%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG011-1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 04:57:46 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 46
% Syntax : Number of formulae : 116 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 522 ( 19 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 764 ( 365 ~; 348 |; 0 &)
% ( 51 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 203 ( 190 !; 0 ?; 203 :)
% Comments :
%------------------------------------------------------------------------------
tff(d_type,type,
d: $i > $o ).
tff(f_type,type,
f: ( $i * $i ) > $i ).
tff(a1_type,type,
a1: $i ).
tff(a2_type,type,
a2: $i ).
tff(c_type,type,
c: $i > $o ).
tff(1,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( f(X,f(Y,Z)) = f(f(X,Y),Z) )
<=> ( f(X,f(Y,Z)) = f(f(X,Y),Z) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_is_associative) ).
tff(5,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) )
| ( f(a2,f(a2,a1)) = f(f(a2,a2),a1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
f(a2,f(a2,a1)) = f(f(a2,a2),a1),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
f(f(f(a2,a2),a1),f(a2,f(a2,a1))) = f(f(f(a2,a2),a1),f(f(a2,a2),a1)),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( f(X,f(Y,Z)) = f(f(X,Y),Z) )
| ( f(f(f(a2,a2),a1),f(a2,f(a2,a1))) = f(f(f(f(a2,a2),a1),a2),f(a2,a1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
f(f(f(a2,a2),a1),f(a2,f(a2,a1))) = f(f(f(f(a2,a2),a1),a2),f(a2,a1)),
inference(unit_resolution,[status(thm)],[11,7]) ).
tff(13,plain,
f(f(f(f(a2,a2),a1),a2),f(a2,a1)) = f(f(f(a2,a2),a1),f(a2,f(a2,a1))),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
f(f(f(f(a2,a2),a1),a2),f(a2,a1)) = f(f(f(a2,a2),a1),f(f(a2,a2),a1)),
inference(transitivity,[status(thm)],[13,10]) ).
tff(15,plain,
( d(f(f(f(f(a2,a2),a1),a2),f(a2,a1)))
<=> d(f(f(f(a2,a2),a1),f(f(a2,a2),a1))) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( d(f(f(f(a2,a2),a1),f(f(a2,a2),a1)))
<=> d(f(f(f(f(a2,a2),a1),a2),f(a2,a1))) ),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
( ~ d(f(f(f(a2,a2),a1),f(f(a2,a2),a1)))
<=> ~ d(f(f(f(f(a2,a2),a1),a2),f(a2,a1))) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
<=> ( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [Y: $i,X: $i] :
rewrite(( ( c(f(X,Y))
| ~ d(X)
| ~ d(Y) )
<=> ( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Y: $i,X: $i] :
( c(f(X,Y))
| ~ d(X)
| ~ d(Y) )
<=> ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [Y: $i,X: $i] :
( c(f(X,Y))
| ~ d(X)
| ~ d(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_2) ).
tff(24,plain,
! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( d(a2)
<=> d(a2) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
d(a2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_d_not_empty) ).
tff(30,plain,
d(a2),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(a2)
| c(f(a2,a2)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(a2)
| c(f(a2,a2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ( ~ d(a2)
| ~ d(a2)
| c(f(a2,a2)) )
<=> ( ~ d(a2)
| c(f(a2,a2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(a2)
| ~ d(a2)
| c(f(a2,a2)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(a2)
| c(f(a2,a2)) ) ),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(a2)
| ~ d(a2)
| c(f(a2,a2)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(a2)
| c(f(a2,a2)) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(a2)
| ~ d(a2)
| c(f(a2,a2)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(a2)
| c(f(a2,a2)) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
c(f(a2,a2)),
inference(unit_resolution,[status(thm)],[36,30,27]) ).
tff(38,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
<=> ( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
^ [Y: $i,X: $i] :
rewrite(( ( d(f(X,Y))
| ~ c(X)
| ~ c(Y) )
<=> ( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [Y: $i,X: $i] :
( d(f(X,Y))
| ~ c(X)
| ~ c(Y) )
<=> ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [Y: $i,X: $i] :
( d(f(X,Y))
| ~ c(X)
| ~ c(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_1) ).
tff(44,plain,
! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( c(a1)
<=> c(a1) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
c(a1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_c_not_empty) ).
