecture,
( zero = tau
| zero = sigma ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,plain,
smaller_or_equal(X1,X1),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_37,negated_conjecture,
( zero = sigma
| tau != sigma ),
inference(ef,[status(thm)],[c_0_35]) ).
cnf(c_0_38,negated_conjecture,
zero = sigma,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_35]),c_0_36])]),c_0_37]) ).
cnf(c_0_39,negated_conjecture,
positional_advantage(esk5_0,esk6_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_38]),c_0_36])]) ).
cnf(c_0_40,negated_conjecture,
~ smaller_or_equal(sigma,tau),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_39]),c_0_30]),c_0_19]),c_0_38])]) ).
cnf(c_0_41,negated_conjecture,
tau = sigma,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_38]),c_0_38]),c_0_40]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT058+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
% 0.15/0.33 % Computer : n001.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 : Mon May 4 23:32:33 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------