%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LDA001-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:17:04 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 64 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 79 ( 77 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 7 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 1 ( 1 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 45 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: ( $i * $i ) > $i ).
tff(u_type,type,
u: $i ).
tff(n2_type,type,
n2: $i ).
tff(n3_type,type,
n3: $i ).
tff(n1_type,type,
n1: $i ).
tff(1,plain,
( ( n2 = f(n1,n1) )
<=> ( n2 = f(n1,n1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
n2 = f(n1,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
tff(3,plain,
n2 = f(n1,n1),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
f(n1,n1) = n2,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
f(f(n1,n1),n1) = f(n2,n1),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
f(n2,n1) = f(f(n1,n1),n1),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
f(f(n2,n1),f(n2,n1)) = f(f(f(n1,n1),n1),f(f(n1,n1),n1)),
inference(monotonicity,[status(thm)],[6,6]) ).
tff(8,plain,
f(f(f(n1,n1),n1),f(f(n1,n1),n1)) = f(f(n2,n1),f(n2,n1)),
inference(symmetry,[status(thm)],[7]) ).
tff(9,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(10,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)],[9]) ).
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(rewrite,[status(thm)],[]) ).
tff(12,axiom,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
tff(13,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,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(17,plain,
f(f(n1,n1),f(n1,n1)) = f(f(f(n1,n1),n1),f(f(n1,n1),n1)),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
f(n2,n2) = f(f(n1,n1),f(n1,n1)),
inference(monotonicity,[status(thm)],[3,3]) ).
tff(19,plain,
( ( u = f(n2,n2) )
<=> ( u = f(n2,n2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
u = f(n2,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
tff(21,plain,
u = f(n2,n2),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
u = f(f(n2,n1),f(n2,n1)),
inference(transitivity,[status(thm)],[21,18,17,8]) ).
tff(23,plain,
f(f(n2,n1),f(f(n1,n1),f(n1,n1))) = f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))),
inference(monotonicity,[status(thm)],[6]) ).
tff(24,plain,
f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))) = f(f(n2,n1),f(f(n1,n1),f(n1,n1))),
inference(symmetry,[status(thm)],[23]) ).
tff(25,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,f(n1,n1))) = f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
f(f(n1,n1),f(n1,f(n1,n1))) = f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))),
inference(unit_resolution,[status(thm)],[25,15]) ).
tff(27,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(n1,f(n1,n1)) = f(f(n1,n1),f(n1,n1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
f(n1,f(n1,n1)) = f(f(n1,n1),f(n1,n1)),
inference(unit_resolution,[status(thm)],[27,15]) ).
tff(29,plain,
f(f(n1,n1),f(n1,f(n1,n1))) = f(f(n1,n1),f(f(n1,n1),f(n1,n1))),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
f(f(n1,n1),f(f(n1,n1),f(n1,n1))) = f(f(n1,n1),f(n1,f(n1,n1))),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(n1,n1),f(f(n1,n1),f(n1,n1))) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
f(f(n1,n1),f(f(n1,n1),f(n1,n1))) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),
inference(unit_resolution,[status(thm)],[31,15]) ).
tff(33,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))) = f(f(n1,n1),f(f(n1,n1),f(n1,n1))),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
u = f(f(n1,n1),f(n1,n1)),
inference(transitivity,[status(thm)],[21,18]) ).
tff(35,plain,
f(u,u) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),
inference(monotonicity,[status(thm)],[34,34]) ).
tff(36,plain,
f(u,u) = f(f(n2,n1),f(f(n1,n1),f(n1,n1))),
inference(transitivity,[status(thm)],[35,33,30,26,24]) ).
tff(37,plain,
f(f(u,u),u) = f(f(f(n2,n1),f(f(n1,n1),f(n1,n1))),f(f(n2,n1),f(n2,n1))),
inference(monotonicity,[status(thm)],[36,22]) ).
