%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV557-1.004 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:35:31 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 26
% Syntax : Number of formulae : 98 ( 76 unt; 0 typ; 0 def)
% Number of atoms : 122 ( 120 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 43 ( 20 ~; 16 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 10 ( 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 : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 82 ( 80 !; 0 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
tff(a2_type,type,
a2: $i ).
tff(a1_type,type,
a1: $i ).
tff(store_type,type,
store: ( $i * $i * $i ) > $i ).
tff(select_type,type,
select: ( $i * $i ) > $i ).
tff(i1_type,type,
i1: $i ).
tff(i2_type,type,
i2: $i ).
tff(i3_type,type,
i3: $i ).
tff(i4_type,type,
i4: $i ).
tff(1,plain,
^ [I: $i,A: $i] :
refl(( ( store(A,I,select(A,I)) = A )
<=> ( store(A,I,select(A,I)) = A ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A )
<=> ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A )
<=> ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
tff(5,plain,
! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A )
| ( store(a2,i1,select(a2,i1)) = a2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
store(a2,i1,select(a2,i1)) = a2,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
<=> ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
( ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
<=> ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
tff(13,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(a2,i1,select(a1,i1)),i1) = select(a1,i1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
select(store(a2,i1,select(a1,i1)),i1) = select(a1,i1),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
( ~ ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A )
| ( store(store(a2,i1,select(a1,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)) = store(a2,i1,select(a1,i1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
store(store(a2,i1,select(a1,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)) = store(a2,i1,select(a1,i1)),
inference(unit_resolution,[status(thm)],[18,7]) ).
tff(20,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i2) = select(store(a1,i1,select(a2,i1)),i2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i2) = select(store(a1,i1,select(a2,i1)),i2),
inference(unit_resolution,[status(thm)],[20,15]) ).
tff(22,plain,
( ~ ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A )
| ( store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)) = store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)) = store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),
inference(unit_resolution,[status(thm)],[22,7]) ).
tff(24,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i3) = select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i3) = select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3),
inference(unit_resolution,[status(thm)],[24,15]) ).
tff(26,plain,
( ~ ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A )
| ( store(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4,select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4)) = store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
store(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4,select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4)) = store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),
inference(unit_resolution,[status(thm)],[26,7]) ).
tff(28,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4,select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4)),i4) = select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
select(store(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4,select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4)),i4) = select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4),
inference(unit_resolution,[status(thm)],[28,15]) ).
tff(30,plain,
( ( store(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4,select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4)) = store(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4,select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4)) )
<=> ( store(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4,select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4)) = store(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4,select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
store(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4,select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4)) = store(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4,select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp0) ).
tff(32,plain,
store(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4,select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4)) = store(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4,select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4)),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
store(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4,select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4)) = store(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4,select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4)),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
select(store(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4,select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4)),i4) = select(store(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4,select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4)),i4),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4,select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4)),i4) = select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
select(store(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4,select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4)),i4) = select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4),
inference(unit_resolution,[status(thm)],[35,15]) ).
tff(37,plain,
select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4) = select(store(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4,select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4)),i4),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4) = select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4),
inference(transitivity,[status(thm)],[37,34,29]) ).
tff(39,plain,
store(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4,select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4)) = store(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4,select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4)),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
store(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4,select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4)) = store(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4,select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4)),
inference(monotonicity,[status(thm)],[38]) ).
tff(41,plain,
( ~ ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A )
| ( store(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4,select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4)) = store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
store(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4,select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4)) = store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),
inference(unit_resolution,[status(thm)],[41,7]) ).
tff(43,plain,
store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)) = store(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4,select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4)),
inference(symmetry,[status(thm)],[42]) ).
tff(44,plain,
store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)) = store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),
inference(transitivity,[status(thm)],[43,40,32,39,27]) ).
tff(45,plain,
select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i3) = select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i3),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i3) = select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i3),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i3) = select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i3) = select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3),
inference(unit_resolution,[status(thm)],[47,15]) ).
tff(49,plain,
select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3) = select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i3),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3) = select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3),
inference(transitivity,[status(thm)],[49,46,25]) ).
tff(51,plain,
store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)) = store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)) = store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
store(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4,select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4)) = store(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4,select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4)),
inference(symmetry,[status(thm)],[40]) ).
tff(54,plain,
store(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4,select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4)) = store(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4,select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i4)),
inference(symmetry,[status(thm)],[39]) ).
tff(55,plain,
store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)) = store(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4,select(store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),i4)),
inference(symmetry,[status(thm)],[27]) ).
tff(56,plain,
select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3) = select(store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),i3),
inference(symmetry,[status(thm)],[25]) ).
