%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV558-1.004 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:35:34 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 58
% Syntax : Number of formulae : 184 ( 146 unt; 0 typ; 0 def)
% Number of atoms : 224 ( 222 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 59 ( 20 ~; 16 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 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 : 24 ( 24 usr; 22 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(e_18_type,type,
e_18: $i ).
tff(i2_type,type,
i2: $i ).
tff(e_22_type,type,
e_22: $i ).
tff(a_19_type,type,
a_19: $i ).
tff(a_17_type,type,
a_17: $i ).
tff(e_16_type,type,
e_16: $i ).
tff(e_20_type,type,
e_20: $i ).
tff(i3_type,type,
i3: $i ).
tff(e_24_type,type,
e_24: $i ).
tff(a_21_type,type,
a_21: $i ).
tff(a_23_type,type,
a_23: $i ).
tff(e_26_type,type,
e_26: $i ).
tff(i4_type,type,
i4: $i ).
tff(e_30_type,type,
e_30: $i ).
tff(a_27_type,type,
a_27: $i ).
tff(a_25_type,type,
a_25: $i ).
tff(e_28_type,type,
e_28: $i ).
tff(a_29_type,type,
a_29: $i ).
tff(a_31_type,type,
a_31: $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,
( ( e_18 = select(a1,i1) )
<=> ( e_18 = select(a1,i1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
e_18 = select(a1,i1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp9) ).
tff(12,plain,
e_18 = select(a1,i1),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
select(a1,i1) = e_18,
inference(symmetry,[status(thm)],[12]) ).
tff(14,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(15,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(16,axiom,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
tff(17,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,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(21,plain,
select(store(a2,i1,select(a1,i1)),i1) = select(a1,i1),
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
store(a2,i1,select(a1,i1)) = store(a2,i1,e_18),
inference(monotonicity,[status(thm)],[13]) ).
tff(23,plain,
store(a2,i1,e_18) = store(a2,i1,select(a1,i1)),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( ~ ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A )
| ( store(store(a2,i1,e_18),i2,select(store(a2,i1,e_18),i2)) = store(a2,i1,e_18) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
store(store(a2,i1,e_18),i2,select(store(a2,i1,e_18),i2)) = store(a2,i1,e_18),
inference(unit_resolution,[status(thm)],[24,7]) ).
tff(26,plain,
( ( e_22 = select(a_17,i2) )
<=> ( e_22 = select(a_17,i2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
e_22 = select(a_17,i2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp11) ).
tff(28,plain,
e_22 = select(a_17,i2),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
select(a_17,i2) = e_22,
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(a2,i1,e_18),i2,select(a_17,i2)),i2) = select(a_17,i2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
select(store(store(a2,i1,e_18),i2,select(a_17,i2)),i2) = select(a_17,i2),
inference(unit_resolution,[status(thm)],[30,19]) ).
tff(32,plain,
( ( e_20 = select(a_19,i2) )
<=> ( e_20 = select(a_19,i2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
e_20 = select(a_19,i2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp10) ).
tff(34,plain,
e_20 = select(a_19,i2),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
select(a_19,i2) = e_20,
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
( ( a_17 = store(a1,i1,e_16) )
<=> ( a_17 = store(a1,i1,e_16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
a_17 = store(a1,i1,e_16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp0) ).
tff(38,plain,
a_17 = store(a1,i1,e_16),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
store(a1,i1,e_16) = a_17,
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
store(store(a1,i1,e_16),i2,select(a_19,i2)) = store(a_17,i2,e_20),
inference(monotonicity,[status(thm)],[39,35]) ).
tff(41,plain,
store(a_17,i2,e_20) = store(store(a1,i1,e_16),i2,select(a_19,i2)),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A )
| ( store(store(a_17,i2,e_20),i3,select(store(a_17,i2,e_20),i3)) = store(a_17,i2,e_20) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
store(store(a_17,i2,e_20),i3,select(store(a_17,i2,e_20),i3)) = store(a_17,i2,e_20),
inference(unit_resolution,[status(thm)],[42,7]) ).
tff(44,plain,
( ( e_24 = select(a_23,i3) )
<=> ( e_24 = select(a_23,i3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
e_24 = select(a_23,i3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp12) ).
tff(46,plain,
e_24 = select(a_23,i3),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
select(a_23,i3) = e_24,
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(a_17,i2,e_20),i3,select(a_23,i3)),i3) = select(a_23,i3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
select(store(store(a_17,i2,e_20),i3,select(a_23,i3)),i3) = select(a_23,i3),
inference(unit_resolution,[status(thm)],[48,19]) ).
