%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL134-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : Mon Sep 7 02:59:22 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 51 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 69 ( 65 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 9 ~; 5 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 58 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
tff(truth_type,type,
truth: $i ).
tff(implies_type,type,
implies: ( $i * $i ) > $i ).
tff(x_type,type,
x: $i ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
<=> ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
<=> ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
<=> ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(truth,x),implies(implies(x,truth),implies(truth,truth))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
implies(implies(truth,x),implies(implies(x,truth),implies(truth,truth))) = truth,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( ( implies(truth,X) = X )
<=> ( implies(truth,X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] : ( implies(truth,X) = X )
<=> ! [X: $i] : ( implies(truth,X) = X ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( implies(truth,X) = X )
<=> ! [X: $i] : ( implies(truth,X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X: $i] : ( implies(truth,X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
tff(14,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( implies(truth,X) = X ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,truth) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
implies(truth,truth) = truth,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
truth = implies(truth,truth),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
implies(implies(x,truth),truth) = implies(implies(x,truth),implies(truth,truth)),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
^ [Y: $i,X: $i] :
refl(( ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
<=> ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
<=> ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
<=> ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
tff(25,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [Y: $i,X: $i] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) )
| ( implies(implies(x,truth),truth) = implies(implies(truth,x),x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
implies(implies(x,truth),truth) = implies(implies(truth,x),x),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
implies(implies(truth,x),x) = implies(implies(x,truth),truth),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
( ~ ! [X: $i] : ( implies(truth,X) = X )
| ( implies(truth,x) = x ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
implies(truth,x) = x,
inference(unit_resolution,[status(thm)],[31,16]) ).
tff(33,plain,
x = implies(truth,x),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
implies(x,x) = implies(implies(truth,x),x),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
implies(x,x) = implies(implies(x,truth),implies(truth,truth)),
inference(transitivity,[status(thm)],[34,30,20]) ).
tff(36,plain,
implies(implies(truth,x),implies(x,x)) = implies(implies(truth,x),implies(implies(x,truth),implies(truth,truth))),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
implies(implies(truth,x),implies(implies(x,truth),implies(truth,truth))) = implies(implies(truth,x),implies(x,x)),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
truth = implies(implies(truth,x),implies(implies(x,truth),implies(truth,truth))),
inference(symmetry,[status(thm)],[9]) ).
tff(39,plain,
implies(truth,truth) = implies(implies(truth,x),implies(x,x)),
inference(transitivity,[status(thm)],[18,38,37]) ).
tff(40,plain,
implies(implies(x,truth),implies(truth,truth)) = implies(implies(x,truth),implies(implies(truth,x),implies(x,x))),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
implies(implies(x,truth),implies(implies(truth,x),implies(x,x))) = implies(implies(x,truth),implies(truth,truth)),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth )
| ( implies(implies(x,truth),implies(implies(truth,x),implies(x,x))) = truth ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
implies(implies(x,truth),implies(implies(truth,x),implies(x,x))) = truth,
inference(unit_resolution,[status(thm)],[42,7]) ).
tff(44,plain,
truth = implies(implies(x,truth),implies(implies(truth,x),implies(x,x))),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
truth = implies(implies(x,truth),implies(truth,truth)),
inference(transitivity,[status(thm)],[44,41]) ).
tff(46,plain,
implies(x,truth) = implies(implies(truth,x),implies(implies(x,truth),implies(truth,truth))),
inference(monotonicity,[status(thm)],[33,45]) ).
tff(47,plain,
implies(x,truth) = truth,
inference(transitivity,[status(thm)],[46,9]) ).
tff(48,plain,
( ( implies(x,truth) != truth )
<=> ( implies(x,truth) != truth ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
implies(x,truth) != truth,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_lemma) ).
tff(50,plain,
implies(x,truth) != truth,
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
$false,
inference(unit_resolution,[status(thm)],[50,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL134-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % 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 : Fri Sep 4 18:17:03 UTC 2026
% 0.07/0.35 % 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
%------------------------------------------------------------------------------