%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT045-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:24:06 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 20
% Syntax : Number of formulae : 43 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 216 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 322 ( 153 ~; 148 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 126 ( 114 !; 0 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
tff(greater_type,type,
greater: ( $i * $i ) > $o ).
tff(external_ties_type,type,
external_ties: ( $i * $i ) > $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(position_type,type,
position: ( $i * $i ) > $i ).
tff(organization_type,type,
organization: $i > $o ).
tff(age_type,type,
age: ( $i * $i ) > $i ).
tff(1,plain,
( ~ greater(position(sk1,sk3),position(sk1,sk2))
<=> ~ greater(position(sk1,sk3),position(sk1,sk2)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ greater(position(sk1,sk3),position(sk1,sk2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_4_35) ).
tff(3,plain,
~ greater(position(sk1,sk3),position(sk1,sk2)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( organization(sk1)
<=> organization(sk1) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
organization(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_4_33) ).
tff(6,plain,
organization(sk1),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
<=> ( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
<=> ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
<=> ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [B: $i,A: $i,C: $i] :
rewrite(( ( ~ organization(A)
| ~ greater(external_ties(A,B),external_ties(A,C))
| greater(position(A,B),position(A,C)) )
<=> ( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ~ greater(external_ties(A,B),external_ties(A,C))
| greater(position(A,B),position(A,C)) )
<=> ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ~ greater(external_ties(A,B),external_ties(A,C))
| greater(position(A,B),position(A,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_6_30) ).
tff(13,plain,
! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
| greater(position(sk1,sk3),position(sk1,sk2))
| ~ organization(sk1)
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
| greater(position(sk1,sk3),position(sk1,sk2))
| ~ organization(sk1)
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( greater(position(sk1,sk3),position(sk1,sk2))
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2))
| ~ organization(sk1) )
<=> ( greater(position(sk1,sk3),position(sk1,sk2))
| ~ organization(sk1)
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
| greater(position(sk1,sk3),position(sk1,sk2))
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2))
| ~ organization(sk1) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
| greater(position(sk1,sk3),position(sk1,sk2))
| ~ organization(sk1)
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
| greater(position(sk1,sk3),position(sk1,sk2))
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2))
| ~ organization(sk1) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
| greater(position(sk1,sk3),position(sk1,sk2))
| ~ organization(sk1)
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
| greater(position(sk1,sk3),position(sk1,sk2))
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2))
| ~ organization(sk1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( greater(position(A,B),position(A,C))
| ~ greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A) )
| greater(position(sk1,sk3),position(sk1,sk2))
| ~ organization(sk1)
| ~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ greater(external_ties(sk1,sk3),external_ties(sk1,sk2)),
inference(unit_resolution,[status(thm)],[22,16,6,3]) ).
tff(24,plain,
( greater(age(sk1,sk3),age(sk1,sk2))
<=> greater(age(sk1,sk3),age(sk1,sk2)) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
greater(age(sk1,sk3),age(sk1,sk2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_4_34) ).
tff(26,plain,
greater(age(sk1,sk3),age(sk1,sk2)),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
<=> ( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
<=> ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
<=> ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
^ [B: $i,A: $i,C: $i] :
rewrite(( ( ~ organization(A)
| ~ greater(age(A,B),age(A,C))
| greater(external_ties(A,B),external_ties(A,C)) )
<=> ( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ~ greater(age(A,B),age(A,C))
| greater(external_ties(A,B),external_ties(A,C)) )
<=> ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ~ greater(age(A,B),age(A,C))
| greater(external_ties(A,B),external_ties(A,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_8_32) ).
tff(33,plain,
! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
| ~ greater(age(sk1,sk3),age(sk1,sk2))
| ~ organization(sk1)
| greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
| ~ greater(age(sk1,sk3),age(sk1,sk2))
| ~ organization(sk1)
| greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( greater(external_ties(sk1,sk3),external_ties(sk1,sk2))
| ~ organization(sk1)
| ~ greater(age(sk1,sk3),age(sk1,sk2)) )
<=> ( ~ greater(age(sk1,sk3),age(sk1,sk2))
| ~ organization(sk1)
| greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
| greater(external_ties(sk1,sk3),external_ties(sk1,sk2))
| ~ organization(sk1)
| ~ greater(age(sk1,sk3),age(sk1,sk2)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
| ~ greater(age(sk1,sk3),age(sk1,sk2))
| ~ organization(sk1)
| greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
| greater(external_ties(sk1,sk3),external_ties(sk1,sk2))
| ~ organization(sk1)
| ~ greater(age(sk1,sk3),age(sk1,sk2)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
| ~ greater(age(sk1,sk3),age(sk1,sk2))
| ~ organization(sk1)
| greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
| greater(external_ties(sk1,sk3),external_ties(sk1,sk2))
| ~ organization(sk1)
| ~ greater(age(sk1,sk3),age(sk1,sk2)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( greater(external_ties(A,B),external_ties(A,C))
| ~ organization(A)
| ~ greater(age(A,B),age(A,C)) )
| ~ greater(age(sk1,sk3),age(sk1,sk2))
| ~ organization(sk1)
| greater(external_ties(sk1,sk3),external_ties(sk1,sk2)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
$false,
inference(unit_resolution,[status(thm)],[42,36,6,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT045-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.06/0.33 % Computer : n019.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.34 % CPULimit : 300
% 0.06/0.34 % WCLimit : 300
% 0.06/0.34 % DateTime : Mon Sep 7 13:10:24 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
% 0.13/0.40 % E exiting
%------------------------------------------------------------------------------