%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG060+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:24:03 AM UTC 2025
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 26
% Syntax : Number of formulae : 90 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 425 ( 98 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 491 ( 185 ~; 165 |; 87 &)
% ( 45 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 29 ( 29 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 117 ( 103 !; 0 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
tff(aScalar0_type,type,
aScalar0: $i > $o ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(xS_type,type,
xS: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xD_type,type,
xD: $i ).
tff(xF_type,type,
xF: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xG_type,type,
xG: $i ).
tff(xC_type,type,
xC: $i ).
tff(xN_type,type,
xN: $i ).
tff(xR_type,type,
xR: $i ).
tff(1,plain,
( ( xS = sdtasdt0(xF,xD) )
<=> ( xS = sdtasdt0(xF,xD) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aScalar0(xS)
& ( xS = sdtasdt0(xF,xD) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
tff(3,plain,
xS = sdtasdt0(xF,xD),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
xS = sdtasdt0(xF,xD),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
sdtasdt0(xF,xD) = xS,
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
smndt0(sdtasdt0(xF,xD)) = smndt0(xS),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( aScalar0(smndt0(sdtasdt0(xF,xD)))
<=> aScalar0(smndt0(xS)) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( aScalar0(sdtasdt0(xF,xD))
<=> aScalar0(xS) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(9,plain,
( aScalar0(xS)
<=> aScalar0(sdtasdt0(xF,xD)) ),
inference(symmetry,[status(thm)],[8]) ).
tff(10,plain,
( aScalar0(xS)
<=> aScalar0(xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
aScalar0(xS),
inference(and_elim,[status(thm)],[2]) ).
tff(12,plain,
aScalar0(xS),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
aScalar0(sdtasdt0(xF,xD)),
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,plain,
^ [W0: $i] :
refl(( ( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
<=> ( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(15,plain,
( ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
<=> ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
<=> ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
^ [W0: $i] :
rewrite(( ( aScalar0(W0)
=> aScalar0(smndt0(W0)) )
<=> ( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [W0: $i] :
( aScalar0(W0)
=> aScalar0(smndt0(W0)) )
<=> ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,axiom,
! [W0: $i] :
( aScalar0(W0)
=> aScalar0(smndt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).
tff(20,plain,
! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[22,15]) ).
tff(24,plain,
( ( ~ ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
| aScalar0(smndt0(sdtasdt0(xF,xD)))
| ~ aScalar0(sdtasdt0(xF,xD)) )
<=> ( ~ ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
| aScalar0(smndt0(sdtasdt0(xF,xD)))
| ~ aScalar0(sdtasdt0(xF,xD)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
| aScalar0(smndt0(sdtasdt0(xF,xD)))
| ~ aScalar0(sdtasdt0(xF,xD)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
| aScalar0(smndt0(sdtasdt0(xF,xD)))
| ~ aScalar0(sdtasdt0(xF,xD)) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
( aScalar0(smndt0(sdtasdt0(xF,xD)))
| ~ aScalar0(sdtasdt0(xF,xD)) ),
inference(unit_resolution,[status(thm)],[26,23]) ).
tff(28,plain,
aScalar0(smndt0(sdtasdt0(xF,xD))),
inference(unit_resolution,[status(thm)],[27,13]) ).
tff(29,plain,
aScalar0(smndt0(xS)),
inference(modus_ponens,[status(thm)],[28,7]) ).
tff(30,plain,
( ( sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS) )
<=> ( sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
( ( sdtasdt0(xR,smndt0(xS)) = smndt0(xN) )
& ( sdtasdt0(smndt0(xS),xR) = smndt0(xN) )
& ( sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2144) ).
tff(32,plain,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(and_elim,[status(thm)],[31]) ).
tff(33,plain,
sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS),
inference(modus_ponens,[status(thm)],[32,30]) ).
tff(34,plain,
( ( sdtasdt0(smndt0(xS),xR) = smndt0(xN) )
<=> ( sdtasdt0(smndt0(xS),xR) = smndt0(xN) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ( sdtasdt0(xR,smndt0(xS)) = smndt0(xN) )
& ( sdtasdt0(smndt0(xS),xR) = smndt0(xN) ) ),
inference(and_elim,[status(thm)],[31]) ).
tff(36,plain,
sdtasdt0(smndt0(xS),xR) = smndt0(xN),
inference(and_elim,[status(thm)],[35]) ).
tff(37,plain,
sdtasdt0(smndt0(xS),xR) = smndt0(xN),
inference(modus_ponens,[status(thm)],[36,34]) ).
tff(38,plain,
( ( xR = sdtasdt0(xC,xG) )
<=> ( xR = sdtasdt0(xC,xG) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
( aScalar0(xR)
& ( xR = sdtasdt0(xC,xG) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
tff(40,plain,
xR = sdtasdt0(xC,xG),
inference(and_elim,[status(thm)],[39]) ).
