TSTP Solution File: RNG090+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG090+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 : Tue Sep 20 03:18:21 EDT 2022
% Result : Theorem 1.02s 0.90s
% Output : Proof 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 78
% Syntax : Number of formulae : 179 ( 49 unt; 14 typ; 0 def)
% Number of atoms : 1008 ( 157 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 1365 ( 585 ~; 542 |; 105 &)
% ( 88 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 63 ( 63 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 6 >; 3 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 332 ( 307 !; 0 ?; 332 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(xl_type,type,
xl: $i ).
tff(xm_type,type,
xm: $i ).
tff(xk_type,type,
xk: $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xI_type,type,
xI: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(aIdeal0_type,type,
aIdeal0: $i > $o ).
tff(xJ_type,type,
xJ: $i ).
tff(xx_type,type,
xx: $i ).
tff(xy_type,type,
xy: $i ).
tff(1,plain,
( aSet0(xI)
<=> aSet0(xI) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [W0: $i] :
( aElementOf0(W0,xJ)
=> ( ! [W1: $i] :
( aElementOf0(W1,xJ)
=> aElementOf0(sdtpldt0(W0,W1),xJ) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xJ) ) ) )
& aIdeal0(xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
tff(3,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [W0: $i] :
( aElementOf0(W0,xJ)
=> ( ! [W1: $i] :
( aElementOf0(W1,xJ)
=> aElementOf0(sdtpldt0(W0,W1),xJ) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xJ) ) ) ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ) ),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI) ),
inference(and_elim,[status(thm)],[4]) ).
tff(6,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) ),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
aSet0(xI),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
aSet0(xI),
inference(modus_ponens,[status(thm)],[7,1]) ).
tff(9,plain,
^ [W0: $i] :
refl(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(transitivity,[status(thm)],[12,10]) ).
tff(14,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
rewrite(
( ( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
rewrite(
( ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
tff(18,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[20,13]) ).
tff(22,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xI)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xI)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xI)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xI)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ),
inference(unit_resolution,[status(thm)],[24,21,8]) ).
tff(26,plain,
( aElementOf0(xk,xI)
<=> aElementOf0(xk,xI) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& ( xx = sdtpldt0(xk,xl) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__934) ).
tff(28,plain,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ) ),
inference(and_elim,[status(thm)],[27]) ).
tff(29,plain,
aElementOf0(xk,xI),
inference(and_elim,[status(thm)],[28]) ).
tff(30,plain,
aElementOf0(xk,xI),
inference(modus_ponens,[status(thm)],[29,26]) ).
tff(31,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xk)
| ~ aElementOf0(xk,xI) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xk)
| ~ aElementOf0(xk,xI) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xk)
| ~ aElementOf0(xk,xI) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xk)
| ~ aElementOf0(xk,xI) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
aElement0(xk),
inference(unit_resolution,[status(thm)],[33,30,25]) ).
tff(35,plain,
( aSet0(xJ)
<=> aSet0(xJ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
aSet0(xJ),
inference(and_elim,[status(thm)],[4]) ).
tff(37,plain,
aSet0(xJ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xJ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xJ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xJ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xJ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ),
inference(unit_resolution,[status(thm)],[40,21,37]) ).
tff(42,plain,
( aElementOf0(sdtpldt0(xl,xn),xJ)
<=> aElementOf0(sdtpldt0(xl,xn),xJ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
( aElementOf0(sdtpldt0(xk,xm),xI)
& aElementOf0(sdtpldt0(xl,xn),xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__994) ).
tff(44,plain,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(and_elim,[status(thm)],[43]) ).
tff(45,plain,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(modus_ponens,[status(thm)],[44,42]) ).
tff(46,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(sdtpldt0(xl,xn))
| ~ aElementOf0(sdtpldt0(xl,xn),xJ) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(sdtpldt0(xl,xn))
| ~ aElementOf0(sdtpldt0(xl,xn),xJ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(sdtpldt0(xl,xn))
| ~ aElementOf0(sdtpldt0(xl,xn),xJ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(sdtpldt0(xl,xn))
| ~ aElementOf0(sdtpldt0(xl,xn),xJ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
aElement0(sdtpldt0(xl,xn)),
inference(unit_resolution,[status(thm)],[48,45,41]) ).
tff(50,plain,
( aElementOf0(xm,xI)
<=> aElementOf0(xm,xI) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
( aElementOf0(xm,xI)
& aElementOf0(xn,xJ)
& ( xy = sdtpldt0(xm,xn) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__967) ).
