%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT116+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n004.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 06:24:15 AM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of formulae : 32 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 278 ( 0 equ)
% Maximal formula atoms : 20 ( 8 avg)
% Number of connectives : 341 ( 122 ~; 106 |; 82 &)
% ( 25 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 27 ( 27 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 126 ( 108 !; 0 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
tff(about_event_type,type,
about_event: ( $i * $i ) > $o ).
tff(e1_type,type,
e1: $i ).
tff(s_type,type,
s: $i ).
tff(founds_rem_type,type,
founds_rem: ( $i * $i * $i ) > $o ).
tff(f1_type,type,
f1: $i ).
tff(rho_r_type,type,
rho_r: $i ).
tff(part_of_type,type,
part_of: ( $i * $i ) > $o ).
tff(cnt_type,type,
cnt: ( $i * $i * $i ) > $o ).
tff(some_target_type,type,
some_target: $i ).
tff(decl_type,type,
decl: $i > $i ).
tff(some_action_type,type,
some_action: $i ).
tff(subjection_type,type,
subjection: $i > $o ).
tff(1,plain,
( ~ about_event(s,e1)
<=> ~ about_event(s,e1) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ about_event(s,e1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture) ).
tff(3,plain,
~ about_event(s,e1),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( founds_rem(e1,rho_r,f1)
<=> founds_rem(e1,rho_r,f1) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
founds_rem(e1,rho_r,f1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',founds_rem1) ).
tff(6,plain,
founds_rem(e1,rho_r,f1),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( part_of(s,rho_r)
<=> part_of(s,rho_r) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
part_of(s,rho_r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partof_s) ).
tff(9,plain,
part_of(s,rho_r),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( cnt(s,decl(some_action),some_target)
<=> cnt(s,decl(some_action),some_target) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
cnt(s,decl(some_action),some_target),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cnt_s) ).
tff(12,plain,
cnt(s,decl(some_action),some_target),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( subjection(s)
<=> subjection(s) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
subjection(s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subj_s) ).
tff(15,plain,
subjection(s),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
^ [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
refl(( ( about_event(S,E)
| ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) )
<=> ( about_event(S,E)
| ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( about_event(S,E)
| ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) )
<=> ! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( about_event(S,E)
| ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
^ [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
<=> ~ ( ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) ) )),
( ~ ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
<=> ~ ~ ( ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) ) )),
rewrite(( ~ ~ ( ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) )
<=> ( ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) ) )),
( ~ ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
<=> ( ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) ) )),
( ( ~ ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
| about_event(S,E) )
<=> ( ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R)
| about_event(S,E) ) )),
rewrite(( ( ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R)
| about_event(S,E) )
<=> ( about_event(S,E)
| ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) ) )),
( ( ~ ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
| about_event(S,E) )
<=> ( about_event(S,E)
| ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( ~ ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
| about_event(S,E) )
<=> ! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( about_event(S,E)
| ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( ~ ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
| about_event(S,E) )
<=> ! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( ~ ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
| about_event(S,E) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho) )
<=> ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho) ) )),
( ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
<=> ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) ) )),
rewrite(( ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
<=> ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) ) )),
( ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
<=> ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) ) )),
( ( ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
=> about_event(S,E) )
<=> ( ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
=> about_event(S,E) ) )),
rewrite(( ( ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
=> about_event(S,E) )
<=> ( ~ ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
| about_event(S,E) ) )),
( ( ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
=> about_event(S,E) )
<=> ( ~ ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
| about_event(S,E) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
=> about_event(S,E) )
<=> ! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( ~ ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
| about_event(S,E) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
=> about_event(S,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_B3) ).
tff(24,plain,
! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( ~ ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
| about_event(S,E) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( ~ ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
| about_event(S,E) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( ~ ( subjection(S)
& cnt(S,decl(A),T)
& part_of(S,Rho)
& founds_rem(E,Rho,R) )
| about_event(S,E) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( about_event(S,E)
| ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( about_event(S,E)
| ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) ),
inference(modus_ponens,[status(thm)],[27,17]) ).
tff(29,plain,
( ( ~ ! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( about_event(S,E)
| ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) )
| about_event(s,e1)
| ~ part_of(s,rho_r)
| ~ cnt(s,decl(some_action),some_target)
| ~ subjection(s)
| ~ founds_rem(e1,rho_r,f1) )
<=> ( ~ ! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( about_event(S,E)
| ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) )
| about_event(s,e1)
| ~ part_of(s,rho_r)
| ~ cnt(s,decl(some_action),some_target)
| ~ subjection(s)
| ~ founds_rem(e1,rho_r,f1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( about_event(S,E)
| ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) )
| about_event(s,e1)
| ~ part_of(s,rho_r)
| ~ cnt(s,decl(some_action),some_target)
| ~ subjection(s)
| ~ founds_rem(e1,rho_r,f1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [S: $i,A: $i,T: $i,Rho: $i,E: $i,R: $i] :
( about_event(S,E)
| ~ part_of(S,Rho)
| ~ cnt(S,decl(A),T)
| ~ subjection(S)
| ~ founds_rem(E,Rho,R) )
| about_event(s,e1)
| ~ part_of(s,rho_r)
| ~ cnt(s,decl(some_action),some_target)
| ~ subjection(s)
| ~ founds_rem(e1,rho_r,f1) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,28,15,12,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT116+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n004.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 14:09:02 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% See solution above
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------