%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LDA002-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 0.11s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 41
% Syntax : Number of formulae : 180 ( 151 unt; 0 typ; 0 def)
% Number of atoms : 211 ( 209 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 50 ( 20 ~; 16 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 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 : 12 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 75 ( 72 !; 0 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: ( $i * $i ) > $i ).
tff(v_type,type,
v: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(n1_type,type,
n1: $i ).
tff(n2_type,type,
n2: $i ).
tff(u_type,type,
u: $i ).
tff(uu_type,type,
uu: $i ).
tff(u3_type,type,
u3: $i ).
tff(u1_type,type,
u1: $i ).
tff(n3_type,type,
n3: $i ).
tff(u2_type,type,
u2: $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_4) ).
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,
f(f(n2,n2),f(n2,n2)) = f(u,u),
inference(monotonicity,[status(thm)],[4,4]) ).
tff(6,plain,
f(u,u) = f(f(n2,n2),f(n2,n2)),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( ( n2 = f(n1,n1) )
<=> ( n2 = f(n1,n1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
n2 = f(n1,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
tff(9,plain,
n2 = f(n1,n1),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
f(n2,n2) = f(f(n1,n1),f(n1,n1)),
inference(monotonicity,[status(thm)],[9,9]) ).
tff(11,plain,
u = f(f(n1,n1),f(n1,n1)),
inference(transitivity,[status(thm)],[3,10]) ).
tff(12,plain,
f(u,u) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),
inference(monotonicity,[status(thm)],[11,11]) ).
tff(13,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))) = f(u,u),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))) = f(f(n2,n2),f(n2,n2)),
inference(transitivity,[status(thm)],[13,6]) ).
tff(15,plain,
f(f(n1,n1),f(n1,n1)) = f(n2,n2),
inference(symmetry,[status(thm)],[10]) ).
tff(16,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(n2,n2),f(f(n2,n2),f(n2,n2))),
inference(monotonicity,[status(thm)],[15,14]) ).
tff(17,plain,
f(f(n2,n2),f(f(n2,n2),f(n2,n2))) = f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[16]) ).
tff(18,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(19,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)],[18]) ).
tff(20,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(21,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(22,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(n2,n2),f(f(n2,n2),f(n2,n2))) = f(f(f(n2,n2),f(n2,n2)),f(f(n2,n2),f(n2,n2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
f(f(n2,n2),f(f(n2,n2),f(n2,n2))) = f(f(f(n2,n2),f(n2,n2)),f(f(n2,n2),f(n2,n2))),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
f(f(f(n2,n2),f(n2,n2)),f(f(n2,n2),f(n2,n2))) = f(f(n2,n2),f(f(n2,n2),f(n2,n2))),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( ( uu = f(u,u) )
<=> ( uu = f(u,u) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
uu = f(u,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
tff(30,plain,
uu = f(u,u),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
f(u,u) = uu,
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
f(f(n2,n2),f(n2,n2)) = uu,
inference(transitivity,[status(thm)],[5,31]) ).
tff(33,plain,
f(f(f(n2,n2),f(n2,n2)),f(f(n2,n2),f(n2,n2))) = f(uu,uu),
inference(monotonicity,[status(thm)],[32,32]) ).
tff(34,plain,
f(uu,uu) = f(f(f(n2,n2),f(n2,n2)),f(f(n2,n2),f(n2,n2))),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
( ( v = f(uu,uu) )
<=> ( v = f(uu,uu) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
v = f(uu,uu),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11) ).
tff(37,plain,
v = f(uu,uu),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
v = f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(transitivity,[status(thm)],[37,34,27,17]) ).
tff(39,plain,
f(n1,n1) = n2,
inference(symmetry,[status(thm)],[9]) ).
tff(40,plain,
f(f(n2,n2),f(n1,n1)) = f(u,n2),
inference(monotonicity,[status(thm)],[4,39]) ).
tff(41,plain,
f(u,n2) = f(f(n2,n2),f(n1,n1)),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
f(f(f(n1,n1),f(n1,n1)),f(u,n2)) = f(f(n2,n2),f(f(n2,n2),f(n1,n1))),
inference(monotonicity,[status(thm)],[15,41]) ).
tff(43,plain,
f(f(n2,n2),f(f(n2,n2),f(n1,n1))) = f(f(f(n1,n1),f(n1,n1)),f(u,n2)),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
f(f(n1,n1),n1) = f(n2,n1),
inference(monotonicity,[status(thm)],[39]) ).