tff(50,plain,
c(a1),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
| ~ c(a1)
| ~ c(f(a2,a2))
| d(f(f(a2,a2),a1)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
| ~ c(a1)
| ~ c(f(a2,a2))
| d(f(f(a2,a2),a1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( ~ c(f(a2,a2))
| ~ c(a1)
| d(f(f(a2,a2),a1)) )
<=> ( ~ c(a1)
| ~ c(f(a2,a2))
| d(f(f(a2,a2),a1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
| ~ c(f(a2,a2))
| ~ c(a1)
| d(f(f(a2,a2),a1)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
| ~ c(a1)
| ~ c(f(a2,a2))
| d(f(f(a2,a2),a1)) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
| ~ c(f(a2,a2))
| ~ c(a1)
| d(f(f(a2,a2),a1)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
| ~ c(a1)
| ~ c(f(a2,a2))
| d(f(f(a2,a2),a1)) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
( ~ ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
| ~ c(f(a2,a2))
| ~ c(a1)
| d(f(f(a2,a2),a1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
| ~ c(a1)
| ~ c(f(a2,a2))
| d(f(f(a2,a2),a1)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
d(f(f(a2,a2),a1)),
inference(unit_resolution,[status(thm)],[56,50,47,37]) ).
tff(58,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(f(f(a2,a2),a1))
| c(f(f(f(a2,a2),a1),f(f(a2,a2),a1))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(f(f(a2,a2),a1))
| c(f(f(f(a2,a2),a1),f(f(a2,a2),a1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ( ~ d(f(f(a2,a2),a1))
| ~ d(f(f(a2,a2),a1))
| c(f(f(f(a2,a2),a1),f(f(a2,a2),a1))) )
<=> ( ~ d(f(f(a2,a2),a1))
| c(f(f(f(a2,a2),a1),f(f(a2,a2),a1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(f(f(a2,a2),a1))
| ~ d(f(f(a2,a2),a1))
| c(f(f(f(a2,a2),a1),f(f(a2,a2),a1))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(f(f(a2,a2),a1))
| c(f(f(f(a2,a2),a1),f(f(a2,a2),a1))) ) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(f(f(a2,a2),a1))
| ~ d(f(f(a2,a2),a1))
| c(f(f(f(a2,a2),a1),f(f(a2,a2),a1))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(f(f(a2,a2),a1))
| c(f(f(f(a2,a2),a1),f(f(a2,a2),a1))) ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(f(f(a2,a2),a1))
| ~ d(f(f(a2,a2),a1))
| c(f(f(f(a2,a2),a1),f(f(a2,a2),a1))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(f(f(a2,a2),a1))
| c(f(f(f(a2,a2),a1),f(f(a2,a2),a1))) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
c(f(f(f(a2,a2),a1),f(f(a2,a2),a1))),
inference(unit_resolution,[status(thm)],[63,27,57]) ).
tff(65,plain,
^ [X: $i] :
refl(( ( ~ c(X)
| ~ d(X) )
<=> ( ~ c(X)
| ~ d(X) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [X: $i] :
( ~ c(X)
| ~ d(X) )
<=> ! [X: $i] :
( ~ c(X)
| ~ d(X) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [X: $i] :
( ~ c(X)
| ~ d(X) )
<=> ! [X: $i] :
( ~ c(X)
| ~ d(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,axiom,
! [X: $i] :
( ~ c(X)
| ~ d(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_exclusive) ).
tff(69,plain,
! [X: $i] :
( ~ c(X)
| ~ d(X) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [X: $i] :
( ~ c(X)
| ~ d(X) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [X: $i] :
( ~ c(X)
| ~ d(X) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
( ( ~ ! [X: $i] :
( ~ c(X)
| ~ d(X) )
| ~ c(f(f(f(a2,a2),a1),f(f(a2,a2),a1)))
| ~ d(f(f(f(a2,a2),a1),f(f(a2,a2),a1))) )
<=> ( ~ ! [X: $i] :
( ~ c(X)
| ~ d(X) )
| ~ c(f(f(f(a2,a2),a1),f(f(a2,a2),a1)))
| ~ d(f(f(f(a2,a2),a1),f(f(a2,a2),a1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [X: $i] :
( ~ c(X)
| ~ d(X) )
| ~ c(f(f(f(a2,a2),a1),f(f(a2,a2),a1)))
| ~ d(f(f(f(a2,a2),a1),f(f(a2,a2),a1))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
( ~ ! [X: $i] :
( ~ c(X)
| ~ d(X) )
| ~ c(f(f(f(a2,a2),a1),f(f(a2,a2),a1)))
| ~ d(f(f(f(a2,a2),a1),f(f(a2,a2),a1))) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
~ d(f(f(f(a2,a2),a1),f(f(a2,a2),a1))),
inference(unit_resolution,[status(thm)],[74,71,64]) ).