tff(50,plain,
( ( e_26 = select(a_21,i3) )
<=> ( e_26 = select(a_21,i3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
e_26 = select(a_21,i3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp13) ).
tff(52,plain,
e_26 = select(a_21,i3),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
select(a_21,i3) = e_26,
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
( ( a_23 = store(a_19,i2,e_22) )
<=> ( a_23 = store(a_19,i2,e_22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
a_23 = store(a_19,i2,e_22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp3) ).
tff(56,plain,
a_23 = store(a_19,i2,e_22),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
store(a_19,i2,e_22) = a_23,
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
store(store(a_19,i2,e_22),i3,select(a_21,i3)) = store(a_23,i3,e_26),
inference(monotonicity,[status(thm)],[57,53]) ).
tff(59,plain,
store(a_23,i3,e_26) = store(store(a_19,i2,e_22),i3,select(a_21,i3)),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
( ~ ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A )
| ( store(store(a_23,i3,e_26),i4,select(store(a_23,i3,e_26),i4)) = store(a_23,i3,e_26) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
store(store(a_23,i3,e_26),i4,select(store(a_23,i3,e_26),i4)) = store(a_23,i3,e_26),
inference(unit_resolution,[status(thm)],[60,7]) ).
tff(62,plain,
( ( e_30 = select(a_25,i4) )
<=> ( e_30 = select(a_25,i4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
e_30 = select(a_25,i4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp15) ).
tff(64,plain,
e_30 = select(a_25,i4),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
select(a_25,i4) = e_30,
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(a_23,i3,e_26),i4,select(a_25,i4)),i4) = select(a_25,i4) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
select(store(store(a_23,i3,e_26),i4,select(a_25,i4)),i4) = select(a_25,i4),
inference(unit_resolution,[status(thm)],[66,19]) ).
tff(68,plain,
( ( e_28 = select(a_27,i4) )
<=> ( e_28 = select(a_27,i4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
e_28 = select(a_27,i4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp14) ).
tff(70,plain,
e_28 = select(a_27,i4),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
select(a_27,i4) = e_28,
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( ( a_25 = store(a_21,i3,e_24) )
<=> ( a_25 = store(a_21,i3,e_24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
a_25 = store(a_21,i3,e_24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp4) ).
tff(74,plain,
a_25 = store(a_21,i3,e_24),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
store(a_21,i3,e_24) = a_25,
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
store(store(a_21,i3,e_24),i4,select(a_27,i4)) = store(a_25,i4,e_28),
inference(monotonicity,[status(thm)],[75,71]) ).
tff(77,plain,
store(a_25,i4,e_28) = store(store(a_21,i3,e_24),i4,select(a_27,i4)),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
( ( a_29 = store(a_25,i4,e_28) )
<=> ( a_29 = store(a_25,i4,e_28) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,axiom,
a_29 = store(a_25,i4,e_28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp6) ).
tff(80,plain,
a_29 = store(a_25,i4,e_28),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
( ( a_29 = a_31 )
<=> ( a_29 = a_31 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,axiom,
a_29 = a_31,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp16) ).
tff(83,plain,
a_29 = a_31,
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
a_31 = a_29,
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
( ( a_31 = store(a_27,i4,e_30) )
<=> ( a_31 = store(a_27,i4,e_30) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,axiom,
a_31 = store(a_27,i4,e_30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp7) ).
tff(87,plain,
a_31 = store(a_27,i4,e_30),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
store(a_27,i4,e_30) = a_31,
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( ( a_27 = store(a_23,i3,e_26) )
<=> ( a_27 = store(a_23,i3,e_26) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,axiom,
a_27 = store(a_23,i3,e_26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp5) ).
tff(91,plain,
a_27 = store(a_23,i3,e_26),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
store(a_23,i3,e_26) = a_27,
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
store(store(a_23,i3,e_26),i4,select(a_25,i4)) = store(a_27,i4,e_30),
inference(monotonicity,[status(thm)],[92,65]) ).
tff(94,plain,
store(store(a_23,i3,e_26),i4,select(a_25,i4)) = store(store(a_21,i3,e_24),i4,select(a_27,i4)),
inference(transitivity,[status(thm)],[93,88,84,80,77]) ).