tff(41,plain,
xR = sdtasdt0(xC,xG),
inference(modus_ponens,[status(thm)],[40,38]) ).
tff(42,plain,
sdtasdt0(xC,xG) = xR,
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)) = sdtasdt0(smndt0(xS),xR),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)) = smndt0(xN),
inference(transitivity,[status(thm)],[43,37]) ).
tff(45,plain,
sdtpldt0(sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)),sdtasdt0(smndt0(xS),smndt0(xS))) = sdtpldt0(smndt0(xN),sdtasdt0(xS,xS)),
inference(monotonicity,[status(thm)],[44,33]) ).
tff(46,plain,
( ( sdtasdt0(xR,smndt0(xS)) = smndt0(xN) )
<=> ( sdtasdt0(xR,smndt0(xS)) = smndt0(xN) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(and_elim,[status(thm)],[35]) ).
tff(48,plain,
sdtasdt0(xR,smndt0(xS)) = smndt0(xN),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
sdtasdt0(sdtasdt0(xC,xG),smndt0(xS)) = sdtasdt0(xR,smndt0(xS)),
inference(monotonicity,[status(thm)],[42]) ).
tff(50,plain,
sdtasdt0(sdtasdt0(xC,xG),smndt0(xS)) = smndt0(xN),
inference(transitivity,[status(thm)],[49,48]) ).
tff(51,plain,
sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)) = sdtasdt0(xR,xR),
inference(monotonicity,[status(thm)],[42,42]) ).
tff(52,plain,
sdtpldt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xC,xG),smndt0(xS))) = sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),
inference(monotonicity,[status(thm)],[51,50]) ).
tff(53,plain,
sdtpldt0(sdtpldt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xC,xG),smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)),sdtasdt0(smndt0(xS),smndt0(xS)))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(monotonicity,[status(thm)],[52,45]) ).
tff(54,plain,
sdtpldt0(sdtasdt0(xC,xG),smndt0(xS)) = sdtpldt0(xR,smndt0(xS)),
inference(monotonicity,[status(thm)],[42]) ).
tff(55,plain,
sdtasdt0(sdtpldt0(sdtasdt0(xC,xG),smndt0(xS)),sdtpldt0(sdtasdt0(xC,xG),smndt0(xS))) = sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))),
inference(monotonicity,[status(thm)],[54,54]) ).
tff(56,plain,
( ( sdtasdt0(sdtpldt0(sdtasdt0(xC,xG),smndt0(xS)),sdtpldt0(sdtasdt0(xC,xG),smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xC,xG),smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)),sdtasdt0(smndt0(xS),smndt0(xS)))) )
<=> ( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) ) ),
inference(monotonicity,[status(thm)],[55,53]) ).
tff(57,plain,
( ( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) )
<=> ( sdtasdt0(sdtpldt0(sdtasdt0(xC,xG),smndt0(xS)),sdtpldt0(sdtasdt0(xC,xG),smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xC,xG),smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)),sdtasdt0(smndt0(xS),smndt0(xS)))) ) ),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
( ( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) )
<=> ( sdtasdt0(sdtpldt0(sdtasdt0(xC,xG),smndt0(xS)),sdtpldt0(sdtasdt0(xC,xG),smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xC,xG),smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)),sdtasdt0(smndt0(xS),smndt0(xS)))) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) )
<=> ( sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,axiom,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(61,plain,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
sdtasdt0(sdtpldt0(sdtasdt0(xC,xG),smndt0(xS)),sdtpldt0(sdtasdt0(xC,xG),smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xC,xG),smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)),sdtasdt0(smndt0(xS),smndt0(xS)))),
inference(modus_ponens,[status(thm)],[61,58]) ).
tff(63,plain,
( aScalar0(sdtasdt0(xC,xG))
<=> aScalar0(xR) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(64,plain,
( aScalar0(xR)
<=> aScalar0(sdtasdt0(xC,xG)) ),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( aScalar0(xR)
<=> aScalar0(xR) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
aScalar0(xR),
inference(and_elim,[status(thm)],[39]) ).
tff(67,plain,
aScalar0(xR),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
aScalar0(sdtasdt0(xC,xG)),
inference(modus_ponens,[status(thm)],[67,64]) ).
tff(69,plain,
^ [W0: $i,W1: $i,W2: $i,W3: $i] :
refl(( ( ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) )
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) )
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) )
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) )
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
^ [W0: $i,W1: $i,W2: $i,W3: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ~ ( ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ~ ~ ( ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(( ~ ~ ( ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ( ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) )
<=> ( ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) ) )),
rewrite(( ( ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) )
<=> ( ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) )
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) )
<=> ( ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) )
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) )
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
^ [W0: $i,W1: $i,W2: $i,W3: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) ) )),
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) ) )),
rewrite(( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) ) )),
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) )
<=> ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) ) )),
rewrite(( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) )
<=> ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) )
<=> ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,axiom,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
=> ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr2) ).
