%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT059-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n015.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 06:24:09 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.41s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 39 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 153 ( 56 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 210 ( 98 ~; 94 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 46 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
tff(hazard_of_mortality_type,type,
hazard_of_mortality: ( $i * $i ) > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(very_low_type,type,
very_low: $i ).
tff(has_immunity_type,type,
has_immunity: ( $i * $i ) > $o ).
tff(organization_type,type,
organization: $i > $o ).
tff(1,plain,
( ( very_low = hazard_of_mortality(sk1,sk3) )
<=> ( hazard_of_mortality(sk1,sk3) = very_low ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
( has_immunity(sk1,sk2)
<=> has_immunity(sk1,sk2) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
has_immunity(sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_2_38) ).
tff(4,plain,
has_immunity(sk1,sk2),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
( organization(sk1)
<=> organization(sk1) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
organization(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_2_37) ).
tff(7,plain,
organization(sk1),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
^ [B: $i,A: $i] :
refl(( ( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) )
<=> ( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) )
<=> ! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) )
<=> ! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
^ [B: $i,A: $i] :
rewrite(( ( ~ organization(A)
| ~ has_immunity(A,B)
| ( hazard_of_mortality(A,B) = very_low ) )
<=> ( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [B: $i,A: $i] :
( ~ organization(A)
| ~ has_immunity(A,B)
| ( hazard_of_mortality(A,B) = very_low ) )
<=> ! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,axiom,
! [B: $i,A: $i] :
( ~ organization(A)
| ~ has_immunity(A,B)
| ( hazard_of_mortality(A,B) = very_low ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_17_32) ).
tff(14,plain,
! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) ),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
( ( ~ ! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) )
| ( hazard_of_mortality(sk1,sk2) = very_low )
| ~ has_immunity(sk1,sk2)
| ~ organization(sk1) )
<=> ( ~ ! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) )
| ( hazard_of_mortality(sk1,sk2) = very_low )
| ~ has_immunity(sk1,sk2)
| ~ organization(sk1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) )
| ( hazard_of_mortality(sk1,sk2) = very_low )
| ~ has_immunity(sk1,sk2)
| ~ organization(sk1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) )
| ( hazard_of_mortality(sk1,sk2) = very_low )
| ~ has_immunity(sk1,sk2)
| ~ organization(sk1) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
hazard_of_mortality(sk1,sk2) = very_low,
inference(unit_resolution,[status(thm)],[20,17,7,4]) ).
tff(22,plain,
( ( hazard_of_mortality(sk1,sk2) = hazard_of_mortality(sk1,sk3) )
<=> ( very_low = hazard_of_mortality(sk1,sk3) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( hazard_of_mortality(sk1,sk2) = hazard_of_mortality(sk1,sk3) )
<=> ( hazard_of_mortality(sk1,sk3) = very_low ) ),
inference(transitivity,[status(thm)],[22,1]) ).
tff(24,plain,
( ( hazard_of_mortality(sk1,sk3) = very_low )
<=> ( hazard_of_mortality(sk1,sk2) = hazard_of_mortality(sk1,sk3) ) ),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( has_immunity(sk1,sk3)
<=> has_immunity(sk1,sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
has_immunity(sk1,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_2_39) ).
tff(27,plain,
has_immunity(sk1,sk3),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ( ~ ! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) )
| ~ organization(sk1)
| ( hazard_of_mortality(sk1,sk3) = very_low )
| ~ has_immunity(sk1,sk3) )
<=> ( ~ ! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) )
| ~ organization(sk1)
| ( hazard_of_mortality(sk1,sk3) = very_low )
| ~ has_immunity(sk1,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( ( hazard_of_mortality(sk1,sk3) = very_low )
| ~ has_immunity(sk1,sk3)
| ~ organization(sk1) )
<=> ( ~ organization(sk1)
| ( hazard_of_mortality(sk1,sk3) = very_low )
| ~ has_immunity(sk1,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ( ~ ! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) )
| ( hazard_of_mortality(sk1,sk3) = very_low )
| ~ has_immunity(sk1,sk3)
| ~ organization(sk1) )
<=> ( ~ ! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) )
| ~ organization(sk1)
| ( hazard_of_mortality(sk1,sk3) = very_low )
| ~ has_immunity(sk1,sk3) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) )
| ( hazard_of_mortality(sk1,sk3) = very_low )
| ~ has_immunity(sk1,sk3)
| ~ organization(sk1) )
<=> ( ~ ! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) )
| ~ organization(sk1)
| ( hazard_of_mortality(sk1,sk3) = very_low )
| ~ has_immunity(sk1,sk3) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) )
| ( hazard_of_mortality(sk1,sk3) = very_low )
| ~ has_immunity(sk1,sk3)
| ~ organization(sk1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [B: $i,A: $i] :
( ( hazard_of_mortality(A,B) = very_low )
| ~ has_immunity(A,B)
| ~ organization(A) )
| ~ organization(sk1)
| ( hazard_of_mortality(sk1,sk3) = very_low )
| ~ has_immunity(sk1,sk3) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
hazard_of_mortality(sk1,sk3) = very_low,
inference(unit_resolution,[status(thm)],[33,17,7,27]) ).
tff(35,plain,
hazard_of_mortality(sk1,sk2) = hazard_of_mortality(sk1,sk3),
inference(modus_ponens,[status(thm)],[34,24]) ).
tff(36,plain,
( ( hazard_of_mortality(sk1,sk2) != hazard_of_mortality(sk1,sk3) )
<=> ( hazard_of_mortality(sk1,sk2) != hazard_of_mortality(sk1,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
hazard_of_mortality(sk1,sk2) != hazard_of_mortality(sk1,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption_2_40) ).
tff(38,plain,
hazard_of_mortality(sk1,sk2) != hazard_of_mortality(sk1,sk3),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
$false,
inference(unit_resolution,[status(thm)],[38,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT059-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 7 13:36:49 UTC 2026
% 0.12/0.35 % CPUTime :
% 0.12/0.41 % SZS status Unsatisfiable
% 0.12/0.41 % SZS output start Proof
% See solution above
% 0.12/0.42 % E exiting
%------------------------------------------------------------------------------