tff(45,plain,
f(n2,n1) = f(f(n1,n1),n1),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
f(n1,f(n2,n1)) = f(n1,f(f(n1,n1),n1)),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
f(n1,f(f(n1,n1),n1)) = f(n1,f(n2,n1)),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(n1,f(f(n1,n1),n1)) = f(f(n1,f(n1,n1)),f(n1,n1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
f(n1,f(f(n1,n1),n1)) = f(f(n1,f(n1,n1)),f(n1,n1)),
inference(unit_resolution,[status(thm)],[48,24]) ).
tff(50,plain,
f(f(n1,f(n1,n1)),f(n1,n1)) = f(n1,f(f(n1,n1),n1)),
inference(symmetry,[status(thm)],[49]) ).
tff(51,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(52,plain,
f(n1,f(n1,n1)) = f(f(n1,n1),f(n1,n1)),
inference(unit_resolution,[status(thm)],[51,24]) ).
tff(53,plain,
f(n1,f(n1,n1)) = u,
inference(transitivity,[status(thm)],[52,15,4]) ).
tff(54,plain,
f(f(n1,f(n1,n1)),f(n1,n1)) = f(u,n2),
inference(monotonicity,[status(thm)],[53,39]) ).
tff(55,plain,
f(u,n2) = f(f(n1,f(n1,n1)),f(n1,n1)),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
f(f(n2,n2),f(n1,n1)) = f(n1,f(n2,n1)),
inference(transitivity,[status(thm)],[40,55,50,47]) ).
tff(57,plain,
f(f(n2,n2),f(f(n2,n2),f(n1,n1))) = f(f(n2,n2),f(n1,f(n2,n1))),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
f(f(n2,n2),f(n1,f(n2,n1))) = f(f(n2,n2),f(f(n2,n2),f(n1,n1))),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(n2,n2),f(n1,f(n2,n1))) = f(f(f(n2,n2),n1),f(f(n2,n2),f(n2,n1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
f(f(n2,n2),f(n1,f(n2,n1))) = f(f(f(n2,n2),n1),f(f(n2,n2),f(n2,n1))),
inference(unit_resolution,[status(thm)],[59,24]) ).
tff(61,plain,
f(f(f(n2,n2),n1),f(f(n2,n2),f(n2,n1))) = f(f(n2,n2),f(n1,f(n2,n1))),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
( ( u3 = f(u,n3) )
<=> ( u3 = f(u,n3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
u3 = f(u,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
tff(64,plain,
u3 = f(u,n3),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
f(u,n3) = u3,
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( ( n3 = f(n2,n1) )
<=> ( n3 = f(n2,n1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
n3 = f(n2,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
tff(68,plain,
n3 = f(n2,n1),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
f(n2,n1) = n3,
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
f(f(n2,n2),f(n2,n1)) = f(u,n3),
inference(monotonicity,[status(thm)],[4,69]) ).
tff(71,plain,
f(f(n2,n2),f(n2,n1)) = u3,
inference(transitivity,[status(thm)],[70,65]) ).
tff(72,plain,
( ( u1 = f(u,n1) )
<=> ( u1 = f(u,n1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
u1 = f(u,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
tff(74,plain,
u1 = f(u,n1),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
f(u,n1) = u1,
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
f(f(n2,n2),n1) = f(u,n1),
inference(monotonicity,[status(thm)],[4]) ).
tff(77,plain,
f(f(n2,n2),n1) = u1,
inference(transitivity,[status(thm)],[76,75]) ).
tff(78,plain,
f(f(f(n2,n2),n1),f(f(n2,n2),f(n2,n1))) = f(u1,u3),
inference(monotonicity,[status(thm)],[77,71]) ).
tff(79,plain,
f(u1,u3) = f(f(f(n2,n2),n1),f(f(n2,n2),f(n2,n1))),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
( ( b = f(u1,u3) )
<=> ( b = f(u1,u3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,axiom,
b = f(u1,u3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10) ).
tff(82,plain,
b = f(u1,u3),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
b = f(f(f(n1,n1),f(n1,n1)),f(u,n2)),
inference(transitivity,[status(thm)],[82,79,61,58,43]) ).
tff(84,plain,
f(b,v) = f(f(f(f(n1,n1),f(n1,n1)),f(u,n2)),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(monotonicity,[status(thm)],[83,38]) ).
tff(85,plain,
f(f(f(f(n1,n1),f(n1,n1)),f(u,n2)),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(b,v),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(f(n1,n1),f(n1,n1)),f(f(u,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(n1,n1),f(n1,n1)),f(u,n2)),f(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(87,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(u,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(n1,n1),f(n1,n1)),f(u,n2)),f(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)],[86,24]) ).