tff(38,plain,
f(f(f(n2,n1),f(f(n1,n1),f(n1,n1))),f(f(n2,n1),f(n2,n1))) = f(f(u,u),u),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(n2,n1),f(f(f(n1,n1),f(n1,n1)),f(n2,n1))) = f(f(f(n2,n1),f(f(n1,n1),f(n1,n1))),f(f(n2,n1),f(n2,n1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
f(f(n2,n1),f(f(f(n1,n1),f(n1,n1)),f(n2,n1))) = f(f(f(n2,n1),f(f(n1,n1),f(n1,n1))),f(f(n2,n1),f(n2,n1))),
inference(unit_resolution,[status(thm)],[39,15]) ).
tff(41,plain,
f(f(n1,n1),f(n2,n1)) = f(f(n1,n1),f(f(n1,n1),n1)),
inference(monotonicity,[status(thm)],[6]) ).
tff(42,plain,
f(f(n1,n1),f(f(n1,n1),n1)) = f(f(n1,n1),f(n2,n1)),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(n1,n1),f(f(n1,n1),n1)) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),n1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
f(f(n1,n1),f(f(n1,n1),n1)) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),n1)),
inference(unit_resolution,[status(thm)],[43,15]) ).
tff(45,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),n1)) = f(f(n1,n1),f(f(n1,n1),n1)),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
f(f(f(n1,n1),f(n1,n1)),f(n2,n1)) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),n1)),
inference(monotonicity,[status(thm)],[6]) ).
tff(47,plain,
f(f(f(n1,n1),f(n1,n1)),f(n2,n1)) = f(f(n1,n1),f(n2,n1)),
inference(transitivity,[status(thm)],[46,45,42]) ).
tff(48,plain,
f(f(n2,n1),f(f(f(n1,n1),f(n1,n1)),f(n2,n1))) = f(f(n2,n1),f(f(n1,n1),f(n2,n1))),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
f(f(n2,n1),f(f(n1,n1),f(n2,n1))) = f(f(n2,n1),f(f(f(n1,n1),f(n1,n1)),f(n2,n1))),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(n2,n1),f(f(n1,n1),f(n2,n1))) = f(f(f(n2,n1),f(n1,n1)),f(f(n2,n1),f(n2,n1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
f(f(n2,n1),f(f(n1,n1),f(n2,n1))) = f(f(f(n2,n1),f(n1,n1)),f(f(n2,n1),f(n2,n1))),
inference(unit_resolution,[status(thm)],[50,15]) ).
tff(52,plain,
f(f(f(n2,n1),f(n1,n1)),f(f(n2,n1),f(n2,n1))) = f(f(n2,n1),f(f(n1,n1),f(n2,n1))),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
( ( n3 = f(n2,n1) )
<=> ( n3 = f(n2,n1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,axiom,
n3 = f(n2,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
tff(55,plain,
n3 = f(n2,n1),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
f(n2,n1) = n3,
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
f(f(n2,n1),f(n1,n1)) = f(n3,n2),
inference(monotonicity,[status(thm)],[56,4]) ).
tff(58,plain,
f(n3,n2) = f(f(n2,n1),f(n1,n1)),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
f(f(n3,n2),u) = f(f(f(n2,n1),f(n1,n1)),f(f(n2,n1),f(n2,n1))),
inference(monotonicity,[status(thm)],[58,22]) ).
tff(60,plain,
f(f(n3,n2),u) = f(f(u,u),u),
inference(transitivity,[status(thm)],[59,52,49,40,38]) ).
tff(61,plain,
( ( f(f(n3,n2),u) != f(f(u,u),u) )
<=> ( f(f(n3,n2),u) != f(f(u,u),u) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,axiom,
f(f(n3,n2),u) != f(f(u,u),u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
tff(63,plain,
f(f(n3,n2),u) != f(f(u,u),u),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
$false,
inference(unit_resolution,[status(thm)],[63,60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : LDA001-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Jun 19 23:21:54 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39 % SZS output start Proof
% See solution above
% 0.21/0.40 % E exiting
%------------------------------------------------------------------------------