%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL414-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n002.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 : Mon Sep 7 02:59:58 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 20
% Syntax : Number of formulae : 45 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 164 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 218 ( 103 ~; 98 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 2 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 : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 102 ( 93 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_truth_type,type,
a_truth: $i > $o ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(sk1_type,type,
sk1: $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(( a_truth(implies(A,implies(B,A)))
<=> a_truth(implies(A,implies(B,A))) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i] : a_truth(implies(A,implies(B,A)))
<=> ! [B: $i,A: $i] : a_truth(implies(A,implies(B,A))) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : a_truth(implies(A,implies(B,A)))
<=> ! [B: $i,A: $i] : a_truth(implies(A,implies(B,A))) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i] : a_truth(implies(A,implies(B,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm147_2) ).
tff(5,plain,
! [B: $i,A: $i] : a_truth(implies(A,implies(B,A))),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : a_truth(implies(A,implies(B,A))),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : a_truth(implies(A,implies(B,A))),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : a_truth(implies(A,implies(B,A)))
| a_truth(implies(sk1,implies(sk1,sk1))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
a_truth(implies(sk1,implies(sk1,sk1))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ a_truth(implies(sk1,sk1))
<=> ~ a_truth(implies(sk1,sk1)) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
~ a_truth(implies(sk1,sk1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm147_5) ).
tff(12,plain,
~ a_truth(implies(sk1,sk1)),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
^ [B: $i,A: $i] :
refl(( ( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) )
<=> ( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) )
<=> ! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) )
<=> ! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
^ [B: $i,A: $i] :
rewrite(( ( a_truth(B)
| ~ a_truth(A)
| ~ a_truth(implies(A,B)) )
<=> ( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [B: $i,A: $i] :
( a_truth(B)
| ~ a_truth(A)
| ~ a_truth(implies(A,B)) )
<=> ! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [B: $i,A: $i] :
( a_truth(B)
| ~ a_truth(A)
| ~ a_truth(implies(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm147_1) ).
tff(19,plain,
! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) )
| a_truth(implies(sk1,sk1))
| ~ a_truth(implies(sk1,implies(sk1,sk1)))
| ~ a_truth(implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1))) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) )
| a_truth(implies(sk1,sk1))
| ~ a_truth(implies(sk1,implies(sk1,sk1)))
| ~ a_truth(implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( ~ a_truth(implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1)))
| ~ a_truth(implies(sk1,implies(sk1,sk1)))
| a_truth(implies(sk1,sk1)) )
<=> ( a_truth(implies(sk1,sk1))
| ~ a_truth(implies(sk1,implies(sk1,sk1)))
| ~ a_truth(implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) )
| ~ a_truth(implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1)))
| ~ a_truth(implies(sk1,implies(sk1,sk1)))
| a_truth(implies(sk1,sk1)) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) )
| a_truth(implies(sk1,sk1))
| ~ a_truth(implies(sk1,implies(sk1,sk1)))
| ~ a_truth(implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1))) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) )
| ~ a_truth(implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1)))
| ~ a_truth(implies(sk1,implies(sk1,sk1)))
| a_truth(implies(sk1,sk1)) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) )
| a_truth(implies(sk1,sk1))
| ~ a_truth(implies(sk1,implies(sk1,sk1)))
| ~ a_truth(implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1))) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) )
| ~ a_truth(implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1)))
| ~ a_truth(implies(sk1,implies(sk1,sk1)))
| a_truth(implies(sk1,sk1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) )
| a_truth(implies(sk1,sk1))
| ~ a_truth(implies(sk1,implies(sk1,sk1)))
| ~ a_truth(implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1))) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ a_truth(implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1))),
inference(unit_resolution,[status(thm)],[28,22,12,9]) ).
tff(30,plain,
( ~ ! [B: $i,A: $i] : a_truth(implies(A,implies(B,A)))
| a_truth(implies(sk1,implies(implies(sk1,sk1),sk1))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
a_truth(implies(sk1,implies(implies(sk1,sk1),sk1))),
inference(unit_resolution,[status(thm)],[30,7]) ).
tff(32,plain,
^ [B: $i,A: $i,C: $i] :
refl(( a_truth(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C))))
<=> a_truth(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [B: $i,A: $i,C: $i] : a_truth(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C))))
<=> ! [B: $i,A: $i,C: $i] : a_truth(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [B: $i,A: $i,C: $i] : a_truth(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C))))
<=> ! [B: $i,A: $i,C: $i] : a_truth(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
! [B: $i,A: $i,C: $i] : a_truth(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm147_3) ).
tff(36,plain,
! [B: $i,A: $i,C: $i] : a_truth(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [B: $i,A: $i,C: $i] : a_truth(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [B: $i,A: $i,C: $i] : a_truth(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C)))),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ~ ! [B: $i,A: $i,C: $i] : a_truth(implies(implies(A,implies(B,C)),implies(implies(A,B),implies(A,C))))
| a_truth(implies(implies(sk1,implies(implies(sk1,sk1),sk1)),implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
a_truth(implies(implies(sk1,implies(implies(sk1,sk1),sk1)),implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1)))),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) )
| ~ a_truth(implies(implies(sk1,implies(implies(sk1,sk1),sk1)),implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1))))
| ~ a_truth(implies(sk1,implies(implies(sk1,sk1),sk1)))
| a_truth(implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1))) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) )
| ~ a_truth(implies(implies(sk1,implies(implies(sk1,sk1),sk1)),implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1))))
| ~ a_truth(implies(sk1,implies(implies(sk1,sk1),sk1)))
| a_truth(implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) )
| ~ a_truth(implies(implies(sk1,implies(implies(sk1,sk1),sk1)),implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1))))
| ~ a_truth(implies(sk1,implies(implies(sk1,sk1),sk1)))
| a_truth(implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [B: $i,A: $i] :
( ~ a_truth(implies(A,B))
| ~ a_truth(A)
| a_truth(B) )
| ~ a_truth(implies(implies(sk1,implies(implies(sk1,sk1),sk1)),implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1))))
| ~ a_truth(implies(sk1,implies(implies(sk1,sk1),sk1)))
| a_truth(implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1))) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ~ a_truth(implies(sk1,implies(implies(sk1,sk1),sk1)))
| a_truth(implies(implies(sk1,implies(sk1,sk1)),implies(sk1,sk1))) ),
inference(unit_resolution,[status(thm)],[43,22,40]) ).
tff(45,plain,
$false,
inference(unit_resolution,[status(thm)],[44,31,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL414-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n002.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 : Fri Sep 4 20:12:52 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
%------------------------------------------------------------------------------