tff(57,plain,
select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3) = select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3),
inference(transitivity,[status(thm)],[56,45,48]) ).
tff(58,plain,
store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)) = store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ~ ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A )
| ( store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)) = store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)) = store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),
inference(unit_resolution,[status(thm)],[59,7]) ).
tff(61,plain,
store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)) = store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)) = store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),
inference(transitivity,[status(thm)],[61,58,55,54,33,53,42,52,23]) ).
tff(63,plain,
select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i2) = select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i2),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i2) = select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i2),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i2) = select(store(a2,i1,select(a1,i1)),i2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i2) = select(store(a2,i1,select(a1,i1)),i2),
inference(unit_resolution,[status(thm)],[65,15]) ).
tff(67,plain,
select(store(a2,i1,select(a1,i1)),i2) = select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i2),
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
select(store(a2,i1,select(a1,i1)),i2) = select(store(a1,i1,select(a2,i1)),i2),
inference(transitivity,[status(thm)],[67,64,21]) ).
tff(69,plain,
store(store(a2,i1,select(a1,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)) = store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)) = store(store(a2,i1,select(a1,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)) = store(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3,select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i3)),
inference(symmetry,[status(thm)],[58]) ).
tff(72,plain,
store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)) = store(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3,select(store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),i3)),
inference(symmetry,[status(thm)],[23]) ).
tff(73,plain,
select(store(a1,i1,select(a2,i1)),i2) = select(store(store(a2,i1,select(a1,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),i2),
inference(symmetry,[status(thm)],[21]) ).
tff(74,plain,
select(store(a1,i1,select(a2,i1)),i2) = select(store(a2,i1,select(a1,i1)),i2),
inference(transitivity,[status(thm)],[73,63,66]) ).
tff(75,plain,
store(store(a1,i1,select(a2,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)) = store(store(a1,i1,select(a2,i1)),i2,select(store(a2,i1,select(a1,i1)),i2)),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ~ ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A )
| ( store(store(a1,i1,select(a2,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)) = store(a1,i1,select(a2,i1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
store(store(a1,i1,select(a2,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)) = store(a1,i1,select(a2,i1)),
inference(unit_resolution,[status(thm)],[76,7]) ).
tff(78,plain,
store(a1,i1,select(a2,i1)) = store(store(a1,i1,select(a2,i1)),i2,select(store(a1,i1,select(a2,i1)),i2)),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
store(a1,i1,select(a2,i1)) = store(a2,i1,select(a1,i1)),
inference(transitivity,[status(thm)],[78,75,72,51,43,40,32,39,27,71,60,70,19]) ).
tff(80,plain,
select(store(a1,i1,select(a2,i1)),i1) = select(store(a2,i1,select(a1,i1)),i1),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(a1,i1,select(a2,i1)),i1) = select(a2,i1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
select(store(a1,i1,select(a2,i1)),i1) = select(a2,i1),
inference(unit_resolution,[status(thm)],[81,15]) ).
tff(83,plain,
select(a2,i1) = select(store(a1,i1,select(a2,i1)),i1),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
select(a2,i1) = select(a1,i1),
inference(transitivity,[status(thm)],[83,80,17]) ).
tff(85,plain,
store(a2,i1,select(a2,i1)) = store(a2,i1,select(a1,i1)),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
store(a2,i1,select(a1,i1)) = store(a2,i1,select(a2,i1)),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
select(store(a2,i1,select(a1,i1)),i1) = select(store(a1,i1,select(a2,i1)),i1),
inference(symmetry,[status(thm)],[80]) ).
tff(88,plain,
select(a1,i1) = select(store(a2,i1,select(a1,i1)),i1),
inference(symmetry,[status(thm)],[17]) ).
tff(89,plain,
select(a1,i1) = select(a2,i1),
inference(transitivity,[status(thm)],[88,87,82]) ).
tff(90,plain,
store(a1,i1,select(a1,i1)) = store(a1,i1,select(a2,i1)),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ~ ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A )
| ( store(a1,i1,select(a1,i1)) = a1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
store(a1,i1,select(a1,i1)) = a1,
inference(unit_resolution,[status(thm)],[91,7]) ).
tff(93,plain,
a1 = store(a1,i1,select(a1,i1)),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
a1 = a2,
inference(transitivity,[status(thm)],[93,90,78,75,72,51,43,40,32,39,27,71,60,70,19,86,9]) ).
tff(95,plain,
( ( a1 != a2 )
<=> ( a1 != a2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,axiom,
a1 != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(97,plain,
a1 != a2,
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
$false,
inference(unit_resolution,[status(thm)],[97,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV557-1.004 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 10:20:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.36 % SZS status Unsatisfiable
% 0.12/0.36 % SZS output start Proof
% See solution above
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------