%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT052-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n018.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 : 37 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 215 ( 0 equ)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 327 ( 159 ~; 146 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 126 ( 114 !; 0 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
tff(is_aligned_type,type,
is_aligned: ( $i * $i ) > $o ).
tff(sk2_type,type,
sk2: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(dissimilar_type,type,
dissimilar: ( $i * $i * $i ) > $o ).
tff(1,plain,
( dissimilar(sk1,sk2,sk2)
<=> dissimilar(sk1,sk2,sk2) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
dissimilar(sk1,sk2,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',background_assumption_1_36) ).
tff(3,plain,
dissimilar(sk1,sk2,sk2),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) )
<=> ( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(rewrite(( ( ~ dissimilar(A,B,C)
| ~ is_aligned(A,B) )
<=> ( ~ dissimilar(A,B,C)
| ~ is_aligned(A,B) ) )),
( ( ~ dissimilar(A,B,C)
| ~ is_aligned(A,B)
| ~ is_aligned(A,C) )
<=> ( ~ dissimilar(A,B,C)
| ~ is_aligned(A,B)
| ~ is_aligned(A,C) ) )),
rewrite(( ( ~ dissimilar(A,B,C)
| ~ is_aligned(A,B)
| ~ is_aligned(A,C) )
<=> ( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) ) )),
( ( ~ dissimilar(A,B,C)
| ~ is_aligned(A,B)
| ~ is_aligned(A,C) )
<=> ( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,B)
| ~ is_aligned(A,C) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,B)
| ~ is_aligned(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_2_31) ).
tff(10,plain,
! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) )
| ~ dissimilar(sk1,sk2,sk2)
| ~ is_aligned(sk1,sk2) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) )
| ~ dissimilar(sk1,sk2,sk2)
| ~ is_aligned(sk1,sk2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ( ~ dissimilar(sk1,sk2,sk2)
| ~ is_aligned(sk1,sk2)
| ~ is_aligned(sk1,sk2) )
<=> ( ~ dissimilar(sk1,sk2,sk2)
| ~ is_aligned(sk1,sk2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) )
| ~ dissimilar(sk1,sk2,sk2)
| ~ is_aligned(sk1,sk2)
| ~ is_aligned(sk1,sk2) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) )
| ~ dissimilar(sk1,sk2,sk2)
| ~ is_aligned(sk1,sk2) ) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) )
| ~ dissimilar(sk1,sk2,sk2)
| ~ is_aligned(sk1,sk2)
| ~ is_aligned(sk1,sk2) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) )
| ~ dissimilar(sk1,sk2,sk2)
| ~ is_aligned(sk1,sk2) ) ),
inference(transitivity,[status(thm)],[16,14]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) )
| ~ dissimilar(sk1,sk2,sk2)
| ~ is_aligned(sk1,sk2)
| ~ is_aligned(sk1,sk2) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| ~ is_aligned(A,C)
| ~ is_aligned(A,B) )
| ~ dissimilar(sk1,sk2,sk2)
| ~ is_aligned(sk1,sk2) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ is_aligned(sk1,sk2),
inference(unit_resolution,[status(thm)],[19,13,3]) ).
tff(21,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) )
<=> ( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [B: $i,A: $i,C: $i] :
rewrite(( ( ~ dissimilar(A,B,C)
| is_aligned(A,B)
| is_aligned(A,C) )
<=> ( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,B)
| is_aligned(A,C) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,B)
| is_aligned(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_2_30) ).
tff(27,plain,
! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) )
| ~ dissimilar(sk1,sk2,sk2)
| is_aligned(sk1,sk2) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) )
| ~ dissimilar(sk1,sk2,sk2)
| is_aligned(sk1,sk2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ( ~ dissimilar(sk1,sk2,sk2)
| is_aligned(sk1,sk2)
| is_aligned(sk1,sk2) )
<=> ( ~ dissimilar(sk1,sk2,sk2)
| is_aligned(sk1,sk2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) )
| ~ dissimilar(sk1,sk2,sk2)
| is_aligned(sk1,sk2)
| is_aligned(sk1,sk2) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) )
| ~ dissimilar(sk1,sk2,sk2)
| is_aligned(sk1,sk2) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) )
| ~ dissimilar(sk1,sk2,sk2)
| is_aligned(sk1,sk2)
| is_aligned(sk1,sk2) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) )
| ~ dissimilar(sk1,sk2,sk2)
| is_aligned(sk1,sk2) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) )
| ~ dissimilar(sk1,sk2,sk2)
| is_aligned(sk1,sk2)
| is_aligned(sk1,sk2) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ dissimilar(A,B,C)
| is_aligned(A,C)
| is_aligned(A,B) )
| ~ dissimilar(sk1,sk2,sk2)
| is_aligned(sk1,sk2) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,30,3,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT052-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.08/0.33 % Computer : n018.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 7 13:24:54 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40 % SZS output start Proof
% See solution above
% 0.13/0.40 % E exiting
%------------------------------------------------------------------------------