tff(95,plain,
select(store(store(a_23,i3,e_26),i4,select(a_25,i4)),i4) = select(store(store(a_21,i3,e_24),i4,select(a_27,i4)),i4),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
select(store(store(a_21,i3,e_24),i4,select(a_27,i4)),i4) = select(store(store(a_23,i3,e_26),i4,select(a_25,i4)),i4),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(a_21,i3,e_24),i4,select(a_27,i4)),i4) = select(a_27,i4) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
select(store(store(a_21,i3,e_24),i4,select(a_27,i4)),i4) = select(a_27,i4),
inference(unit_resolution,[status(thm)],[97,19]) ).
tff(99,plain,
select(a_27,i4) = select(store(store(a_21,i3,e_24),i4,select(a_27,i4)),i4),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
select(store(a_23,i3,e_26),i4) = select(a_27,i4),
inference(monotonicity,[status(thm)],[92]) ).
tff(101,plain,
select(store(a_23,i3,e_26),i4) = e_30,
inference(transitivity,[status(thm)],[100,99,96,67,65]) ).
tff(102,plain,
store(store(a_23,i3,e_26),i4,select(store(a_23,i3,e_26),i4)) = store(a_27,i4,e_30),
inference(monotonicity,[status(thm)],[92,101]) ).
tff(103,plain,
store(a_27,i4,e_30) = store(store(a_23,i3,e_26),i4,select(store(a_23,i3,e_26),i4)),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
store(a_25,i4,e_28) = a_29,
inference(symmetry,[status(thm)],[80]) ).
tff(105,plain,
select(a_25,i4) = select(store(store(a_23,i3,e_26),i4,select(a_25,i4)),i4),
inference(symmetry,[status(thm)],[67]) ).
tff(106,plain,
select(store(a_21,i3,e_24),i4) = select(a_25,i4),
inference(monotonicity,[status(thm)],[75]) ).
tff(107,plain,
select(store(a_21,i3,e_24),i4) = e_28,
inference(transitivity,[status(thm)],[106,105,95,98,71]) ).
tff(108,plain,
store(store(a_21,i3,e_24),i4,select(store(a_21,i3,e_24),i4)) = store(a_25,i4,e_28),
inference(monotonicity,[status(thm)],[75,107]) ).
tff(109,plain,
( ~ ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A )
| ( store(store(a_21,i3,e_24),i4,select(store(a_21,i3,e_24),i4)) = store(a_21,i3,e_24) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
store(store(a_21,i3,e_24),i4,select(store(a_21,i3,e_24),i4)) = store(a_21,i3,e_24),
inference(unit_resolution,[status(thm)],[109,7]) ).
tff(111,plain,
store(a_21,i3,e_24) = store(store(a_21,i3,e_24),i4,select(store(a_21,i3,e_24),i4)),
inference(symmetry,[status(thm)],[110]) ).
tff(112,plain,
( ( a_21 = store(a_17,i2,e_20) )
<=> ( a_21 = store(a_17,i2,e_20) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,axiom,
a_21 = store(a_17,i2,e_20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp2) ).
tff(114,plain,
a_21 = store(a_17,i2,e_20),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
store(a_17,i2,e_20) = a_21,
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
store(store(a_17,i2,e_20),i3,select(a_23,i3)) = store(a_21,i3,e_24),
inference(monotonicity,[status(thm)],[115,47]) ).
tff(117,plain,
store(store(a_17,i2,e_20),i3,select(a_23,i3)) = store(store(a_19,i2,e_22),i3,select(a_21,i3)),
inference(transitivity,[status(thm)],[116,111,108,104,83,87,103,61,59]) ).
tff(118,plain,
select(store(store(a_17,i2,e_20),i3,select(a_23,i3)),i3) = select(store(store(a_19,i2,e_22),i3,select(a_21,i3)),i3),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
select(store(store(a_19,i2,e_22),i3,select(a_21,i3)),i3) = select(store(store(a_17,i2,e_20),i3,select(a_23,i3)),i3),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(a_19,i2,e_22),i3,select(a_21,i3)),i3) = select(a_21,i3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
select(store(store(a_19,i2,e_22),i3,select(a_21,i3)),i3) = select(a_21,i3),
inference(unit_resolution,[status(thm)],[120,19]) ).
tff(122,plain,
select(a_21,i3) = select(store(store(a_19,i2,e_22),i3,select(a_21,i3)),i3),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
select(store(a_17,i2,e_20),i3) = select(a_21,i3),
inference(monotonicity,[status(thm)],[115]) ).