tff(76,plain,
~ d(f(f(f(f(a2,a2),a1),a2),f(a2,a1))),
inference(modus_ponens,[status(thm)],[75,17]) ).
tff(77,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(a2)
| ~ d(f(f(a2,a2),a1))
| c(f(f(f(a2,a2),a1),a2)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(a2)
| ~ d(f(f(a2,a2),a1))
| c(f(f(f(a2,a2),a1),a2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
( ( ~ d(f(f(a2,a2),a1))
| ~ d(a2)
| c(f(f(f(a2,a2),a1),a2)) )
<=> ( ~ d(a2)
| ~ d(f(f(a2,a2),a1))
| c(f(f(f(a2,a2),a1),a2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(f(f(a2,a2),a1))
| ~ d(a2)
| c(f(f(f(a2,a2),a1),a2)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(a2)
| ~ d(f(f(a2,a2),a1))
| c(f(f(f(a2,a2),a1),a2)) ) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(f(f(a2,a2),a1))
| ~ d(a2)
| c(f(f(f(a2,a2),a1),a2)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(a2)
| ~ d(f(f(a2,a2),a1))
| c(f(f(f(a2,a2),a1),a2)) ) ),
inference(transitivity,[status(thm)],[79,77]) ).
tff(81,plain,
( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(f(f(a2,a2),a1))
| ~ d(a2)
| c(f(f(f(a2,a2),a1),a2)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(a2)
| ~ d(f(f(a2,a2),a1))
| c(f(f(f(a2,a2),a1),a2)) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
c(f(f(f(a2,a2),a1),a2)),
inference(unit_resolution,[status(thm)],[82,30,27,57]) ).
tff(84,plain,
( c(f(a2,f(a2,a1)))
<=> c(f(f(a2,a2),a1)) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(85,plain,
( c(f(f(a2,a2),a1))
<=> c(f(a2,f(a2,a1))) ),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
( ~ c(f(f(a2,a2),a1))
<=> ~ c(f(a2,f(a2,a1))) ),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
( ( ~ ! [X: $i] :
( ~ c(X)
| ~ d(X) )
| ~ c(f(f(a2,a2),a1))
| ~ d(f(f(a2,a2),a1)) )
<=> ( ~ ! [X: $i] :
( ~ c(X)
| ~ d(X) )
| ~ c(f(f(a2,a2),a1))
| ~ d(f(f(a2,a2),a1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ~ ! [X: $i] :
( ~ c(X)
| ~ d(X) )
| ~ c(f(f(a2,a2),a1))
| ~ d(f(f(a2,a2),a1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
( ~ ! [X: $i] :
( ~ c(X)
| ~ d(X) )
| ~ c(f(f(a2,a2),a1))
| ~ d(f(f(a2,a2),a1)) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
~ c(f(f(a2,a2),a1)),
inference(unit_resolution,[status(thm)],[89,71,57]) ).
tff(91,plain,
~ c(f(a2,f(a2,a1))),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(a2)
| ~ d(f(a2,a1))
| c(f(a2,f(a2,a1))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(a2)
| ~ d(f(a2,a1))
| c(f(a2,f(a2,a1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(a2)
| ~ d(f(a2,a1))
| c(f(a2,f(a2,a1))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
( ~ ! [Y: $i,X: $i] :
( ~ d(X)
| ~ d(Y)
| c(f(X,Y)) )
| ~ d(a2)
| ~ d(f(a2,a1))
| c(f(a2,f(a2,a1))) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
( ~ d(f(a2,a1))
| c(f(a2,f(a2,a1))) ),
inference(unit_resolution,[status(thm)],[94,30,27]) ).