tff(52,plain,
( aElementOf0(xm,xI)
& aElementOf0(xn,xJ) ),
inference(and_elim,[status(thm)],[51]) ).
tff(53,plain,
aElementOf0(xm,xI),
inference(and_elim,[status(thm)],[52]) ).
tff(54,plain,
aElementOf0(xm,xI),
inference(modus_ponens,[status(thm)],[53,50]) ).
tff(55,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xm)
| ~ aElementOf0(xm,xI) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xm)
| ~ aElementOf0(xm,xI) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xm)
| ~ aElementOf0(xm,xI) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xm)
| ~ aElementOf0(xm,xI) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
aElement0(xm),
inference(unit_resolution,[status(thm)],[57,54,25]) ).
tff(59,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(
( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
<=> ~ ( ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
<=> ~ ~ ( ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(
( ~ ~ ( ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
<=> ( ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0)
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) )),
rewrite(
( ( ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0)
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(
monotonicity(
rewrite(
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
<=> ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) ) )),
( ( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) )),
rewrite(
( ( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) )),
( ( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
tff(67,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[70,60]) ).
tff(72,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xk)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) )
| ~ aElement0(sdtpldt0(xl,xn)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xk)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) )
| ~ aElement0(sdtpldt0(xl,xn)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ( ( sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) )
| ~ aElement0(sdtpldt0(xl,xn))
| ~ aElement0(xm)
| ~ aElement0(xk) )
<=> ( ~ aElement0(xk)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) )
| ~ aElement0(sdtpldt0(xl,xn)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) )
| ~ aElement0(sdtpldt0(xl,xn))
| ~ aElement0(xm)
| ~ aElement0(xk) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xk)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) )
| ~ aElement0(sdtpldt0(xl,xn)) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) )
| ~ aElement0(sdtpldt0(xl,xn))
| ~ aElement0(xm)
| ~ aElement0(xk) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xk)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) )
| ~ aElement0(sdtpldt0(xl,xn)) ) ),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) )
| ~ aElement0(sdtpldt0(xl,xn))
| ~ aElement0(xm)
| ~ aElement0(xk) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xk)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) )
| ~ aElement0(sdtpldt0(xl,xn)) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
( ~ aElement0(xk)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) )
| ~ aElement0(sdtpldt0(xl,xn)) ),
inference(unit_resolution,[status(thm)],[77,71]) ).
tff(79,plain,
sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) = sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))),
inference(unit_resolution,[status(thm)],[78,58,49,34]) ).
tff(80,plain,
sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
( aElementOf0(xl,xJ)
<=> aElementOf0(xl,xJ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
aElementOf0(xl,xJ),
inference(and_elim,[status(thm)],[28]) ).
tff(83,plain,
aElementOf0(xl,xJ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xl)
| ~ aElementOf0(xl,xJ) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xl)
| ~ aElementOf0(xl,xJ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xl)
| ~ aElementOf0(xl,xJ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xl)
| ~ aElementOf0(xl,xJ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
aElement0(xl),
inference(unit_resolution,[status(thm)],[86,83,41]) ).
tff(88,plain,
( aElementOf0(xn,xJ)
<=> aElementOf0(xn,xJ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
aElementOf0(xn,xJ),
inference(and_elim,[status(thm)],[52]) ).
tff(90,plain,
aElementOf0(xn,xJ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xn)
| ~ aElementOf0(xn,xJ) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xn)
| ~ aElementOf0(xn,xJ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xn)
| ~ aElementOf0(xn,xJ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xn)
| ~ aElementOf0(xn,xJ) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
aElement0(xn),
inference(unit_resolution,[status(thm)],[93,90,41]) ).
tff(95,plain,
^ [W0: $i,W1: $i] :
refl(
( ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aElement0(W0)
& aElement0(W1) )
<=> ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(
( ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(
( ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(101,plain,
( ! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,axiom,
! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(103,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[103,99]) ).
tff(105,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(skolemize,[status(sab)],[104]) ).
tff(106,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[105,98]) ).
tff(107,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[106,96]) ).
tff(108,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtpldt0(xm,xn))
| ~ aElement0(xn)
| ~ aElement0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtpldt0(xm,xn))
| ~ aElement0(xn)
| ~ aElement0(xm) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtpldt0(xm,xn))
| ~ aElement0(xn)
| ~ aElement0(xm) ),
inference(quant_inst,[status(thm)],]) ).