tff(124,plain,
select(store(a_17,i2,e_20),i3) = e_24,
inference(transitivity,[status(thm)],[123,122,119,49,47]) ).
tff(125,plain,
store(store(a_17,i2,e_20),i3,select(store(a_17,i2,e_20),i3)) = store(a_21,i3,e_24),
inference(monotonicity,[status(thm)],[115,124]) ).
tff(126,plain,
store(a_21,i3,e_24) = store(store(a_17,i2,e_20),i3,select(store(a_17,i2,e_20),i3)),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
store(a_25,i4,e_28) = store(store(a_21,i3,e_24),i4,select(store(a_21,i3,e_24),i4)),
inference(symmetry,[status(thm)],[108]) ).
tff(128,plain,
store(a_23,i3,e_26) = store(store(a_23,i3,e_26),i4,select(store(a_23,i3,e_26),i4)),
inference(symmetry,[status(thm)],[61]) ).
tff(129,plain,
select(a_23,i3) = select(store(store(a_17,i2,e_20),i3,select(a_23,i3)),i3),
inference(symmetry,[status(thm)],[49]) ).
tff(130,plain,
select(store(a_19,i2,e_22),i3) = select(a_23,i3),
inference(monotonicity,[status(thm)],[57]) ).
tff(131,plain,
select(store(a_19,i2,e_22),i3) = e_26,
inference(transitivity,[status(thm)],[130,129,118,121,53]) ).
tff(132,plain,
store(store(a_19,i2,e_22),i3,select(store(a_19,i2,e_22),i3)) = store(a_23,i3,e_26),
inference(monotonicity,[status(thm)],[57,131]) ).
tff(133,plain,
( ~ ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A )
| ( store(store(a_19,i2,e_22),i3,select(store(a_19,i2,e_22),i3)) = store(a_19,i2,e_22) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
store(store(a_19,i2,e_22),i3,select(store(a_19,i2,e_22),i3)) = store(a_19,i2,e_22),
inference(unit_resolution,[status(thm)],[133,7]) ).
tff(135,plain,
store(a_19,i2,e_22) = store(store(a_19,i2,e_22),i3,select(store(a_19,i2,e_22),i3)),
inference(symmetry,[status(thm)],[134]) ).
tff(136,plain,
( ( a_19 = store(a2,i1,e_18) )
<=> ( a_19 = store(a2,i1,e_18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(137,axiom,
a_19 = store(a2,i1,e_18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp1) ).
tff(138,plain,
a_19 = store(a2,i1,e_18),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
store(a2,i1,e_18) = a_19,
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
store(store(a2,i1,e_18),i2,select(a_17,i2)) = store(a_19,i2,e_22),
inference(monotonicity,[status(thm)],[139,29]) ).
tff(141,plain,
store(store(a2,i1,e_18),i2,select(a_17,i2)) = store(store(a1,i1,e_16),i2,select(a_19,i2)),
inference(transitivity,[status(thm)],[140,135,132,128,102,88,84,80,127,110,126,43,41]) ).
tff(142,plain,
select(store(store(a2,i1,e_18),i2,select(a_17,i2)),i2) = select(store(store(a1,i1,e_16),i2,select(a_19,i2)),i2),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
select(store(store(a1,i1,e_16),i2,select(a_19,i2)),i2) = select(store(store(a2,i1,e_18),i2,select(a_17,i2)),i2),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(a1,i1,e_16),i2,select(a_19,i2)),i2) = select(a_19,i2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
select(store(store(a1,i1,e_16),i2,select(a_19,i2)),i2) = select(a_19,i2),
inference(unit_resolution,[status(thm)],[144,19]) ).
tff(146,plain,
select(a_19,i2) = select(store(store(a1,i1,e_16),i2,select(a_19,i2)),i2),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
select(store(a2,i1,e_18),i2) = select(a_19,i2),
inference(monotonicity,[status(thm)],[139]) ).
tff(148,plain,
select(store(a2,i1,e_18),i2) = e_22,
inference(transitivity,[status(thm)],[147,146,143,31,29]) ).
tff(149,plain,
store(store(a2,i1,e_18),i2,select(store(a2,i1,e_18),i2)) = store(a_19,i2,e_22),
inference(monotonicity,[status(thm)],[139,148]) ).