tff(96,plain,
~ d(f(a2,a1)),
inference(unit_resolution,[status(thm)],[95,91]) ).
tff(97,plain,
^ [X: $i] :
refl(( ( c(X)
| d(X) )
<=> ( c(X)
| d(X) ) )),
inference(bind,[status(th)],[]) ).
tff(98,plain,
( ! [X: $i] :
( c(X)
| d(X) )
<=> ! [X: $i] :
( c(X)
| d(X) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
( ! [X: $i] :
( c(X)
| d(X) )
<=> ! [X: $i] :
( c(X)
| d(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,axiom,
! [X: $i] :
( c(X)
| d(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_union) ).
tff(101,plain,
! [X: $i] :
( c(X)
| d(X) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
! [X: $i] :
( c(X)
| d(X) ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [X: $i] :
( c(X)
| d(X) ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
( ( ~ ! [X: $i] :
( c(X)
| d(X) )
| c(f(a2,a1))
| d(f(a2,a1)) )
<=> ( ~ ! [X: $i] :
( c(X)
| d(X) )
| c(f(a2,a1))
| d(f(a2,a1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [X: $i] :
( c(X)
| d(X) )
| c(f(a2,a1))
| d(f(a2,a1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,plain,
( ~ ! [X: $i] :
( c(X)
| d(X) )
| c(f(a2,a1))
| d(f(a2,a1)) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
c(f(a2,a1)),
inference(unit_resolution,[status(thm)],[106,103,96]) ).
tff(108,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
| ~ c(f(a2,a1))
| ~ c(f(f(f(a2,a2),a1),a2))
| d(f(f(f(f(a2,a2),a1),a2),f(a2,a1))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
| ~ c(f(a2,a1))
| ~ c(f(f(f(a2,a2),a1),a2))
| d(f(f(f(f(a2,a2),a1),a2),f(a2,a1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(109,plain,
( ( ~ c(f(f(f(a2,a2),a1),a2))
| ~ c(f(a2,a1))
| d(f(f(f(f(a2,a2),a1),a2),f(a2,a1))) )
<=> ( ~ c(f(a2,a1))
| ~ c(f(f(f(a2,a2),a1),a2))
| d(f(f(f(f(a2,a2),a1),a2),f(a2,a1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
| ~ c(f(f(f(a2,a2),a1),a2))
| ~ c(f(a2,a1))
| d(f(f(f(f(a2,a2),a1),a2),f(a2,a1))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
| ~ c(f(a2,a1))
| ~ c(f(f(f(a2,a2),a1),a2))
| d(f(f(f(f(a2,a2),a1),a2),f(a2,a1))) ) ),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
| ~ c(f(f(f(a2,a2),a1),a2))
| ~ c(f(a2,a1))
| d(f(f(f(f(a2,a2),a1),a2),f(a2,a1))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
| ~ c(f(a2,a1))
| ~ c(f(f(f(a2,a2),a1),a2))
| d(f(f(f(f(a2,a2),a1),a2),f(a2,a1))) ) ),
inference(transitivity,[status(thm)],[110,108]) ).
tff(112,plain,
( ~ ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
| ~ c(f(f(f(a2,a2),a1),a2))
| ~ c(f(a2,a1))
| d(f(f(f(f(a2,a2),a1),a2),f(a2,a1))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
( ~ ! [Y: $i,X: $i] :
( ~ c(X)
| ~ c(Y)
| d(f(X,Y)) )
| ~ c(f(a2,a1))
| ~ c(f(f(f(a2,a2),a1),a2))
| d(f(f(f(f(a2,a2),a1),a2),f(a2,a1))) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
( ~ c(f(f(f(a2,a2),a1),a2))
| d(f(f(f(f(a2,a2),a1),a2),f(a2,a1))) ),
inference(unit_resolution,[status(thm)],[113,47,107]) ).
tff(115,plain,
d(f(f(f(f(a2,a2),a1),a2),f(a2,a1))),
inference(unit_resolution,[status(thm)],[114,83]) ).
tff(116,plain,
$false,
inference(unit_resolution,[status(thm)],[115,76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG011-1 : TPTP v9.0.0. Released v2.7.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 10:41:55 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% See solution above
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------