tff(110,plain,
( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtpldt0(xm,xn))
| ~ aElement0(xn)
| ~ aElement0(xm) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
( aElement0(sdtpldt0(xm,xn))
| ~ aElement0(xn)
| ~ aElement0(xm) ),
inference(unit_resolution,[status(thm)],[110,107]) ).
tff(112,plain,
aElement0(sdtpldt0(xm,xn)),
inference(unit_resolution,[status(thm)],[111,94,58]) ).
tff(113,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aElement0(W0)
& aElement0(W1) )
<=> ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(
( ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0)
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ) )),
rewrite(
( ( ~ aElement0(W1)
| ~ aElement0(W0)
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(116,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( aElement0(W0)
& aElement0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(119,plain,
( ! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,axiom,
! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
tff(121,plain,
! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[121,117]) ).
tff(123,plain,
! [W0: $i,W1: $i] :
( ~ ( aElement0(W0)
& aElement0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[123,116]) ).
tff(125,plain,
! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[124,114]) ).
tff(126,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(sdtpldt0(xm,xn))
| ~ aElement0(xl)
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xl,sdtpldt0(xm,xn)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(sdtpldt0(xm,xn))
| ~ aElement0(xl)
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xl,sdtpldt0(xm,xn)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
( ( ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xl,sdtpldt0(xm,xn)) )
| ~ aElement0(xl)
| ~ aElement0(sdtpldt0(xm,xn)) )
<=> ( ~ aElement0(sdtpldt0(xm,xn))
| ~ aElement0(xl)
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xl,sdtpldt0(xm,xn)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xl,sdtpldt0(xm,xn)) )
| ~ aElement0(xl)
| ~ aElement0(sdtpldt0(xm,xn)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(sdtpldt0(xm,xn))
| ~ aElement0(xl)
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xl,sdtpldt0(xm,xn)) ) ) ),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xl,sdtpldt0(xm,xn)) )
| ~ aElement0(xl)
| ~ aElement0(sdtpldt0(xm,xn)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(sdtpldt0(xm,xn))
| ~ aElement0(xl)
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xl,sdtpldt0(xm,xn)) ) ) ),
inference(transitivity,[status(thm)],[128,126]) ).
tff(130,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xl,sdtpldt0(xm,xn)) )
| ~ aElement0(xl)
| ~ aElement0(sdtpldt0(xm,xn)) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(sdtpldt0(xm,xn))
| ~ aElement0(xl)
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xl,sdtpldt0(xm,xn)) ) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xl,sdtpldt0(xm,xn)),
inference(unit_resolution,[status(thm)],[131,125,112,87]) ).
tff(133,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xm,sdtpldt0(xn,xl)) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xm,sdtpldt0(xn,xl)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
( ( ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xm,sdtpldt0(xn,xl)) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ~ aElement0(xm) )
<=> ( ~ aElement0(xl)
| ~ aElement0(xn)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xm,sdtpldt0(xn,xl)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(135,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xm,sdtpldt0(xn,xl)) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ~ aElement0(xm) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xm,sdtpldt0(xn,xl)) ) ) ),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xm,sdtpldt0(xn,xl)) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ~ aElement0(xm) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xm,sdtpldt0(xn,xl)) ) ) ),
inference(transitivity,[status(thm)],[135,133]) ).
tff(137,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xm,sdtpldt0(xn,xl)) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ~ aElement0(xm) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ~ aElement0(xm)
| ( sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xm,sdtpldt0(xn,xl)) ) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
sdtpldt0(sdtpldt0(xm,xn),xl) = sdtpldt0(xm,sdtpldt0(xn,xl)),
inference(unit_resolution,[status(thm)],[138,71,87,94,58]) ).
tff(140,plain,
sdtpldt0(xm,sdtpldt0(xn,xl)) = sdtpldt0(sdtpldt0(xm,xn),xl),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ( sdtpldt0(xn,xl) = sdtpldt0(xl,xn) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ( sdtpldt0(xn,xl) = sdtpldt0(xl,xn) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(142,plain,
( ( ( sdtpldt0(xn,xl) = sdtpldt0(xl,xn) )
| ~ aElement0(xl)
| ~ aElement0(xn) )
<=> ( ~ aElement0(xl)
| ~ aElement0(xn)
| ( sdtpldt0(xn,xl) = sdtpldt0(xl,xn) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(143,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(xn,xl) = sdtpldt0(xl,xn) )
| ~ aElement0(xl)
| ~ aElement0(xn) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ( sdtpldt0(xn,xl) = sdtpldt0(xl,xn) ) ) ),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(xn,xl) = sdtpldt0(xl,xn) )
| ~ aElement0(xl)
| ~ aElement0(xn) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ( sdtpldt0(xn,xl) = sdtpldt0(xl,xn) ) ) ),
inference(transitivity,[status(thm)],[143,141]) ).