tff(150,plain,
store(a_19,i2,e_22) = store(store(a2,i1,e_18),i2,select(store(a2,i1,e_18),i2)),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
store(a_23,i3,e_26) = store(store(a_19,i2,e_22),i3,select(store(a_19,i2,e_22),i3)),
inference(symmetry,[status(thm)],[132]) ).
tff(152,plain,
store(a_17,i2,e_20) = store(store(a_17,i2,e_20),i3,select(store(a_17,i2,e_20),i3)),
inference(symmetry,[status(thm)],[43]) ).
tff(153,plain,
select(a_17,i2) = select(store(store(a2,i1,e_18),i2,select(a_17,i2)),i2),
inference(symmetry,[status(thm)],[31]) ).
tff(154,plain,
select(store(a1,i1,e_16),i2) = select(a_17,i2),
inference(monotonicity,[status(thm)],[39]) ).
tff(155,plain,
select(store(a1,i1,e_16),i2) = e_20,
inference(transitivity,[status(thm)],[154,153,142,145,35]) ).
tff(156,plain,
store(store(a1,i1,e_16),i2,select(store(a1,i1,e_16),i2)) = store(a_17,i2,e_20),
inference(monotonicity,[status(thm)],[39,155]) ).
tff(157,plain,
( ~ ! [I: $i,A: $i] : ( store(A,I,select(A,I)) = A )
| ( store(store(a1,i1,e_16),i2,select(store(a1,i1,e_16),i2)) = store(a1,i1,e_16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(158,plain,
store(store(a1,i1,e_16),i2,select(store(a1,i1,e_16),i2)) = store(a1,i1,e_16),
inference(unit_resolution,[status(thm)],[157,7]) ).
tff(159,plain,
store(a1,i1,e_16) = store(store(a1,i1,e_16),i2,select(store(a1,i1,e_16),i2)),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
( ( e_16 = select(a2,i1) )
<=> ( e_16 = select(a2,i1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(161,axiom,
e_16 = select(a2,i1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp8) ).
tff(162,plain,
e_16 = select(a2,i1),
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
select(a2,i1) = e_16,
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
store(a1,i1,select(a2,i1)) = store(a1,i1,e_16),
inference(monotonicity,[status(thm)],[163]) ).
tff(165,plain,
store(a1,i1,select(a2,i1)) = store(a2,i1,select(a1,i1)),
inference(transitivity,[status(thm)],[164,159,156,152,125,111,108,104,83,87,103,61,151,134,150,25,23]) ).
tff(166,plain,
select(store(a1,i1,select(a2,i1)),i1) = select(store(a2,i1,select(a1,i1)),i1),
inference(monotonicity,[status(thm)],[165]) ).
tff(167,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(168,plain,
select(store(a1,i1,select(a2,i1)),i1) = select(a2,i1),
inference(unit_resolution,[status(thm)],[167,19]) ).
tff(169,plain,
select(a2,i1) = select(store(a1,i1,select(a2,i1)),i1),
inference(symmetry,[status(thm)],[168]) ).
tff(170,plain,
select(a2,i1) = e_18,
inference(transitivity,[status(thm)],[169,166,21,13]) ).
tff(171,plain,
store(a2,i1,select(a2,i1)) = store(a2,i1,e_18),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
store(a2,i1,e_18) = store(a2,i1,select(a2,i1)),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
select(store(a2,i1,select(a1,i1)),i1) = select(store(a1,i1,select(a2,i1)),i1),
inference(symmetry,[status(thm)],[166]) ).
tff(174,plain,
select(a1,i1) = select(store(a2,i1,select(a1,i1)),i1),
inference(symmetry,[status(thm)],[21]) ).
tff(175,plain,
select(a1,i1) = e_16,
inference(transitivity,[status(thm)],[174,173,168,163]) ).
tff(176,plain,
store(a1,i1,select(a1,i1)) = store(a1,i1,e_16),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,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(178,plain,
store(a1,i1,select(a1,i1)) = a1,
inference(unit_resolution,[status(thm)],[177,7]) ).
tff(179,plain,
a1 = store(a1,i1,select(a1,i1)),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
a1 = a2,
inference(transitivity,[status(thm)],[179,176,159,156,152,125,111,108,104,83,87,103,61,151,134,150,25,172,9]) ).
tff(181,plain,
( ( a1 != a2 )
<=> ( a1 != a2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(182,axiom,
a1 != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(183,plain,
a1 != a2,
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
$false,
inference(unit_resolution,[status(thm)],[183,180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV558-1.004 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 10:19:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% See solution above
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------