tff(88,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(89,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)],[88,24]) ).
tff(90,plain,
f(f(n1,n1),f(n2,n2)) = f(f(n1,n1),f(f(n1,n1),f(n1,n1))),
inference(monotonicity,[status(thm)],[10]) ).
tff(91,plain,
f(f(n1,n1),f(n2,n2)) = f(f(n2,n2),f(n2,n2)),
inference(transitivity,[status(thm)],[90,89,13,6]) ).
tff(92,plain,
f(f(n2,n2),f(f(n1,n1),f(n2,n2))) = f(f(n2,n2),f(f(n2,n2),f(n2,n2))),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(n2,n2),f(f(n1,n1),f(n2,n2))) = f(f(f(n2,n2),f(n1,n1)),f(f(n2,n2),f(n2,n2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
f(f(n2,n2),f(f(n1,n1),f(n2,n2))) = f(f(f(n2,n2),f(n1,n1)),f(f(n2,n2),f(n2,n2))),
inference(unit_resolution,[status(thm)],[93,24]) ).
tff(95,plain,
f(f(f(n2,n2),f(n1,n1)),f(f(n2,n2),f(n2,n2))) = f(f(n2,n2),f(f(n1,n1),f(n2,n2))),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
f(f(u,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(f(n2,n2),f(n1,n1)),f(f(n2,n2),f(n2,n2))),
inference(monotonicity,[status(thm)],[41,14]) ).
tff(97,plain,
f(f(u,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(transitivity,[status(thm)],[96,95,92,17]) ).
tff(98,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(u,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(n1,n1),f(n1,n1)),f(f(u,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(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(101,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(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)],[100,24]) ).
tff(102,plain,
f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
f(f(u,u),f(u,u)) = f(uu,uu),
inference(monotonicity,[status(thm)],[31,31]) ).
tff(104,plain,
f(uu,uu) = f(f(u,u),f(u,u)),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(u,u),f(u,u)),
inference(transitivity,[status(thm)],[16,26,33,104]) ).
tff(106,plain,
f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(u,u),f(f(u,u),f(u,u))),
inference(monotonicity,[status(thm)],[13,105]) ).
tff(107,plain,
f(f(u,u),f(f(u,u),f(u,u))) = f(f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),f(f(f(n1,n1),f(n1,n1)),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(symmetry,[status(thm)],[106]) ).
tff(108,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)],[52]) ).
tff(109,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(110,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)],[109,24]) ).
tff(111,plain,
f(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))) = f(f(n1,n1),f(n1,f(n1,n1))),
inference(symmetry,[status(thm)],[110]) ).
tff(112,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)],[45]) ).
tff(113,plain,
f(f(n2,n1),f(f(n1,n1),f(n1,n1))) = f(f(n2,n2),f(n2,n2)),
inference(transitivity,[status(thm)],[112,111,108,89,13,6]) ).
tff(114,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(115,plain,
f(f(n1,n1),f(n1,n1)) = f(f(f(n1,n1),n1),f(f(n1,n1),n1)),
inference(unit_resolution,[status(thm)],[114,24]) ).
tff(116,plain,
f(f(f(n1,n1),n1),f(f(n1,n1),n1)) = f(f(n1,n1),f(n1,n1)),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
f(f(n2,n1),f(n2,n1)) = f(f(f(n1,n1),n1),f(f(n1,n1),n1)),
inference(monotonicity,[status(thm)],[45,45]) ).
tff(118,plain,
f(f(n2,n1),f(n2,n1)) = f(n2,n2),
inference(transitivity,[status(thm)],[117,116,15]) ).
tff(119,plain,
f(f(f(n2,n1),f(n2,n1)),f(f(n2,n1),f(f(n1,n1),f(n1,n1)))) = f(f(n2,n2),f(f(n2,n2),f(n2,n2))),
inference(monotonicity,[status(thm)],[118,113]) ).
tff(120,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(n2,n1),f(f(n1,n1),f(n1,n1)))) = f(f(f(n2,n1),f(n2,n1)),f(f(n2,n1),f(f(n1,n1),f(n1,n1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
f(f(n2,n1),f(f(n2,n1),f(f(n1,n1),f(n1,n1)))) = f(f(f(n2,n1),f(n2,n1)),f(f(n2,n1),f(f(n1,n1),f(n1,n1)))),
inference(unit_resolution,[status(thm)],[120,24]) ).
tff(122,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)],[112]) ).
tff(123,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)],[108]) ).