tff(77,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2)
& aScalar0(W3) )
| ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) ) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) )
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) )
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[80,70]) ).
tff(82,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) )
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(sdtasdt0(xC,xG))
| ( sdtasdt0(sdtpldt0(sdtasdt0(xC,xG),smndt0(xS)),sdtpldt0(sdtasdt0(xC,xG),smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xC,xG),smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)),sdtasdt0(smndt0(xS),smndt0(xS)))) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) )
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(sdtasdt0(xC,xG))
| ( sdtasdt0(sdtpldt0(sdtasdt0(xC,xG),smndt0(xS)),sdtpldt0(sdtasdt0(xC,xG),smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xC,xG),smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)),sdtasdt0(smndt0(xS),smndt0(xS)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ( ( sdtasdt0(sdtpldt0(sdtasdt0(xC,xG),smndt0(xS)),sdtpldt0(sdtasdt0(xC,xG),smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xC,xG),smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)),sdtasdt0(smndt0(xS),smndt0(xS)))) )
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(sdtasdt0(xC,xG)) )
<=> ( ~ aScalar0(smndt0(xS))
| ~ aScalar0(sdtasdt0(xC,xG))
| ( sdtasdt0(sdtpldt0(sdtasdt0(xC,xG),smndt0(xS)),sdtpldt0(sdtasdt0(xC,xG),smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xC,xG),smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)),sdtasdt0(smndt0(xS),smndt0(xS)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) )
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ( sdtasdt0(sdtpldt0(sdtasdt0(xC,xG),smndt0(xS)),sdtpldt0(sdtasdt0(xC,xG),smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xC,xG),smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)),sdtasdt0(smndt0(xS),smndt0(xS)))) )
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(sdtasdt0(xC,xG)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) )
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(sdtasdt0(xC,xG))
| ( sdtasdt0(sdtpldt0(sdtasdt0(xC,xG),smndt0(xS)),sdtpldt0(sdtasdt0(xC,xG),smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xC,xG),smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)),sdtasdt0(smndt0(xS),smndt0(xS)))) ) ) ),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) )
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ( sdtasdt0(sdtpldt0(sdtasdt0(xC,xG),smndt0(xS)),sdtpldt0(sdtasdt0(xC,xG),smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xC,xG),smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)),sdtasdt0(smndt0(xS),smndt0(xS)))) )
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(sdtasdt0(xC,xG)) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) )
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(sdtasdt0(xC,xG))
| ( sdtasdt0(sdtpldt0(sdtasdt0(xC,xG),smndt0(xS)),sdtpldt0(sdtasdt0(xC,xG),smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xC,xG),smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)),sdtasdt0(smndt0(xS),smndt0(xS)))) ) ) ),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,plain,
( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) )
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ( sdtasdt0(sdtpldt0(sdtasdt0(xC,xG),smndt0(xS)),sdtpldt0(sdtasdt0(xC,xG),smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xC,xG),smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)),sdtasdt0(smndt0(xS),smndt0(xS)))) )
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(sdtasdt0(xC,xG)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( sdtasdt0(sdtpldt0(W0,W1),sdtpldt0(W2,W3)) = sdtpldt0(sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W0,W3)),sdtpldt0(sdtasdt0(W1,W2),sdtasdt0(W1,W3))) )
| ~ aScalar0(W3)
| ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(smndt0(xS))
| ~ aScalar0(sdtasdt0(xC,xG))
| ( sdtasdt0(sdtpldt0(sdtasdt0(xC,xG),smndt0(xS)),sdtpldt0(sdtasdt0(xC,xG),smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xC,xG),smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)),sdtasdt0(smndt0(xS),smndt0(xS)))) ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
( ~ aScalar0(smndt0(xS))
| ~ aScalar0(sdtasdt0(xC,xG))
| ( sdtasdt0(sdtpldt0(sdtasdt0(xC,xG),smndt0(xS)),sdtpldt0(sdtasdt0(xC,xG),smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xC,xG),smndt0(xS))),sdtpldt0(sdtasdt0(smndt0(xS),sdtasdt0(xC,xG)),sdtasdt0(smndt0(xS),smndt0(xS)))) ) ),
inference(unit_resolution,[status(thm)],[87,81]) ).
tff(89,plain,
~ aScalar0(smndt0(xS)),
inference(unit_resolution,[status(thm)],[88,68,62]) ).
tff(90,plain,
$false,
inference(unit_resolution,[status(thm)],[89,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG060+2 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 03:18:11 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% See solution above
% 0.20/0.44 % E exiting
%------------------------------------------------------------------------------