tff(145,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(xn,xl) = sdtpldt0(xl,xn) )
| ~ aElement0(xl)
| ~ aElement0(xn) ),
inference(quant_inst,[status(thm)],]) ).
tff(146,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xl)
| ~ aElement0(xn)
| ( sdtpldt0(xn,xl) = sdtpldt0(xl,xn) ) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
( ~ aElement0(xl)
| ~ aElement0(xn)
| ( sdtpldt0(xn,xl) = sdtpldt0(xl,xn) ) ),
inference(unit_resolution,[status(thm)],[146,125]) ).
tff(148,plain,
sdtpldt0(xn,xl) = sdtpldt0(xl,xn),
inference(unit_resolution,[status(thm)],[147,94,87]) ).
tff(149,plain,
sdtpldt0(xm,sdtpldt0(xn,xl)) = sdtpldt0(xm,sdtpldt0(xl,xn)),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
sdtpldt0(xm,sdtpldt0(xl,xn)) = sdtpldt0(xm,sdtpldt0(xn,xl)),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
sdtpldt0(xm,sdtpldt0(xl,xn)) = sdtpldt0(xl,sdtpldt0(xm,xn)),
inference(transitivity,[status(thm)],[150,140,132]) ).
tff(152,plain,
sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))) = sdtpldt0(xk,sdtpldt0(xl,sdtpldt0(xm,xn))),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
sdtpldt0(xk,sdtpldt0(xl,sdtpldt0(xm,xn))) = sdtpldt0(xk,sdtpldt0(xm,sdtpldt0(xl,xn))),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) = sdtpldt0(xk,sdtpldt0(xl,sdtpldt0(xm,xn))) )
| ~ aElement0(sdtpldt0(xm,xn))
| ~ aElement0(xl)
| ~ aElement0(xk) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) = sdtpldt0(xk,sdtpldt0(xl,sdtpldt0(xm,xn))) )
| ~ aElement0(sdtpldt0(xm,xn))
| ~ aElement0(xl)
| ~ aElement0(xk) ) ),
inference(rewrite,[status(thm)],]) ).
tff(155,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) = sdtpldt0(xk,sdtpldt0(xl,sdtpldt0(xm,xn))) )
| ~ aElement0(sdtpldt0(xm,xn))
| ~ aElement0(xl)
| ~ aElement0(xk) ),
inference(quant_inst,[status(thm)],]) ).
tff(156,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) = sdtpldt0(xk,sdtpldt0(xl,sdtpldt0(xm,xn))) )
| ~ aElement0(sdtpldt0(xm,xn))
| ~ aElement0(xl)
| ~ aElement0(xk) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
( ( sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) = sdtpldt0(xk,sdtpldt0(xl,sdtpldt0(xm,xn))) )
| ~ aElement0(sdtpldt0(xm,xn))
| ~ aElement0(xl)
| ~ aElement0(xk) ),
inference(unit_resolution,[status(thm)],[156,71]) ).
tff(158,plain,
sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) = sdtpldt0(xk,sdtpldt0(xl,sdtpldt0(xm,xn))),
inference(unit_resolution,[status(thm)],[157,112,87,34]) ).
tff(159,plain,
sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(transitivity,[status(thm)],[158,153,80]) ).
tff(160,plain,
( ( sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) )
<=> ( sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(161,plain,
( ( sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) )
<=> ( sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(162,axiom,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(163,plain,
sdtpldt0(xx,xy) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
sdtpldt0(sdtpldt0(xk,xl),sdtpldt0(xm,xn)) != sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(modus_ponens,[status(thm)],[163,160]) ).
tff(165,plain,
$false,
inference(unit_resolution,[status(thm)],[164,159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG090+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n014.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Sep 2 22:25:46 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 1.02/0.90 % SZS status Theorem
% 1.02/0.90 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------