tff(124,plain,
f(f(n1,n1),f(f(n1,n1),f(n1,n1))) = f(f(n2,n1),f(f(n1,n1),f(n1,n1))),
inference(transitivity,[status(thm)],[123,110,122]) ).
tff(125,plain,
f(f(f(n1,n1),n1),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))) = f(f(n2,n1),f(f(n2,n1),f(f(n1,n1),f(n1,n1)))),
inference(monotonicity,[status(thm)],[44,124]) ).
tff(126,plain,
f(f(n2,n1),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))) = f(f(f(n1,n1),n1),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))),
inference(monotonicity,[status(thm)],[45]) ).
tff(127,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(f(n1,n1),f(n1,n1)))) = f(f(f(n2,n1),f(n1,n1)),f(f(n2,n1),f(f(n1,n1),f(n1,n1)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
f(f(n2,n1),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))) = f(f(f(n2,n1),f(n1,n1)),f(f(n2,n1),f(f(n1,n1),f(n1,n1)))),
inference(unit_resolution,[status(thm)],[127,24]) ).
tff(129,plain,
f(f(f(n2,n1),f(n1,n1)),f(f(n2,n1),f(f(n1,n1),f(n1,n1)))) = f(f(n2,n1),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[128]) ).
tff(130,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)],[89]) ).
tff(131,plain,
f(f(n2,n2),f(f(n1,n1),f(n1,n1))) = f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))),
inference(monotonicity,[status(thm)],[10]) ).
tff(132,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(n2,n2),f(f(n1,n1),f(n1,n1))) = f(f(f(n2,n2),f(n1,n1)),f(f(n2,n2),f(n1,n1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
f(f(n2,n2),f(f(n1,n1),f(n1,n1))) = f(f(f(n2,n2),f(n1,n1)),f(f(n2,n2),f(n1,n1))),
inference(unit_resolution,[status(thm)],[132,24]) ).
tff(134,plain,
f(f(f(n2,n2),f(n1,n1)),f(f(n2,n2),f(n1,n1))) = f(f(n2,n2),f(f(n1,n1),f(n1,n1))),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
f(f(u,n2),f(u,n2)) = f(f(f(n2,n2),f(n1,n1)),f(f(n2,n2),f(n1,n1))),
inference(monotonicity,[status(thm)],[41,41]) ).
tff(136,plain,
f(f(u,n2),f(u,n2)) = f(f(n2,n1),f(f(n1,n1),f(n1,n1))),
inference(transitivity,[status(thm)],[135,134,131,130,123,110,122]) ).
tff(137,plain,
f(f(n2,n1),f(n1,n1)) = f(n3,n2),
inference(monotonicity,[status(thm)],[69,39]) ).
tff(138,plain,
f(n3,n2) = f(f(n2,n1),f(n1,n1)),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
f(f(n3,n2),f(f(u,n2),f(u,n2))) = f(f(f(n2,n1),f(n1,n1)),f(f(n2,n1),f(f(n1,n1),f(n1,n1)))),
inference(monotonicity,[status(thm)],[138,136]) ).
tff(140,plain,
f(f(f(n2,n2),f(n1,n1)),f(f(n2,n2),f(n1,n1))) = f(f(u,n2),f(u,n2)),
inference(symmetry,[status(thm)],[135]) ).
tff(141,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))) = f(f(n2,n2),f(f(n1,n1),f(n1,n1))),
inference(symmetry,[status(thm)],[131]) ).
tff(142,plain,
f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))) = f(f(u,n2),f(u,n2)),
inference(transitivity,[status(thm)],[141,133,140]) ).
tff(143,plain,
f(f(n3,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(n3,n2),f(f(u,n2),f(u,n2))),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
f(f(n3,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(u,u),f(u,u)),
inference(transitivity,[status(thm)],[143,139,129,126,125,121,119,26,33,104]) ).
tff(145,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(n1,n1))) = f(f(f(n2,n1),f(n1,n1)),f(f(n2,n1),f(n1,n1))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(146,plain,
f(f(n2,n1),f(f(n1,n1),f(n1,n1))) = f(f(f(n2,n1),f(n1,n1)),f(f(n2,n1),f(n1,n1))),
inference(unit_resolution,[status(thm)],[145,24]) ).
tff(147,plain,
f(f(f(n2,n1),f(n1,n1)),f(f(n2,n1),f(n1,n1))) = f(f(n2,n1),f(f(n1,n1),f(n1,n1))),
inference(symmetry,[status(thm)],[146]) ).
tff(148,plain,
f(f(n3,n2),f(n3,n2)) = f(f(f(n2,n1),f(n1,n1)),f(f(n2,n1),f(n1,n1))),
inference(monotonicity,[status(thm)],[138,138]) ).
