%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT049-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n010.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 06:24:07 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 34 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 148 ( 89 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 212 ( 101 ~; 96 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 102 ( 93 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
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(1,plain,
( ( position(sk1,sk3) != position(sk1,sk2) )
<=> ( position(sk1,sk3) != position(sk1,sk2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
position(sk1,sk3) != position(sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_6_35) ).
tff(3,plain,
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_6_33) ).
tff(6,plain,
organization(sk1),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) )
<=> ( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [B: $i,A: $i,C: $i] :
rewrite(( ( ~ organization(A)
| ( external_ties(A,B) != external_ties(A,C) )
| ( position(A,B) = position(A,C) ) )
<=> ( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( external_ties(A,B) != external_ties(A,C) )
| ( position(A,B) = position(A,C) ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( external_ties(A,B) != external_ties(A,C) )
| ( position(A,B) = position(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_6_31) ).
tff(13,plain,
! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) )
| ( position(sk1,sk3) = position(sk1,sk2) )
| ~ organization(sk1)
| ( external_ties(sk1,sk3) != external_ties(sk1,sk2) ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) )
| ( position(sk1,sk3) = position(sk1,sk2) )
| ~ organization(sk1)
| ( external_ties(sk1,sk3) != external_ties(sk1,sk2) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ organization(sk1)
| ( position(sk1,sk3) = position(sk1,sk2) )
| ( external_ties(sk1,sk3) != external_ties(sk1,sk2) ) )
<=> ( ( position(sk1,sk3) = position(sk1,sk2) )
| ~ organization(sk1)
| ( external_ties(sk1,sk3) != external_ties(sk1,sk2) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) )
| ~ organization(sk1)
| ( position(sk1,sk3) = position(sk1,sk2) )
| ( external_ties(sk1,sk3) != external_ties(sk1,sk2) ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) )
| ( position(sk1,sk3) = position(sk1,sk2) )
| ~ organization(sk1)
| ( external_ties(sk1,sk3) != external_ties(sk1,sk2) ) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) )
| ~ organization(sk1)
| ( position(sk1,sk3) = position(sk1,sk2) )
| ( external_ties(sk1,sk3) != external_ties(sk1,sk2) ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) )
| ( position(sk1,sk3) = position(sk1,sk2) )
| ~ organization(sk1)
| ( external_ties(sk1,sk3) != external_ties(sk1,sk2) ) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) )
| ~ organization(sk1)
| ( position(sk1,sk3) = position(sk1,sk2) )
| ( external_ties(sk1,sk3) != external_ties(sk1,sk2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( position(A,B) = position(A,C) )
| ( external_ties(A,B) != external_ties(A,C) ) )
| ( position(sk1,sk3) = position(sk1,sk2) )
| ~ organization(sk1)
| ( external_ties(sk1,sk3) != external_ties(sk1,sk2) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
external_ties(sk1,sk3) != external_ties(sk1,sk2),
inference(unit_resolution,[status(thm)],[22,16,6,3]) ).
tff(24,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ organization(A)
| ( external_ties(A,B) = external_ties(A,C) ) )
<=> ( ~ organization(A)
| ( external_ties(A,B) = external_ties(A,C) ) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( external_ties(A,B) = external_ties(A,C) ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( external_ties(A,B) = external_ties(A,C) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( external_ties(A,B) = external_ties(A,C) ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( external_ties(A,B) = external_ties(A,C) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( external_ties(A,B) = external_ties(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_11_32) ).
tff(28,plain,
! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( external_ties(A,B) = external_ties(A,C) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( external_ties(A,B) = external_ties(A,C) ) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( external_ties(A,B) = external_ties(A,C) ) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( external_ties(A,B) = external_ties(A,C) ) )
| ~ organization(sk1)
| ( external_ties(sk1,sk3) = external_ties(sk1,sk2) ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( external_ties(A,B) = external_ties(A,C) ) )
| ~ organization(sk1)
| ( external_ties(sk1,sk3) = external_ties(sk1,sk2) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( external_ties(A,B) = external_ties(A,C) ) )
| ~ organization(sk1)
| ( external_ties(sk1,sk3) = external_ties(sk1,sk2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ organization(A)
| ( external_ties(A,B) = external_ties(A,C) ) )
| ~ organization(sk1)
| ( external_ties(sk1,sk3) = external_ties(sk1,sk2) ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,30,6,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT049-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n010.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 7 13:17:27 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40 % SZS output start Proof
% See solution above
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------