%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LDA003-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:17:05 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 45 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 62 ( 35 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 9 ~; 2 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 45 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
tff(left_type,type,
left: ( $i * $i ) > $o ).
tff(f_type,type,
f: ( $i * $i ) > $i ).
tff(n1_type,type,
n1: $i ).
tff(n2_type,type,
n2: $i ).
tff(u_type,type,
u: $i ).
tff(n3_type,type,
n3: $i ).
tff(1,plain,
( ( u = f(n2,n2) )
<=> ( u = f(n2,n2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
u = f(n2,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
tff(3,plain,
u = f(n2,n2),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
f(n2,n2) = u,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ( n2 = f(n1,n1) )
<=> ( n2 = f(n1,n1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
n2 = f(n1,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
tff(7,plain,
n2 = f(n1,n1),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
f(n2,n2) = f(f(n1,n1),f(n1,n1)),
inference(monotonicity,[status(thm)],[7,7]) ).
tff(9,plain,
f(f(n1,n1),f(n1,n1)) = f(n2,n2),
inference(symmetry,[status(thm)],[8]) ).
tff(10,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
<=> ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(n1,n1),f(n1,n1)) = f(f(f(n1,n1),n1),f(f(n1,n1),n1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
f(f(n1,n1),f(n1,n1)) = f(f(f(n1,n1),n1),f(f(n1,n1),n1)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
f(f(f(n1,n1),n1),f(f(n1,n1),n1)) = f(f(n1,n1),f(n1,n1)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
f(n1,n1) = n2,
inference(symmetry,[status(thm)],[7]) ).
tff(21,plain,
f(f(n1,n1),n1) = f(n2,n1),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
f(n2,n1) = f(f(n1,n1),n1),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
f(f(n2,n1),f(n2,n1)) = f(f(f(n1,n1),n1),f(f(n1,n1),n1)),
inference(monotonicity,[status(thm)],[22,22]) ).
tff(24,plain,
f(f(n2,n1),f(n2,n1)) = u,
inference(transitivity,[status(thm)],[23,19,9,4]) ).
tff(25,plain,
( ( n3 = f(n2,n1) )
<=> ( n3 = f(n2,n1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
n3 = f(n2,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
tff(27,plain,
n3 = f(n2,n1),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
f(n2,n1) = n3,
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
( left(f(n2,n1),f(f(n2,n1),f(n2,n1)))
<=> left(n3,u) ),
inference(monotonicity,[status(thm)],[28,24]) ).
tff(30,plain,
( left(n3,u)
<=> left(f(n2,n1),f(f(n2,n1),f(n2,n1))) ),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
( ~ left(n3,u)
<=> ~ left(f(n2,n1),f(f(n2,n1),f(n2,n1))) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ~ left(n3,u)
<=> ~ left(n3,u) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
~ left(n3,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
tff(34,plain,
~ left(n3,u),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
~ left(f(n2,n1),f(f(n2,n1),f(n2,n1))),
inference(modus_ponens,[status(thm)],[34,31]) ).
tff(36,plain,
^ [Y: $i,X: $i] :
refl(( left(X,f(X,Y))
<=> left(X,f(X,Y)) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [Y: $i,X: $i] : left(X,f(X,Y))
<=> ! [Y: $i,X: $i] : left(X,f(X,Y)) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [Y: $i,X: $i] : left(X,f(X,Y))
<=> ! [Y: $i,X: $i] : left(X,f(X,Y)) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
! [Y: $i,X: $i] : left(X,f(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
tff(40,plain,
! [Y: $i,X: $i] : left(X,f(X,Y)),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [Y: $i,X: $i] : left(X,f(X,Y)),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [Y: $i,X: $i] : left(X,f(X,Y)),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ~ ! [Y: $i,X: $i] : left(X,f(X,Y))
| left(f(n2,n1),f(f(n2,n1),f(n2,n1))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
left(f(n2,n1),f(f(n2,n1),f(n2,n1))),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
$false,
inference(unit_resolution,[status(thm)],[44,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LDA003-1 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 23:21:47 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38 % SZS output start Proof
% See solution above
% 0.13/0.39 % E exiting
%------------------------------------------------------------------------------