tff(149,plain,
f(f(n3,n2),f(n3,n2)) = f(u,u),
inference(transitivity,[status(thm)],[148,147,112,111,108,89,13]) ).
tff(150,plain,
f(f(f(n3,n2),f(n3,n2)),f(f(n3,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(u,u),f(f(u,u),f(u,u))),
inference(monotonicity,[status(thm)],[149,144]) ).
tff(151,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(n3,n2),f(f(n3,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(n3,n2),f(n3,n2)),f(f(n3,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(152,plain,
f(f(n3,n2),f(f(n3,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(n3,n2),f(n3,n2)),f(f(n3,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(unit_resolution,[status(thm)],[151,24]) ).
tff(153,plain,
f(f(n3,n2),f(f(u,n2),f(u,n2))) = f(f(n3,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[143]) ).
tff(154,plain,
f(f(f(n2,n1),f(n1,n1)),f(f(n2,n1),f(f(n1,n1),f(n1,n1)))) = f(f(n3,n2),f(f(u,n2),f(u,n2))),
inference(symmetry,[status(thm)],[139]) ).
tff(155,plain,
f(f(f(n1,n1),n1),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))) = f(f(n2,n1),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[126]) ).
tff(156,plain,
f(f(n2,n1),f(f(n2,n1),f(f(n1,n1),f(n1,n1)))) = f(f(f(n1,n1),n1),f(f(n1,n1),f(f(n1,n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[125]) ).
tff(157,plain,
f(f(f(n2,n1),f(n2,n1)),f(f(n2,n1),f(f(n1,n1),f(n1,n1)))) = f(f(n2,n1),f(f(n2,n1),f(f(n1,n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[121]) ).
tff(158,plain,
f(f(n2,n2),f(f(n2,n2),f(n2,n2))) = f(f(f(n2,n1),f(n2,n1)),f(f(n2,n1),f(f(n1,n1),f(n1,n1)))),
inference(symmetry,[status(thm)],[119]) ).
tff(159,plain,
f(f(u,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))) = f(f(n3,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(transitivity,[status(thm)],[96,95,92,158,157,156,155,128,154,153]) ).
tff(160,plain,
f(f(n3,n2),f(f(u,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(n3,n2),f(f(n3,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) )
| ( f(f(n3,n2),f(f(u,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(n3,n2),f(u,n2)),f(f(n3,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(162,plain,
f(f(n3,n2),f(f(u,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(f(n3,n2),f(u,n2)),f(f(n3,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(unit_resolution,[status(thm)],[161,24]) ).
tff(163,plain,
f(f(f(n3,n2),f(u,n2)),f(f(n3,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))) = f(f(n3,n2),f(f(u,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
v = f(f(n3,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1)))),
inference(transitivity,[status(thm)],[37,34,27,158,157,156,155,128,154,153]) ).
tff(165,plain,
( ( u2 = f(u,n2) )
<=> ( u2 = f(u,n2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(166,axiom,
u2 = f(u,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
tff(167,plain,
u2 = f(u,n2),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
f(u,n2) = u2,
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
f(f(n3,n2),f(u,n2)) = f(f(n3,n2),u2),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
f(f(n3,n2),u2) = f(f(n3,n2),f(u,n2)),
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
( ( a = f(f(n3,n2),u2) )
<=> ( a = f(f(n3,n2),u2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,axiom,
a = f(f(n3,n2),u2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
tff(173,plain,
a = f(f(n3,n2),u2),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
a = f(f(n3,n2),f(u,n2)),
inference(transitivity,[status(thm)],[173,170]) ).
tff(175,plain,
f(a,v) = f(f(f(n3,n2),f(u,n2)),f(f(n3,n2),f(f(f(n1,n1),f(n1,n1)),f(f(n1,n1),f(n1,n1))))),
inference(monotonicity,[status(thm)],[174,164]) ).
tff(176,plain,
f(a,v) = f(b,v),
inference(transitivity,[status(thm)],[175,163,160,152,150,107,102,99,87,85]) ).
tff(177,plain,
( ( f(a,v) != f(b,v) )
<=> ( f(a,v) != f(b,v) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,axiom,
f(a,v) != f(b,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
tff(179,plain,
f(a,v) != f(b,v),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
$false,
inference(unit_resolution,[status(thm)],[179,176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : LDA002-1 : TPTP v9.0.0. Released v1.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 23:21:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Unsatisfiable
% 0.11/0.38 % SZS output start Proof
% See solution above
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------